# NCERT solutions for Mathematics Exemplar Class 8 chapter 7 - Algebraic Expression, Identities and Factorisation [Latest edition]

## Chapter 7: Algebraic Expression, Identities and Factorisation

Exercise
Exercise [Pages 224 - 240]

### NCERT solutions for Mathematics Exemplar Class 8 Chapter 7 Algebraic Expression, Identities and Factorisation Exercise [Pages 224 - 240]

#### Choose the correct alternative:

Exercise | Q 1 | Page 224

The product of a monomial and a binomial is a ______.

• Monomial

• Binomial

• Trinomial

• None of these

Exercise | Q 2 | Page 224

In a polynomial, the exponents of the variables are always ______.

• Integers

• Positive integers

• Non-negative integers

• Non-positive integers

Exercise | Q 3 | Page 224

Which of the following is correct?

• (a - b)^2 = a^2 + 2ab - b^2

• (a - b)^2 = a^2 - 2ab + b^2

• (a - b)^2 = a^2 - b^2

• (a + b)^2 = a^2 + 2ab - b^2

Exercise | Q 4 | Page 224

The sum of –7pq and 2pq is ______.

• –9pq

• 9pq

• 5pq

• – 5pq

Exercise | Q 5 | Page 224

If we subtract –3x2y2 from x2y2, then we get ______.

• – 4x2y2

• – 2x2y2

• 2x2y2

• 4x2y2

Exercise | Q 6 | Page 224

Like term as 4m3n2 is ______.

• 4m2n2

• – 6m3n2

• 6pm3n2

• 4m3n

Exercise | Q 7 | Page 225

Which of the following is a binomial?

• 7 × a + a

• 6a2 + 7b + 2c

• 4a × 3b × 2c

• 6(a2 + b)

Exercise | Q 8 | Page 225

Sum of a – b + ab, b + c – bc and c – a – ac is ______.

• 2c + ab – ac – bc

• 2c – ab – ac – bc

• 2c + ab + ac + bc

• 2c – ab + ac + bc

Exercise | Q 9 | Page 225

Product of the following monomials 4p, – 7q3, –7pq is ______.

• 196 p2q4

• 196 pq4

• – 196 p2q4

• 196 p2q3

Exercise | Q 10 | Page 225

Area of a rectangle with length 4ab and breadth 6b2 is ______.

• 24a2b2

• 24ab3

• 24ab2

• 24ab

Exercise | Q 11 | Page 225

Volume of a rectangular box (cuboid) with length = 2ab, breadth = 3ac and height = 2ac is ______.

• 12a3bc2

• 12a3bc

• 12a2bc

• 2ab + 3ac + 2ac

Exercise | Q 12 | Page 226

Product of 6a2 – 7b + 5ab and 2ab is ______.

• 12a3b – 14ab2 + 10ab

• 12a3b – 14ab2 + 10a2b2

• 6a2 – 7b + 7ab

• 12a2b – 7ab2 + 10ab

Exercise | Q 13 | Page 226

Square of 3x – 4y is ______.

• 9x2 – 16y2

• 6x2 – 8y2

• 9x2 + 16y2 + 24xy

• 9x2 + 16y2 – 24xy

Exercise | Q 14 | Page 226

Which of the following are like terms?

• 5xyz2, – 3xy2z

• – 5xyz2, 7xyz2

• 5xyz2, 5x2yz

• 5xyz2, x2y2z2

Exercise | Q 15 | Page 226

Coefficient of y in the term (-y)/3 is ______.

• – 1

• – 3

• (-1)/3

• 1/3

Exercise | Q 16 | Page 226

a2 – b2 is equal to ______.

• (a – b)2

• (a – b)(a – b)

• (a + b)(a – b)

• (a + b)(a + b)

Exercise | Q 17 | Page 226

Common factor of 17abc, 34ab2, 51a2b is ______.

• 17abc

• 17ab

• 17ac

• 17a2b2c

Exercise | Q 18 | Page 226

Square of 9x – 7xy is ______.

• 81x2 + 49x2y2

• 81x2 – 49x2y2

• 81x2 + 49x2y2 –126x2y

• 81x2 + 49x2y2 – 63x2y

Exercise | Q 19 | Page 226

Factorised form of 23xy – 46x + 54y – 108 is ______.

• (23x + 54)(y – 2)

• (23x + 54y)(y – 2)

• (23xy + 54y)(– 46x – 108)

• (23x + 54)(y + 2)

Exercise | Q 20 | Page 226

Factorised form of r2 – 10r + 21 is ______.

• (r – 1)(r – 4)

• (r – 7)(r – 3)

• (r – 7)(r + 3)

• (r + 7)(r + 3)

Exercise | Q 21 | Page 226

Factorised form of p2 – 17p – 38 is ______.

• (p – 19)(p + 2)

• (p – 19)(p – 2)

• p + 19)(p + 2)

• (p + 19)(p – 2)

Exercise | Q 22 | Page 227

On dividing 57p2qr by 114pq, we get ______.

• 1/4 pr

• 3/4 pr

• 1/2 pr

• 2pr

Exercise | Q 23 | Page 227

On dividing p(4p2 – 16) by 4p(p – 2), we get ______.

• 2p + 4

• 2p – 4

• p + 2

• p + 2

Exercise | Q 24 | Page 227

The common factor of 3ab and 2cd is ______.

• 1

• – 1

• a

• c

Exercise | Q 25 | Page 227

An irreducible factor of 24x2y2 is ______.

• x2

• y2

• x

• 24x

Exercise | Q 26 | Page 227

Number of factors of (a + b)2 is ______.

• 4

• 3

• 2

• 1

Exercise | Q 27 | Page 227

The factorised form of 3x – 24 is ______.

• 3x × 24

• 3(x – 8)

• 24(x – 3)

• 3(x – 12)

Exercise | Q 28 | Page 227

The factors of x2 – 4 are ______.

• (x – 2), (x – 2)

• (x + 2), (x – 2)

• (x + 2), (x + 2)

• (x – 4), (x – 4)

Exercise | Q 29 | Page 227

The value of (– 27x2y) ÷ (– 9xy) is ______.

• 3xy

• – 3xy

• – 3x

• 3x

Exercise | Q 30 | Page 227

The value of (2x2 + 4) ÷ 2 is ______.

• 2x2 + 2

• x2 + 2

• x2 + 4

• 2x2 + 4

Exercise | Q 31 | Page 227

The value of (3x3 +9x2 + 27x) ÷ 3x is ______.

• x2 + 9 + 27x

• 3x3 + 3x2 + 27x

• 3x3 + 9x2 + 9

• x2 + 3x + 9

Exercise | Q 32 | Page 227

The value of (a + b)2 + (a – b)2 is ______.

• 2a + 2b

• 2a – 2b

• 2a2 + 2b2

• 2a2 – 2b2

Exercise | Q 33 | Page 227

The value of (a + b)2 – (a – b)2 is ______.

• 4ab

• – 4ab

• 2a2 + 2b2

• 2a2 – 2b2

#### Fill in the blanks:

Exercise | Q 34 | Page 227

The product of two terms with like signs is a ______ term.

Exercise | Q 35 | Page 227

The product of two terms with unlike signs is a ______ term.

Exercise | Q 36 | Page 228

a(b + c) = ax ____ × ax _____.

Exercise | Q 37 | Page 228

(a – b) ______ = a2 – 2ab + b2

Exercise | Q 38 | Page 228

a2 – b2 = (a + b) ______.

Exercise | Q 39 | Page 228

(a – b)2 + ______ = a2 – b2

Exercise | Q 40 | Page 228

(a + b)2 – 2ab = ______ + ______.

Exercise | Q 41 | Page 228

(x + a)(x + b) = x2 + (a + b) x + ______.

Exercise | Q 42 | Page 228

The product of two polynomials is a ______.

Exercise | Q 43 | Page 228

Common factor of ax2 + bx is ______.

Exercise | Q 44 | Page 228

Factorised form of 18mn + 10mnp is ______.

Exercise | Q 45 | Page 228

Factorised form of 4y2 – 12y + 9 is ______.

Exercise | Q 46 | Page 228

38x3y2z ÷ 19xy2 is equal to ______.

Exercise | Q 47 | Page 228

Volume of a rectangular box with length 2x, breadth 3y and height 4z is ______.

Exercise | Q 48 | Page 228

672 – 372 = (67 – 37) × ______ = ______.

Exercise | Q 49 | Page 228

1032 – 1022 = ______ × (103 – 102) = ______.

Exercise | Q 50 | Page 228

Area of a rectangular plot with sides 4x2 and 3y2 is ______.

Exercise | Q 51 | Page 228

Volume of a rectangular box with l = b = h = 2x is ______.

Exercise | Q 52 | Page 228

The coefficient in – 37abc is ______.

Exercise | Q 53 | Page 228

Number of terms in the expression a2 + bc × d is ______.

Exercise | Q 54 | Page 228

The sum of areas of two squares with sides 4a and 4b is ______.

Exercise | Q 55 | Page 228

The common factor method of factorisation for a polynomial is based on ______ property.

Exercise | Q 56 | Page 228

The side of the square of area 9y2 is ______.

Exercise | Q 57 | Page 228

On simplification (3x + 3)/3 = ______.

Exercise | Q 58 | Page 228

The factorisation of 2x + 4y is ______.

#### State whether the following statement is True or False:

Exercise | Q 59 | Page 229

(a + b)2 = a2 + b2

• True

• False

Exercise | Q 60 | Page 229

(a – b)2 = a2 – b2

• True

• False

Exercise | Q 61 | Page 229

(a + b)(a – b) = a2 – b2

• True

• False

Exercise | Q 62 | Page 229

The product of two negative terms is a negative term.

• True

• False

Exercise | Q 63 | Page 229

The product of one negative and one positive term is a negative term

• True

• False

Exercise | Q 64 | Page 229

The coefficient of the term – 6x2y2 is – 6.

• True

• False

Exercise | Q 65 | Page 229

p2q + q2r + r2q is a binomial.

• True

• False

Exercise | Q 66 | Page 229

The factors of a2 – 2ab + b2 are (a + b) and (a + b).

• True

• False

Exercise | Q 67 | Page 229

h is a factor of 2π(h + r).

• True

• False

Exercise | Q 68 | Page 229

Some of the factors of n^2/2 + n/2 are 1/2, n and (n + 1)

• True

• False

Exercise | Q 69 | Page 229

An equation is true for all values of its variables.

• True

• False

Exercise | Q 70 | Page 229

x^2 + (a + b)x + ab = (a + b)(x + ab)

• True

• False

Exercise | Q 71 | Page 229

Common factor of 11pq2, 121p2q3, 1331p2q is 11p2q2.

• True

• False

Exercise | Q 72 | Page 229

Common factor of 12a2b2 + 4ab2 – 32 is 4.

• True

• False

Exercise | Q 73 | Page 229

Factorisation of – 3a2 + 3ab + 3ac is 3a(– a – b – c).

• True

• False

Exercise | Q 74 | Page 229

Factorised form of p2 + 30p + 216 is (p + 18)(p – 12).

• True

• False

Exercise | Q 75 | Page 229

The difference of the squares of two consecutive numbers is their sum

• True

• False

Exercise | Q 76 | Page 229

abc + bca + cab is a monomial.

• True

• False

Exercise | Q 77 | Page 229

On dividing p/3 by 3/p, the quotient is 9.

• True

• False

Exercise | Q 78 | Page 229

The value of p for 512 – 492 = 100p is 2.

• True

• False

Exercise | Q 79 | Page 229

(9x – 51) ÷ 9 is x – 51

• True

• False

Exercise | Q 80 | Page 229

The value of (a + 1)(a – 1)(a2 + 1) is a4 – 1.

• True

• False

Exercise | Q 81.(i) | Page 230

Add: 7a2bc, – 3abc2, 3a2bc, 2abc2

Exercise | Q 81.(ii) | Page 230

Add: 9ax, + 3by – cz, – 5by + ax + 3cz

Exercise | Q 81.(iii) | Page 230

Add: xy2z2 + 3x2y2z – 4x2yz2, – 9x2y2z + 3xy2z2 + x2yz2

Exercise | Q 81.(iv) | Page 230

Add: 5x2 – 3xy + 4y2 – 9, 7y2 + 5xy – 2x2 + 13

Exercise | Q 81.(v) | Page 230

Add: 2p4 – 3p3 + p2 – 5p +7, –3p4 – 7p3 – 3p2 – p – 12

Exercise | Q 81.(vi) | Page 230

Add: 3a(a – b + c), 2b(a – b + c)

Exercise | Q 81.(vii) | Page 230

Add: 3a(2b + 5c), 3c(2a + 2b)

Exercise | Q 82.(i) | Page 230

Subtract: 5a2b2c2 from – 7a2b2c2

Exercise | Q 82.(ii) | Page 230

Subtract: 6x2 – 4xy + 5y2 from 8y2 + 6xy – 3x2

Exercise | Q 82.(iii) | Page 230

Subtract: 2ab2c2 + 4a2b2c – 5a2bc2 from –10a2b2c + 4ab2c2 + 2a2bc2

Exercise | Q 82.(iv) | Page 230

Subtract: 3t4 – 4t3 + 2t2 – 6t + 6 from – 4t4 + 8t3 – 4t2 – 2t + 11

Exercise | Q 82.(v) | Page 230

Subtract: 2ab + 5bc – 7ac from 5ab – 2bc – 2ac + 10abc

Exercise | Q 82.(vi) | Page 230

Subtract: 7p(3q + 7p) from 8p(2p – 7q)

Exercise | Q 82.(vii) | Page 230

Subtract: –3p2 + 3pq + 3px from 3p(– p – a – r)

Exercise | Q 83.(i) | Page 230

Multiply the following:

– 7pq2r3, – 13p3q2r

Exercise | Q 83.(ii) | Page 230

Multiply the following:

3x2y2z2, 17xyz

Exercise | Q 83.(iii) | Page 230

Multiply the following:

15xy2, 17yz2

Exercise | Q 83.(iv) | Page 230

Multiply the following:

–5a2bc, 11ab, 13abc2

Exercise | Q 83.(v) | Page 230

Multiply the following:

–3x2y, (5y – xy)

Exercise | Q 83.(vi) | Page 230

Multiply the following:

abc, (bc + ca)

Exercise | Q 83.(vii) | Page 230

Multiply the following:

7pqr, (p – q + r)

Exercise | Q 83.(viii) | Page 230

Multiply the following:

x2y2z2, (xy – yz + zx)

Exercise | Q 83.(ix) | Page 230

Multiply the following:

(p + 6), (q – 7)

Exercise | Q 83.(x) | Page 231

Multiply the following:

6mn, 0mn

Exercise | Q 83.(xi) | Page 231

Multiply the following:

a, a5, a6

Exercise | Q 83.(xii) | Page 231

Multiply the following:

–7st, –1, – 13st2

Exercise | Q 83.(xiii) | Page 231

Multiply the following:

b3, 3b2, 7ab5

Exercise | Q 83.(xiv) | Page 231

Multiply the following:

- 100/9 rs; 3/4 r^3s^2

Exercise | Q 83.(xv) | Page 231

Multiply the following:

(a2 – b2), (a2 + b2

Exercise | Q 83.(xvi) | Page 231

Multiply the following:

(ab + c), (ab + c)

Exercise | Q 83.(xvii) | Page 231

Multiply the following:

(pq – 2r), (pq – 2r)

Exercise | Q 83.(xviii) | Page 231

Multiply the following:

(3/4x - 4/3 y), (2/3x + 3/2y)

Exercise | Q 83.(xix) | Page 231

Multiply the following:

3/2 p^2 + 2/3 q^2, (2p^2 - 3q^2)

Exercise | Q 83.(xx) | Page 231

Multiply the following:

(x2 – 5x + 6), (2x + 7)

Exercise | Q 83.(xxi) | Page 231

Multiply the following:

(3x2 + 4x – 8), (2x2 – 4x + 3)

Exercise | Q 83.(xxii) | Page 231

Multiply the following:

(2x – 2y – 3), (x + y + 5)

Exercise | Q 84.(i) | Page 231

Simplify: (3x + 2y)^2 + (3x - 2y)^2

Exercise | Q 84.(ii) | Page 231

Simplify: (3x + 2y)^2 - (3x - 2y)^2

Exercise | Q 84.(iii) | Page 231

Simplify: (7/9 a + 9/7 b)^2 - ab

Exercise | Q 84.(iv) | Page 231

Simplify: (3/4x - 4/3y)^2 + 2xy

Exercise | Q 84.(v) | Page 231

Simplify: (1.5p + 1.2q)^2 - (1.5p - 1.2q)^2

Exercise | Q 84.(vi) | Page 231

Simplify: (2.5m + 1.5q)^2 + (2.5m - 1.5q)^2

Exercise | Q 84.(vii) | Page 231

Simplify: (x^2 - 4) + (x^2 + 4) + 16

Exercise | Q 84.(viii) | Page 231

Simplify: (ab - c)^2 + 2abc

Exercise | Q 84.(ix) | Page 231

Simplify: (a - b) (a^2 + b^2 + ab) - (a + b) (a^2 + b^2 - ab)

Exercise | Q 84.(x) | Page 231

Simplify: (b^2 - 49) (b + 7) + 343

Exercise | Q 84.(xi) | Page 231

Simplify: (4.5a + 1.5b)^2 + (4.5b + 1.5a)^2

Exercise | Q 84.(xii) | Page 231

Simplify: (pq - qr)^2  + 4pq^2r

Exercise | Q 84.(xiii) | Page 231

Simplify: (s^2t + tq^2)^2 - (2stq)^2

Exercise | Q 85.(i) | Page 232

Expand the following, using suitable identities.

(xy + yz)^2

Exercise | Q 85.(ii) | Page 232

Expand the following, using suitable identities.

(x^2y - xy^2)^2

Exercise | Q 85.(iii) | Page 232

Expand the following, using suitable identities.

(4/5a + 5/4b)^2

Exercise | Q 85.(iv) | Page 232

Expand the following, using suitable identities.

(2/3x - 3/2y)^2

Exercise | Q 85.(v) | Page 232

Expand the following, using suitable identities.

(4/5p + 5/3q)^2

Exercise | Q 85.(vi) | Page 232

Expand the following, using suitable identities.

(x + 3)(x + 7)

Exercise | Q 85.(vii) | Page 232

Expand the following, using suitable identities.

(2x + 9)(2x – 7)

Exercise | Q 85.(viii) | Page 232

Expand the following, using suitable identities.

((4x)/5 + y/4)((4x)/5 + (3y)/4)

Exercise | Q 85.(ix) | Page 232

Expand the following, using suitable identities.

((2x)/3 - 2/3)((2x)/3 + (2a)/3)

Exercise | Q 85.(x) | Page 232

Expand the following, using suitable identities.

(2x - 5y) (2x - 5y)

Exercise | Q 85.(xi) | Page 232

Expand the following, using suitable identities.

((2a)/3 + b/3)((2a)/3 - b/3)

Exercise | Q 85.(xii) | Page 232

Expand the following, using suitable identities.

(x^2 + y^2)(x^2 - y^2)

Exercise | Q 85.(xiii) | Page 232

Expand the following, using suitable identities.

(a^2 + b^2)^2

Exercise | Q 85.(xiv) | Page 232

Expand the following, using suitable identities.

(7x + 5)^2

Exercise | Q 85.(xv) | Page 232

Expand the following, using suitable identities.

(0.9p - 0.5q)^2

Exercise | Q 86.(i) | Page 233

Using suitable identities, evaluate the following.

(52)2

Exercise | Q 86.(ii) | Page 233

Using suitable identities, evaluate the following.

(49)2

Exercise | Q 86.(iii) | Page 233

Using suitable identities, evaluate the following.

(103)2

Exercise | Q 86.(iv) | Page 233

Using suitable identities, evaluate the following.

(98)2

Exercise | Q 86.(v) | Page 233

Using suitable identities, evaluate the following.

(1005)2

Exercise | Q 86.(vi) | Page 233

Using suitable identities, evaluate the following.

(995)2

Exercise | Q 86.(vii) | Page 233

Using suitable identities, evaluate the following.

47 × 53

Exercise | Q 86.(viii) | Page 233

Using suitable identities, evaluate the following.

52 × 53

Exercise | Q 86.(ix) | Page 233

Using suitable identities, evaluate the following.

105 × 95

Exercise | Q 86.(x) | Page 233

Using suitable identities, evaluate the following.

104 × 97

Exercise | Q 86.(xi) | Page 233

Using suitable identities, evaluate the following.

101 × 103

Exercise | Q 86.(xii) | Page 233

Using suitable identities, evaluate the following.

98 × 103

Exercise | Q 86.(xiii) | Page 233

Using suitable identities, evaluate the following.

(9.9)2

Exercise | Q 86.(xiv) | Page 233

Using suitable identities, evaluate the following.

9.8 × 10.2

Exercise | Q 86.(xv) | Page 233

Using suitable identities, evaluate the following.

10.1 × 10.2

Exercise | Q 86.(xvi) | Page 233

Using suitable identities, evaluate the following.

(35.4)2 – (14.6)2

Exercise | Q 86.(vii) | Page 233

Using suitable identities, evaluate the following.

(69.3)2 – (30.7)2

Exercise | Q 86.(viii) | Page 233

Using suitable identities, evaluate the following.

(9.7)2 – (0.3)2

Exercise | Q 86.(xix) | Page 233

Using suitable identities, evaluate the following.

(132)2 – (68)2

Exercise | Q 86.(xx) | Page 233

Using suitable identities, evaluate the following.

(339)2 – (161)2

Exercise | Q 86.(xxi) | Page 233

Using suitable identities, evaluate the following.

(729)2 – (271)2

Exercise | Q 87.(i) | Page 233

Write the greatest common factor in the following terms.

– 18a2, 108a

Exercise | Q 87.(ii) | Page 233

Write the greatest common factor in the following terms.

3x2y, 18xy2, – 6xy

Exercise | Q 87.(iii) | Page 233

Write the greatest common factor in the following terms.

2xy, –y2, 2x2y

Exercise | Q 87.(iv) | Page 233

Write the greatest common factor in the following terms.

l2m2n, lm2n2, l2mn2

Exercise | Q 87.(v) | Page 233

Write the greatest common factor in the following terms.

21pqr, –7p2q2r2, 49p2qr

Exercise | Q 87.(vi) | Page 233

Write the greatest common factor in the following terms.

qrxy, pryz, rxyz

Exercise | Q 87.(vii) | Page 233

Write the greatest common factor in the following terms.

3x3y2z, – 6xy3z2, 12x2yz3

Exercise | Q 87.(viii) | Page 233

Write the greatest common factor in the following terms.

63p2a2r2s, – 9pq2r2s2, 15p2qr2s2, – 60p2a2rs2

Exercise | Q 87.(ix) | Page 233

Write the greatest common factor in the following terms.

13x2y, 169xy

Exercise | Q 87.(x) | Page 233

Write the greatest common factor in the following terms.

11x2, 12y2

Exercise | Q 88.(i) | Page 233

Factorise the following expression.

6ab + 12bc

Exercise | Q 88.(ii) | Page 233

Factorise the following expression.

–xy – ay

Exercise | Q 88.(iii) | Page 233

Factorise the following expression.

ax3 – bx2 + cx

Exercise | Q 88.(iv) | Page 233

Factorise the following expression.

l2m2n – lm2n2 – l2mn2

Exercise | Q 88.(v) | Page 233

Factorise the following expression.

3pqr – 6p2q2r2 – 15r2

Exercise | Q 88.(vi) | Page 233

Factorise the following expression.

x3y2 + x2y3 – xy4 + xy

Exercise | Q 88.(vii) | Page 233

Factorise the following expression.

4xy2 – 10x2y + 16x2y2 + 2xy

Exercise | Q 88.(viii) | Page 233

Factorise the following expression.

2a3 – 3a2b + 5ab2 – ab

Exercise | Q 88.(ix) | Page 233

Factorise the following expression.

63p2q2r2s – 9pq2r2s2 + 15p2qr2s2 – 60p2q2rs2

Exercise | Q 88.(x) | Page 233

Factorise the following expression.

24x2yz3 – 6xy3z2 + 15x2y2z – 5xyz

Exercise | Q 88.(xi) | Page 233

Factorise the following expression.

a3 + a2 + a + 1

Exercise | Q 88.(xii) | Page 233

Factorise the following expression.

lx + my + mx + ly

Exercise | Q 88.(xiii) | Page 233

Factorise the following expression.

a3x – x4 + a2x2 – ax

Exercise | Q 88.(iv) | Page 233

Factorise the following expression.

2x2 – 2y + 4xy – x

Exercise | Q 88.(xv) | Page 233

Factorise the following expression.

y2 + 8zx – 2xy – 4yz

Exercise | Q 88.(xvi) | Page 233

Factorise the following expression.

ax2y – bxyz – ax2z + bxy2

Exercise | Q 88.(xvii) | Page 233

Factorise the following expression.

a2b + a2c + ab + ac + b2c + c2b

Exercise | Q 88.(xviii) | Page 233

Factorise the following expression.

2ax2 + 4axy + 3bx2 + 2ay2 + 6bxy + 3by

Exercise | Q 89.(i) | Page 234

Factorise the following, using the identity a2 + 2ab + b2 = (a + b)2

x2 + 6x + 9

Exercise | Q 89.(ii) | Page 234

Factorise the following, using the identity a2 + 2ab + b2 = (a + b)2

x2 + 12x + 36

Exercise | Q 89.(iii) | Page 234

Factorise the following, using the identity a2 + 2ab + b2 = (a + b)2

x2 + 14x + 49

Exercise | Q 89.(iv) | Page 234

Factorise the following, using the identity a2 + 2ab + b2 = (a + b)2

x2 + 2x + 1

Exercise | Q 89.(v) | Page 234

Factorise the following, using the identity a2 + 2ab + b2 = (a + b)2

4x2 + 4x + 1

Exercise | Q 89.(vi) | Page 234

Factorise the following, using the identity a2 + 2ab + b2 = (a + b)2

a2x2 + 2ax + 1

Exercise | Q 89.(vii) | Page 234

Factorise the following, using the identity a2 + 2ab + b2 = (a + b)2

a2x2 + 2abx + b2

Exercise | Q 89.(viii) | Page 234

Factorise the following, using the identity a2 + 2ab + b2 = (a + b)2

a2x2 + 2abxy + b2y

Exercise | Q 89.(ix) | Page 234

Factorise the following, using the identity a2 + 2ab + b2 = (a + b)2

4x2 + 12x + 9

Exercise | Q 89.(x) | Page 234

Factorise the following, using the identity a2 + 2ab + b2 = (a + b)2

16x2 + 40x + 25

Exercise | Q 89.(xi) | Page 234

Factorise the following, using the identity a2 + 2ab + b2 = (a + b)2

9x2 + 24x + 16

Exercise | Q 89.(xii) | Page 234

Factorise the following, using the identity a2 + 2ab + b2 = (a + b)2

9x2 + 30x + 25

Exercise | Q 89.(xiii) | Page 234

Factorise the following, using the identity a2 + 2ab + b2 = (a + b)2

2x3 + 24x2 + 72x

Exercise | Q 89.(xiv) | Page 234

Factorise the following, using the identity a2 + 2ab + b2 = (a + b)2

a2x3 + 2abx2 + b2x

Exercise | Q 89.(xv) | Page 234

Factorise the following, using the identity a2 + 2ab + b2 = (a + b)2

4x4 + 12x3 + 9x2

Exercise | Q 89.(xvi) | Page 234

Factorise the following, using the identity a2 + 2ab + b2 = (a + b)2

x^2/4 + 2x + 4

Exercise | Q 89.(xvii) | Page 234

Factorise the following, using the identity a2 + 2ab + b2 = (a + b)2

9x^4 + 12x^3 + y^2/9

Exercise | Q 90.(i) | Page 234

Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.

x2 – 8x + 16

Exercise | Q 90.(ii) | Page 234

Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.

x2 – 10x + 25

Exercise | Q 90.(iii) | Page 234

Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.

y2 – 14y + 49

Exercise | Q 90.(iv) | Page 234

Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.

p2 – 2p + 1

Exercise | Q 90.(v) | Page 234

Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.

4a2 – 4ab + b2

Exercise | Q 90.(vi) | Page 234

Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.

p2y2 – 2py + 1

Exercise | Q 90.(vii) | Page 234

Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.

a2y2 – 2aby + b2

Exercise | Q 90.(viii) | Page 234

Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.

9x2 – 12x + 4

Exercise | Q 90.(ix) | Page 234

Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.

4y2 – 12y + 9

Exercise | Q 90.(x) | Page 234

Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.

x^2/4 - 2x + 4

Exercise | Q 90.(xi) | Page 234

Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.

a2y3 – 2aby2 + b2y

Exercise | Q 90.(xii) | Page 234

Factorise the following, using the identity a2 – 2ab + b2 = (a – b)2.

9y^2 - 4xy + (4x^2)/9

Exercise | Q 91.(i) | Page 235

Factorise the following.

x2 + 15x + 26

Exercise | Q 91.(ii) | Page 235

Factorise the following.

x2 + 9x + 20

Exercise | Q 91.(iii) | Page 235

Factorise the following.

y2 + 18x + 65

Exercise | Q 91.(iv) | Page 235

Factorise the following.

p2 + 14p + 13

Exercise | Q 91.(v) | Page 235

Factorise the following.

y2 + 4y – 21

Exercise | Q 91.(vi) | Page 235

Factorise the following.

y2 – 2y – 15

Exercise | Q 91.(vii) | Page 235

Factorise the following.

18 + 11x + x2

Exercise | Q 91.(viii) | Page 235

Factorise the following.

x2 – 10x + 21

Exercise | Q 91.(ix) | Page 235

Factorise the following.

x2 – 17x + 60

Exercise | Q 91.(x) | Page 235

Factorise the following.

x2 + 4x – 77

Exercise | Q 91.(xi) | Page 235

Factorise the following.

y2 + 7y + 12

Exercise | Q 91.(xii) | Page 235

Factorise the following.

p2 – 13p – 30

Exercise | Q 91.(xiii) | Page 235

Factorise the following.

a2 – 16p – 80

Exercise | Q 92.(i) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

x2 – 9

Exercise | Q 92.(ii) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

4x2 – 25y2

Exercise | Q 92.(iii) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

4x2 – 49y2

Exercise | Q 92.(iv) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

3a2b3 – 27a4b

Exercise | Q 92.(v) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

28ay2 – 175ax2

Exercise | Q 92.(vi) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

9x2 – 1

Exercise | Q 92.(vii) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

25ax2 – 25a

Exercise | Q 92.(viii) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

x^2/9 - y^2/25

Exercise | Q 92.(ix) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

(2p^2)/25 - 32q^2

Exercise | Q 92.(x) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

49x2 – 36y2

Exercise | Q 92.(xi) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

y^3 - y/9

Exercise | Q 92.(xii) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

x^2/25 - 625

Exercise | Q 92.(xiii) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

x^2/8 - y^2/18

Exercise | Q 92.(xiv) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

(4x^2)/9 - (9y^2)/16

Exercise | Q 92.(xv) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

(x^3y)/9 - (xy^3)/16

Exercise | Q 92.(xvi) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

1331x3y – 11y3x

Exercise | Q 92.(xvii) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

1/36a^2b^2 - 16/49b^2c^2

Exercise | Q 92.(xviii) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

a4 – (a – b)4

Exercise | Q 92.(xix) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

x4 – 1

Exercise | Q 92.(xx) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

y4 – 625

Exercise | Q 92.(xxi) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

p5 – 16p

Exercise | Q 92.(xxii) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

16x4 – 81

Exercise | Q 92.(xxiii) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

x4 – y4

Exercise | Q 92.(xxiv) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

y4 – 81

Exercise | Q 92.(xxv) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

16x4 – 625y4

Exercise | Q 92.(xxvi) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

(a – b)2 – (b – c)2

Exercise | Q 92.(xxvii) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

(x + y)4 – (x – y)4

Exercise | Q 92.(xxviii) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

x4 – y4 + x2 – y2

Exercise | Q 92.(xxix) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

8a3 – 2a

Exercise | Q 92.(xxx) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

x^2 - y^2/100

Exercise | Q 92.(xxxi) | Page 235

Factorise the following using the identity a2 – b2 = (a + b)(a – b).

9x2 – (3y + z)2

Exercise | Q 93.(i) | Page 236

The following expression are the area of rectangles. Find the possible length and breadth of these rectangles.

x2 – 6x + 8

Exercise | Q 93.(ii) | Page 236

The following expression are the area of rectangles. Find the possible length and breadth of these rectangles.

x2 – 3x + 2

Exercise | Q 93.(iii) | Page 236

The following expression are the area of rectangles. Find the possible length and breadth of these rectangles.

x2 – 7x + 10

Exercise | Q 93.(iv) | Page 236

The following expression are the area of rectangles. Find the possible length and breadth of these rectangles.

x2 + 19x – 20

Exercise | Q 93.(v) | Page 236

The following expression are the area of rectangles. Find the possible length and breadth of these rectangles.

x2 + 9x + 20

Exercise | Q 94.(i) | Page 236

Carry out the following divisions:

51x3y2z ÷ 17xyz

Exercise | Q 94.(ii) | Page 236

Carry out the following divisions:

76x3yz3 ÷ 19x2y2

Exercise | Q 94.(iii) | Page 236

Carry out the following divisions:

17ab2c3 ÷ (– abc2)

Exercise | Q 94.(iv) | Page 236

Carry out the following divisions:

–121p3q3r3 ÷ (–11xy2z3)

Exercise | Q 95.(i) | Page 236

Perform the following divisions:

(3pqr – 6p2q2r2) ÷ 3pq

Exercise | Q 95.(ii) | Page 236

Perform the following divisions:

(ax3 – bx2 + cx) ÷ (– dx)

Exercise | Q 95.(iii) | Page 236

Perform the following divisions:

(x3y3 + x2y3 – xy4 + xy) ÷ xy

Exercise | Q 95.(iv) | Page 236

Perform the following divisions:

(– qrxy + pryz – rxyz) ÷ (– xyz)

Exercise | Q 96.(i) | Page 236

Factorise the expressions and divide them as directed:

(x2 – 22x + 117) ÷ (x – 13)

Exercise | Q 96.(ii) | Page 236

Factorise the expressions and divide them as directed:

(x3 + x2 – 132x) ÷ x(x – 11)

Exercise | Q 96.(iii) | Page 236

Factorise the expressions and divide them as directed:

(2x3 – 12x2 + 16x) ÷ (x – 2)(x – 4)

Exercise | Q 96.(iv) | Page 236

Factorise the expressions and divide them as directed:

(9x2 – 4) ÷ (3x + 2)

Exercise | Q 96.(v) | Page 236

Factorise the expressions and divide them as directed:

(3x2 – 48) ÷ (x – 4)

Exercise | Q 96.(vi) | Page 236

Factorise the expressions and divide them as directed:

(x4 – 16) ÷ x3 + 2x2 + 4x + 8

Exercise | Q 96.(vii) | Page 236

Factorise the expressions and divide them as directed:

(3x4 – 1875) ÷ (3x2 – 7)

Exercise | Q 97 | Page 236

The area of a square is given by 4x2 + 12xy + 9y2. Find the side of the square.

Exercise | Q 98 | Page 236

The area of a square is 9x2 + 24xy + 16y2. Find the side of the square.

Exercise | Q 99 | Page 237

The area of a rectangle is x2 + 7x + 12. If its breadth is (x + 3), then find its length.

Exercise | Q 100 | Page 237

The curved surface area of a cylinder is 2π(y2 – 7y + 12) and its radius is (y – 3). Find the height of the cylinder (C.S.A. of cylinder = 2πrh).

Exercise | Q 101 | Page 237

The area of a circle is given by the expression πx2 + 6πx + 9π. Find the radius of the circle.

Exercise | Q 102 | Page 237

The sum of first n natural numbers is given by the expression n^2/2 + n/2. Factorise this expression.

Exercise | Q 103 | Page 237

The sum of (x + 5) observations is x4 – 625. Find the mean of the observations.

Exercise | Q 104 | Page 237

The height of a triangle is x4 + y4 and its base is 14xy. Find the area of the triangle.

Exercise | Q 105 | Page 237

The cost of a chocolate is Rs (x + y) and Rohit bought (x + y) chocolates. Find the total amount paid by him in terms of x. If x = 10, find the amount paid by him.

Exercise | Q 106 | Page 237

The base of a parallelogram is (2x + 3 units) and the corresponding height is (2x – 3 units). Find the area of the parallelogram in terms of x. What will be the area of parallelogram of x = 30 units?

Exercise | Q 107 | Page 237

The radius of a circle is 7ab – 7bc – 14ac. Find the circumference of the circle. (pi = 22/7)

Exercise | Q 108 | Page 237

If p + q = 12 and pq = 22, then find p2 + q2.

Exercise | Q 109 | Page 237

If a + b = 25 and a2 + b2 = 225, then find ab.

Exercise | Q 110 | Page 237

If x – y = 13 and xy = 28, then find x2 + y2.

Exercise | Q 111 | Page 237

If m – n = 16 and m2 + n2 = 400, then find mn.

Exercise | Q 112 | Page 237

If a2 + b2 = 74 and ab = 35, then find a + b.

Exercise | Q 113.(i) | Page 238

Verify the following:

(ab + bc)(ab – bc) + (bc + ca)(bc – ca) + (ca + ab)(ca – ab) = 0

Exercise | Q 113.(ii) | Page 238

Verify the following:

(a + b + c) (a2 + b2 + c2 – ab – bc – ca) = a3 + b3+ c3 – 3abc

Exercise | Q 113.(iii) | Page 238

Verify the following:

(p – q)(p2 + pq + q2) = p3 – q3

Exercise | Q 113.(iv) | Page 238

Verify the following:

(m + n) (m2 – mn + n2) = m3 + n3

Exercise | Q 113.(v) | Page 238

Verify the following:

(a + b)(a + b)(a + b) = a3 + 3a2b + 3ab2 + b3

Exercise | Q 113.(vi) | Page 238

Verify the following:

(a – b)(a – b)(a – b) = a3 – 3a2b + 3ab2 – b3

Exercise | Q 113.(vii) | Page 238

Verify the following:

(a2 – b2)(a2 + b2) + (b2 – c2)(b2 + c2) + (c2 – a2) + (c2 + a2) = 0

Exercise | Q 113.(viii) | Page 238

Verify the following:

(5x + 8)2 – 160x = (5x – 8)2

Exercise | Q 113.(ix) | Page 238

Verify the following:

(7p – 13q)2 + 364pq = (7p + 13q)2

Exercise | Q 113.(x) | Page 238

Verify the following:

((3p)/7 + 7/(6p))^2 - (3/7p  + 7/(6p))^2 = 2

Exercise | Q 114.(i) | Page 238

Find the value of a, if 8a = 352 – 272

Exercise | Q 114.(ii) | Page 238

Find the value of a, if 9a = (76)2 – (67)2

Exercise | Q 114.(iii) | Page 238

Find the value of a, if pqa = (3p + q)2 – (3p – q)2

Exercise | Q 114.(iv) | Page 238

Find the value of a, if  pq2a = (4pq + 3q)2 – (4pq – 3q)

Exercise | Q 115 | Page 238

What should be added to 4c(– a + b + c) to obtain 3a(a + b + c) – 2b(a – b + c)?

Exercise | Q 116 | Page 238

Subtract b(b2 + b – 7) + 5 from 3b2 – 8 and find the value of expression obtained for b = – 3.

Exercise | Q 117 | Page 238

If x - 1/x = 7 then find the value of x^2 + 1/x^2.

Exercise | Q 118 | Page 238

Factorise x^2 + 1/x^2 + 2 - 3x - 3/x

Exercise | Q 119 | Page 238

Factorise p4 + q4 + p2q2.

Exercise | Q 120.(i) | Page 238

Find the value of (6.25 xx 6.25 - 1.75 xx 1.75)/(4.5)

Exercise | Q 120.(ii) | Page 238

Find the value of (198 xx 198 - 102 xx 102)/96

Exercise | Q 121 | Page 239

The product of two expressions is x5 + x3 + x. If one of them is x2 + x + 1, find the other.

Exercise | Q 122 | Page 239

Find the length of the side of the given square if area of the square is 625 square units and then find the value of x.

Exercise | Q 123 (i) | Page 239

Take suitable number of cards given in the adjoining diagram [G(x × x) representing x2, R(x × 1) representing x and Y(1 × 1) representing 1] to factorise the following expressions, by arranging the cards in the form of rectangles: (i) 2x2 + 6x + 4. Factorise 2x2 + 6x + 4 by using the figure.

Calculate the area of figure.

Exercise | Q 123. (ii) | Page 239

Take suitable number of cards given in the adjoining diagram [G(x × x) representing x2, R(x × 1) representing x and Y(1 × 1) representing 1] to factorise the following expressions, by arranging the cards in the form of rectangles: x2 + 4x + 4. Factorise 2x2 + 6x + 4 by using the figure.

Calculate the area of figure.

Exercise | Q 124 | Page 239

The figure shows the dimensions of a wall having a window and a door of a room. Write an algebraic expression for the area of the wall to be painted.

#### Match the expressions of column I with that of column II:

Exercise | Q 125 | Page 240
 Column I Column II (1) (21x + 13y)^2 (a) 441x^2 - 169y^2 (2) (21x - 13y)^2 (b) 441x^2 + 169y^2 + 546xy (3) (21x - 13y)(21x + 13y) (c) 441x^2 + 169y^2 - 546xy (d) 441x^2 - 169y^2 + 546xy

Exercise

## NCERT solutions for Mathematics Exemplar Class 8 chapter 7 - Algebraic Expression, Identities and Factorisation

NCERT solutions for Mathematics Exemplar Class 8 chapter 7 (Algebraic Expression, Identities and Factorisation) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Exemplar Class 8 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics Exemplar Class 8 chapter 7 Algebraic Expression, Identities and Factorisation are Algebraic Expressions, Terms, Factors and Coefficients of Expression, Types of Algebraic Expressions as Monomials, Binomials, Trinomials, and Polynomials, Addition of Algebraic Expressions, Multiplication of Algebraic Expressions, Multiplying Monomial by Monomials, Multiplying a Monomial by a Binomial, Like and Unlike Terms, Subtraction of Algebraic Expressions, Multiplying a Monomial by a Trinomial, Multiplying a Binomial by a Binomial, Multiplying a Binomial by a Trinomial, Concept of Identity, Expansion of (a + b)2 = a2 + 2ab + b2, Expansion of (a - b)2 = a2 - 2ab + b2, Expansion of (a + b)(a - b), Expansion of (x + a)(x + b), Factors and Multiples, Factorisation by Taking Out Common Factors, Factorising Algebraic Expressions, Factorisation by Regrouping Terms, Factorisation Using Identities, Factors of the Form (x + a)(x + b), Dividing a Monomial by a Monomial, Dividing a Polynomial by a Monomial, Dividing a Polynomial by a Polynomial, Concept of Find the Error.

Using NCERT Class 8 solutions Algebraic Expression, Identities and Factorisation exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 8 prefer NCERT Textbook Solutions to score more in exam.

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