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NCERT solutions Mathematics Textbook for Class 8 chapter 9 Algebraic Expressions and Identities

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Chapter 9 - Algebraic Expressions and Identities

Page 140

Identify the terms, their coefficients for the following expressions.

5xyz2 − 3zy

Q 1.1 | Page 140 | view solution

Identify the terms, their coefficients for the following expressions.

1 + x + x2

Q 1.2 | Page 140 | view solution

Identify the terms, their coefficients for the following expressions.

4x2y2 − 4x2y2z2 + z2

Q 1.3 | Page 140 | view solution

Identify the terms, their coefficients for the following expressions.

3 − pq + qr − rp

Q 1.4 | Page 140 | view solution

Identify the terms, their coefficients for the following expressions.

`x/2 + y/2 - xy`

Q 1.5 | Page 140 | view solution

Identify the terms, their coefficients for the following expressions.

0.3a − 0.6ab + 0.5b

Q 1.6 | Page 140 | view solution

Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?

x + y, 1000, x + x2 + x3 + x4, 7 + y + 5x, 2y − 3y2, 2y − 3y2 + 4y3, 5x − 4y + 3xy, 4z − 15z2, ab + bc + cd + da, pqr, p2q + pq2, 2p + 2q

Q 2 | Page 140 | view solution

Add the following. ab − bc, bc − ca, ca − ab

Q 3.1 | Page 140 | view solution

Add the following a − b + ab, b − c + bc, c − a + ac

Q 3.2 | Page 140 | view solution

Add the following 2p2q2 − 3pq + 4, 5 + 7pq − 3p2q2

Q 3.3 | Page 140 | view solution

Add the following.  l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl

Q 3.4 | Page 140 | view solution

 Subtract 4a − 7ab + 3b + 12 from 12a − 9ab + 5b − 3

Q 4.1 | Page 140 | view solution

Subtract 3xy + 5yz − 7zx from 5xy − 2yz − 2zx + 10xyz

Q 4.2 | Page 140 | view solution

Subtract 4p2q − 3pq + 5pq2 − 8p + 7q − 10 from 18 − 3p − 11q + 5pq − 2pq2 + 5p2q

Q 4.3 | Page 140 | view solution

Pages 143 - 144

Find the product of the given pairs of monomials.

4, 7p

Q 1.1 | Page 143 | view solution

Find the product of the given pairs of monomials.

− 4p, 7p

Q 1.2 | Page 143 | view solution

Find the product of the given pairs of monomials.

− 4p, 7pq

Q 1.3 | Page 143 | view solution

Find the product of the given pairs of monomials.

4p3, − 3p

Q 1.4 | Page 143 | view solution

Find the product of the given pairs of monomials.

4p, 0

Q 1.5 | Page 143 | view solution

Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively.

(p, q); (10m, 5n); (20x2, 5y2); (4x, 3x2); (3mn, 4np)

Q 2 | Page 143 | view solution

Complete the table of products.

First monomial →

Second monomial ↓

2x –5y 3x2 – 4xy 7x2y –9x2y2
2x 4x2 ... ... ... ... ...
–5y ... ... –15x2y ... ... ...
3x2 ... ... ... ... ... ...
– 4xy ... ... ... ... ... ...
7x2y ... ... ... ... ... ...
–9x2y2 ... ... ... ... ... ...
Q 3 | Page 144 | view solution

Obtain the volume of rectangular boxes with the following length, breadth and height respectively.

5a, 3a2, 7a4

Q 4.1 | Page 144 | view solution

Obtain the volume of rectangular boxes with the following length, breadth and height respectively.

2p, 4q, 8r

Q 4.2 | Page 144 | view solution

Obtain the volume of rectangular boxes with the following length, breadth and height respectively.

xy, 2x2y, 2xy2

Q 4.3 | Page 144 | view solution

Obtain the volume of rectangular boxes with the following length, breadth and height respectively.

a, 2b, 3c

Q 4.4 | Page 144 | view solution

Obtain the product of xy, yz, zx

Q 5.1 | Page 144 | view solution

Obtain the product of a, − a2, a3

Q 5.2 | Page 144 | view solution

Obtain the product of 2, 4y, 8y2, 16y3

Q 5.3 | Page 144 | view solution

Obtain the product of  a, 2b, 3c, 6abc

Q 5.4 | Page 144 | view solution

Obtain the product of m, − mn, mnp

Q 5.5 | Page 144 | view solution

Page 146

Carry out the multiplication of the expressions of the following pairs.

4p, q + r

Q 1.1 | Page 146 | view solution

Carry out the multiplication of the expressions of the following pairs.

ab, a − b

Q 1.2 | Page 146 | view solution

Carry out the multiplication of the expressions of the following pairs.

a + b, 7a2b2

Q 1.3 | Page 146 | view solution

Carry out the multiplication of the expressions of the following pairs.

a2 − 9, 4a

Q 1.4 | Page 146 | view solution

Carry out the multiplication of the expressions of the following pairs.

pq + qr + rp, 0

Q 1.5 | Page 146 | view solution

Complete the table

  First expression Second Expression Product
1 a b + c + d -
2 x + y − 5 xy -
3 p 6p− 7p + 5 -
4 4p2q2 p− q2 -
5 a + b + c abc -
Q 2 | Page 146 | view solution

Find the product  (a2) × (2a22) × (4a26)

Q 3.1 | Page 146 | view solution

Find the product `(2/3 xy) xx ((-9)/10 x^2y^2)`

Q 3.2 | Page 146 | view solution

Find the product `(-10/3 pq^3) xx (6/5p^3q)`

Q 3.3 | Page 146 | view solution

Find the product x × x2 × x3 × x4

Q 3.4 | Page 146 | view solution

Simplify 3x (4x −5) + 3 and find its values for (1) x = 3, (2) x = `1/2`.

Q 4.1 | Page 146 | view solution

a (a2 + a + 1) + 5 and find its values for (1) a = 0, (2) a = 1, (3) a = − 1.

Q 4.2 | Page 146 | view solution

Add: p (p − q), q (q ­­­− r) and r (r ­− p)

Q 5.1 | Page 146 | view solution

Add: 2x (z − x − y) and 2y (z − y − x)

Q 5.2 | Page 146 | view solution

Subtract: 3l (l − 4m + 5n) from 4l (10n − 3m + 2l)

Q 5.3 | Page 146 | view solution

Subtract: 3a (a + b + c) − 2b (a − b + c) from 4c (− a + b + c)

Q 5.4 | Page 146 | view solution

Page 148

Multiply the binomials (2x + 5) and (4x − 3)

Q 1.1 | Page 148 | view solution

Multiply the binomials (y − 8) and (3y − 4)

Q 1.2 | Page 148 | view solution

Multiply the binomials (2.5l − 0.5m) and (2.5l + 0.5m)

Q 1.3 | Page 148 | view solution

Multiply the binomials (a + 3b) and (x + 5)

Q 1.4 | Page 148 | view solution

Multiply the binomials (2pq + 3q2) and (3pq − 2q2)

Q 1.5 | Page 148 | view solution

Multiply the binomials `(3/4 a^2 + 3b^2) and 4(a^2 - 2/3 b^2)`

Q 1.6 | Page 148 | view solution

Find the product (5 − 2x) (3 + x)

Q 2.1 | Page 148 | view solution

Find the product (x + 7y) (7x − y)

Q 2.2 | Page 148 | view solution

Find the product (a2 + b) (a + b2)

Q 2.3 | Page 148 | view solution

Find the product (p2 − q2) (2p + q)

Q 2.4 | Page 148 | view solution

Simplify (x2 − 5) (x + 5) + 25

Q 3.1 | Page 148 | view solution

Simplify (a2 + 5) (b3 + 3) + 5

Q 3.2 | Page 148 | view solution

Simplify (t + s2) (t2 − s)

Q 3.3 | Page 148 | view solution

Simplify (a + b) (c − d) + (a − b) (c + d) + 2 (ac + bd)

Q 3.4 | Page 148 | view solution

Simplify (x + y) (2x + y) + (x + 2y) (x − y)

Q 3.5 | Page 148 | view solution

Simplify (x + y) (x2 − xy + y2)

Q 3.6 | Page 148 | view solution

Simplify (1.5x − 4y) (1.5x + 4y + 3) − 4.5x + 12y

Q 3.7 | Page 148 | view solution

Simplify (a + b + c) (a + b − c)

Q 3.8 | Page 148 | view solution

Pages 151 - 152

Use a suitable identity to get the following products.

(x + 3) (x + 3)

Q 1.1 | Page 151 | view solution

Use a suitable identity to get the following products.

(7a − 9b) (7a − 9b)

Q 1.1 | Page 151 | view solution

Use a suitable identity to get the following products.

(2y + 5) (2y + 5)

Q 1.2 | Page 151 | view solution

Use a suitable identity to get the following products

(2a ­− 7) (2a − 7)

Q 1.3 | Page 151 | view solution

Use a suitable identity to get the following products.

`(3a - 1/2)(3a - 1/2)`

Q 1.4 | Page 151 | view solution

Use a suitable identity to get the following products.

(1.1m − 0.4) (1.1 m + 0.4)

Q 1.5 | Page 151 | view solution

Use a suitable identity to get the following products.

(a2 + b2) (− a2 + b2)

Q 1.6 | Page 151 | view solution

Use a suitable identity to get the following products.

(6x − 7) (6x + 7)

Q 1.7 | Page 151 | view solution

Use a suitable identity to get the following products.

(− a + c) (− a + c)

Q 1.8 | Page 151 | view solution

Use a suitable identity to get the following products.

`(x/2 + (3y)/4)(x/2 + (3y)/4)`

Q 1.9 | Page 151 | view solution

Find the following squares by suing the identities.

(b − 7)2

Q 3.1 | Page 151 | view solution

Find the following squares by suing the identities

(xy + 3z)2

Q 3.2 | Page 151 | view solution

Find the following squares by suing the identities.

(6x2 − 5y)2

Q 3.3 | Page 151 | view solution

Find the following squares by suing the identities.

`(2/3 m + 3/4 n)^2`

Q 3.4 | Page 151 | view solution

Find the following squares by suing the identities 

(0.4p − 0.5q)2

Q 3.5 | Page 151 | view solution

Find the following squares by suing the identities.

(2xy + 5y)2

Q 3.6 | Page 151 | view solution

Simplify (a2 − b2)2

Q 4.1 | Page 151 | view solution

Simplify (2x +5)2 − (2x − 5)2

Q 4.2 | Page 151 | view solution

Simplify (7m − 8n)2 + (7m + 8n)2

Q 4.3 | Page 151 | view solution

Simplify (4m + 5n)2 + (5m + 4n)2

Q 4.4 | Page 151 | view solution

Simplify (2.5p − 1.5q)2 − (1.5p − 2.5q)2

Q 4.5 | Page 151 | view solution

Simplify (ab + bc)2 − 2ab2c

Q 4.6 | Page 151 | view solution

Simplify (m2 − n2m)2 + 2m3n2

Q 4.7 | Page 151 | view solution

Show that (3x + 7)2 − 84x = (3x − 7)2

Q 5.1 | Page 151 | view solution

Show that (9p - 5q)2 + 180pq = (9p + 5q)2

Q 5.2 | Page 151 | view solution

Show that `(4/3 m - 3/4 n)^2 + 2mn = 16/9 m^2 + 9/16 n^2`

Q 5.3 | Page 151 | view solution

Show that `(4pq + 3q)^2 - (4pq - 3q)^2 = 48pq^2`

Q 5.4 | Page 151 | view solution

Show that (a - b)(a + b) + (b - c) (b + c) + (c - a) (c + a) = 0

Q 5.5 | Page 151 | view solution

Using identities, evaluate 712

 

Q 6.1 | Page 152 | view solution

Using identities, evaluate 992

Q 6.2 | Page 152 | view solution

Using identities, evaluate 1022

Q 6.3 | Page 152 | view solution

Using identities, evaluate 9982

Q 6.4 | Page 152 | view solution

Using identities, evaluate (5.2)2

Q 6.5 | Page 152 | view solution

Using identities, evaluate 297 × 303

Q 6.6 | Page 152 | view solution

Using identities, evaluate 78 × 82

Q 6.7 | Page 152 | view solution

Using identities, evaluate 8.92

Q 6.8 | Page 152 | view solution

Using identities, evaluate 1.05 × 9.5

Q 6.9 | Page 152 | view solution

Using a− b2 = (a + b) (a − b), find 512 − 492

Q 7.1 | Page 152 | view solution

Using a− b2 = (a + b) (a − b), find  (1.02)2 − (0.98)2

Q 7.2 | Page 152 | view solution

Using a− b2 = (a + b) (a − b), find 1532 − 1472

Q 7.3 | Page 152 | view solution

Using a− b2 = (a + b) (a − b), find 12.12 − 7.92

Q 7.4 | Page 152 | view solution

Using (x + a) (x + b) = x2 + (a + b) x + ab, find 103 × 104

Q 8.1 | Page 152 | view solution

Using (x + a) (x + b) = x2 + (a + b) x + ab, find 5.1 × 5.2

Q 8.2 | Page 152 | view solution

Using (x + a) (x + b) = x2 + (a + b) x + ab, find 103 × 98

Q 8.3 | Page 152 | view solution

Using (x + a) (x + b) = x2 + (a + b) x + ab, find 9.7 × 9.8

Q 8.4 | Page 152 | view solution

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