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

Mathematics Textbook for Class 8

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NCERT Mathematics Class 8

Mathematics Textbook for Class 8 - Shaalaa.com

Chapter 9: Algebraic Expressions and Identities

Ex. 9.10Ex. 9.20Ex. 9.30Ex. 9.40Ex. 9.50

Chapter 9: Algebraic Expressions and Identities Exercise 9.10 solutions [Page 140]

Ex. 9.10 | Q 1.1 | Page 140

Identify the terms, their coefficients for the following expressions.

5xyz2 − 3zy

Ex. 9.10 | Q 1.2 | Page 140

Identify the terms, their coefficients for the following expressions.

1 + x + x2

Ex. 9.10 | Q 1.3 | Page 140

Identify the terms, their coefficients for the following expressions.

4x2y2 − 4x2y2z2 + z2

Ex. 9.10 | Q 1.4 | Page 140

Identify the terms, their coefficients for the following expressions.

3 − pq + qr − rp

Ex. 9.10 | Q 1.5 | Page 140

Identify the terms, their coefficients for the following expressions.

`x/2 + y/2 - xy`

Ex. 9.10 | Q 1.6 | Page 140

Identify the terms, their coefficients for the following expressions.

0.3a − 0.6ab + 0.5b

Ex. 9.10 | Q 2 | Page 140

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

Ex. 9.10 | Q 3.1 | Page 140

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

Ex. 9.10 | Q 3.2 | Page 140

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

Ex. 9.10 | Q 3.3 | Page 140

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

Ex. 9.10 | Q 3.4 | Page 140

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

Ex. 9.10 | Q 4.1 | Page 140

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

Ex. 9.10 | Q 4.2 | Page 140

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

Ex. 9.10 | Q 4.3 | Page 140

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

Chapter 9: Algebraic Expressions and Identities Exercise 9.20 solutions [Pages 143 - 144]

Ex. 9.20 | Q 1.1 | Page 143

Find the product of the given pairs of monomials.

4, 7p

Ex. 9.20 | Q 1.2 | Page 143

Find the product of the given pairs of monomials.

− 4p, 7p

Ex. 9.20 | Q 1.3 | Page 143

Find the product of the given pairs of monomials.

− 4p, 7pq

Ex. 9.20 | Q 1.4 | Page 143

Find the product of the given pairs of monomials.

4p3, − 3p

Ex. 9.20 | Q 1.5 | Page 143

Find the product of the given pairs of monomials.

4p, 0

Ex. 9.20 | Q 2 | Page 143

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)

Ex. 9.20 | Q 3 | Page 144

Complete the table of products.

First monomial →

Second monomial ↓

2x –5y 3x2 – 4xy 7x2y –9x2y2
2x 4x2 ... ... ... ... ...
–5y ... ... –15x2y ... ... ...
3x2 ... ... ... ... ... ...
– 4xy ... ... ... ... ... ...
7x2y ... ... ... ... ... ...
–9x2y2 ... ... ... ... ... ...
Ex. 9.20 | Q 4.1 | Page 144

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

5a, 3a2, 7a4

Ex. 9.20 | Q 4.2 | Page 144

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

2p, 4q, 8r

Ex. 9.20 | Q 4.3 | Page 144

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

xy, 2x2y, 2xy2

Ex. 9.20 | Q 4.4 | Page 144

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

a, 2b, 3c

Ex. 9.20 | Q 5.1 | Page 144

Obtain the product of xy, yz, zx

Ex. 9.20 | Q 5.2 | Page 144

Obtain the product of a, − a2, a3

Ex. 9.20 | Q 5.3 | Page 144

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

Ex. 9.20 | Q 5.4 | Page 144

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

Ex. 9.20 | Q 5.5 | Page 144

Obtain the product of m, − mn, mnp

Chapter 9: Algebraic Expressions and Identities Exercise 9.30 solutions [Page 146]

Ex. 9.30 | Q 1.1 | Page 146

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

4p, q + r

Ex. 9.30 | Q 1.2 | Page 146

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

ab, a − b

Ex. 9.30 | Q 1.3 | Page 146

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

a + b, 7a2b2

Ex. 9.30 | Q 1.4 | Page 146

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

a2 − 9, 4a

Ex. 9.30 | Q 1.5 | Page 146

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

pq + qr + rp, 0

Ex. 9.30 | Q 2 | Page 146

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 -
Ex. 9.30 | Q 3.1 | Page 146

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

Ex. 9.30 | Q 3.2 | Page 146

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

Ex. 9.30 | Q 3.3 | Page 146

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

Ex. 9.30 | Q 3.4 | Page 146

Find the product x × x2 × x3 × x4

Ex. 9.30 | Q 4.1 | Page 146

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

Ex. 9.30 | Q 4.2 | Page 146

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

Ex. 9.30 | Q 5.1 | Page 146

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

Ex. 9.30 | Q 5.2 | Page 146

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

Ex. 9.30 | Q 5.3 | Page 146

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

Ex. 9.30 | Q 5.4 | Page 146

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

Chapter 9: Algebraic Expressions and Identities Exercise 9.40 solutions [Page 148]

Ex. 9.40 | Q 1.1 | Page 148

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

Ex. 9.40 | Q 1.2 | Page 148

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

Ex. 9.40 | Q 1.3 | Page 148

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

Ex. 9.40 | Q 1.4 | Page 148

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

Ex. 9.40 | Q 1.5 | Page 148

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

Ex. 9.40 | Q 1.6 | Page 148

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

Ex. 9.40 | Q 2.1 | Page 148

Find the product (5 − 2x) (3 + x)

Ex. 9.40 | Q 2.2 | Page 148

Find the product (x + 7y) (7x − y)

Ex. 9.40 | Q 2.3 | Page 148

Find the product (a2 + b) (a + b2)

Ex. 9.40 | Q 2.4 | Page 148

Find the product (p2 − q2) (2p + q)

Ex. 9.40 | Q 3.1 | Page 148

Simplify (x2 − 5) (x + 5) + 25

Ex. 9.40 | Q 3.2 | Page 148

Simplify (a2 + 5) (b3 + 3) + 5

Ex. 9.40 | Q 3.3 | Page 148

Simplify (t + s2) (t2 − s)

Ex. 9.40 | Q 3.4 | Page 148

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

Ex. 9.40 | Q 3.5 | Page 148

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

Ex. 9.40 | Q 3.6 | Page 148

Simplify (x + y) (x2 − xy + y2)

Ex. 9.40 | Q 3.7 | Page 148

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

Ex. 9.40 | Q 3.8 | Page 148

Simplify (a + b + c) (a + b − c)

Chapter 9: Algebraic Expressions and Identities Exercise 9.50 solutions [Pages 151 - 152]

Ex. 9.50 | Q 1.01 | Page 151

Use a suitable identity to get the following products.

(x + 3) (x + 3)

Ex. 9.50 | Q 1.02 | Page 151

Use a suitable identity to get the following products.

(2y + 5) (2y + 5)

Ex. 9.50 | Q 1.03 | Page 151

Use a suitable identity to get the following products

(2a ­− 7) (2a − 7)

Ex. 9.50 | Q 1.04 | Page 151

Use a suitable identity to get the following products.

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

Ex. 9.50 | Q 1.05 | Page 151

Use a suitable identity to get the following products.

(1.1m − 0.4) (1.1 m + 0.4)

Ex. 9.50 | Q 1.06 | Page 151

Use a suitable identity to get the following products.

(a2 + b2) (− a2 + b2)

Ex. 9.50 | Q 1.07 | Page 151

Use a suitable identity to get the following products.

(6x − 7) (6x + 7)

Ex. 9.50 | Q 1.08 | Page 151

Use a suitable identity to get the following products.

(− a + c) (− a + c)

Ex. 9.50 | Q 1.09 | Page 151

Use a suitable identity to get the following products.

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

Ex. 9.50 | Q 1.1 | Page 151

Use a suitable identity to get the following products.

(7a − 9b) (7a − 9b)

Ex. 9.50 | Q 3.1 | Page 151

Find the following squares by suing the identities.

(b − 7)2

Ex. 9.50 | Q 3.2 | Page 151

Find the following squares by suing the identities

(xy + 3z)2

Ex. 9.50 | Q 3.3 | Page 151

Find the following squares by suing the identities.

(6x2 − 5y)2

Ex. 9.50 | Q 3.4 | Page 151

Find the following squares by suing the identities.

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

Ex. 9.50 | Q 3.5 | Page 151

Find the following squares by suing the identities 

(0.4p − 0.5q)2

Ex. 9.50 | Q 3.6 | Page 151

Find the following squares by suing the identities.

(2xy + 5y)2

Ex. 9.50 | Q 4.1 | Page 151

Simplify (a2 − b2)2

Ex. 9.50 | Q 4.2 | Page 151

Simplify (2x +5)2 − (2x − 5)2

Ex. 9.50 | Q 4.3 | Page 151

Simplify (7m − 8n)2 + (7m + 8n)2

Ex. 9.50 | Q 4.4 | Page 151

Simplify (4m + 5n)2 + (5m + 4n)2

Ex. 9.50 | Q 4.5 | Page 151

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

Ex. 9.50 | Q 4.6 | Page 151

Simplify (ab + bc)2 − 2ab2c

Ex. 9.50 | Q 4.7 | Page 151

Simplify (m2 − n2m)2 + 2m3n2

Ex. 9.50 | Q 5.1 | Page 151

Show that (3x + 7)2 − 84x = (3x − 7)2

Ex. 9.50 | Q 5.2 | Page 151

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

Ex. 9.50 | Q 5.3 | Page 151

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

Ex. 9.50 | Q 5.4 | Page 151

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

Ex. 9.50 | Q 5.5 | Page 151

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

Ex. 9.50 | Q 6.1 | Page 152

Using identities, evaluate 712

 

Ex. 9.50 | Q 6.2 | Page 152

Using identities, evaluate 992

Ex. 9.50 | Q 6.3 | Page 152

Using identities, evaluate 1022

Ex. 9.50 | Q 6.4 | Page 152

Using identities, evaluate 9982

Ex. 9.50 | Q 6.5 | Page 152

Using identities, evaluate (5.2)2

Ex. 9.50 | Q 6.6 | Page 152

Using identities, evaluate 297 × 303

Ex. 9.50 | Q 6.7 | Page 152

Using identities, evaluate 78 × 82

Ex. 9.50 | Q 6.8 | Page 152

Using identities, evaluate 8.92

Ex. 9.50 | Q 6.9 | Page 152

Using identities, evaluate 1.05 × 9.5

Ex. 9.50 | Q 7.1 | Page 152

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

Ex. 9.50 | Q 7.2 | Page 152

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

Ex. 9.50 | Q 7.3 | Page 152

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

Ex. 9.50 | Q 7.4 | Page 152

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

Ex. 9.50 | Q 8.1 | Page 152

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

Ex. 9.50 | Q 8.2 | Page 152

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

Ex. 9.50 | Q 8.3 | Page 152

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

Ex. 9.50 | Q 8.4 | Page 152

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

Chapter 9: Algebraic Expressions and Identities

Ex. 9.10Ex. 9.20Ex. 9.30Ex. 9.40Ex. 9.50

NCERT Mathematics Class 8

Mathematics Textbook for Class 8 - Shaalaa.com

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

NCERT solutions for Class 8 Maths chapter 9 (Algebraic Expressions and Identities) 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 Textbook for Class 8 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com are providing such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 8 Mathematics chapter 9 Algebraic Expressions and Identities are Concept of Expression, Terms, Factors and Coefficients, Monomials, Binomials and Polynomials, Like and Unlike Terms, Addition and Subtraction of Algebraic Expressions, Multiplication of Algebraic Expressions: Introduction, Multiplying Two Monomials, Multiplying Three Or More Monomials, Multiplying a Monomial by a Binomial, Multiplying a Monomial by a Trinomial, Multiplying a Binomial by a Binomial, Multiplying a Binomial by a Trinomial, Concept of Identity, Standard Identities, Applying Identities.

Using NCERT Class 8 solutions Algebraic Expressions and Identities 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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