# NCERT Solutions for class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.4

NCERT Solutions have been structured in a logical and easy language for quick revisions. Well-illustrated solutions for CBSE Class 8 MathsÂ Exercise 9.4 are extremely accurate and solved using step by step problem solving approach. This exercise help students to learn how to perform multiplication of two polynomials. Download free NCERT Solutions for Maths Chapter 9 prepared by BYJUâ€™S subject experts and practice offline.

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## Exercise 9.4 Page No: 148

1.Â Multiply the binomials.
(i) (2x + 5) and (4x â€“ 3)
(ii) (y â€“ 8) and (3y â€“ 4)
(iii)Â (2.5l â€“ 0.5m) and (2.5l + 0.5m)
(iv)Â (a + 3b) and (x + 5)
(v)Â (2pq + 3q2) andÂ (3pq â€“ 2q2)

(vi) (3/4Â a2 + 3b2) and 4(Â a2 â€“ 2/3Â b2 )

Solution :

(i) (2x + 5)(4x â€“ 3)
=Â 2xÂ xÂ 4xÂ â€“Â 2xÂ x 3 +Â 5Â xÂ 4xÂ â€“Â 5Â xÂ 3
=Â 8xÂ² â€“ 6x + 20x -15
=Â 8xÂ² + 14x -15

(ii) ( y â€“ 8)(3y â€“ 4)
= y x 3y â€“ 4y â€“ 8 x 3y + 32
= 3y2Â â€“ 4y â€“ 24y + 32
= 3y2Â â€“ 28y + 32

(iii) (2.5lÂ â€“ 0.5m)(2.5l + 0.5m)

= 2.5l x 2.5 l + 2.5l x 0.5m â€“ 0.5m x 2.5l â€“ 0.5m x 0.5m

= 6.25l2 + 1.25 lm â€“ 1.25 lm â€“ 0.25Â m2

= 6.25l2â€“ 0.25 m2

(iv) (a + 3b) (x + 5)
= ax + 5a + 3bx + 15b

(v) (2pq + 3q2)Â (3pq â€“ 2q2)

= 2pq x 3pq â€“ 2pq x 2q2Â + 3q2Â x 3pq â€“ 3q2Â x 2q2
= 6p2q2Â â€“ 4pq3Â + 9pq3Â â€“ 6q4

= 6p2q2Â + 5pq3Â â€“ 6q4

(vi) (3/4Â aÂ² + 3bÂ² ) and 4( aÂ² â€“ 2/3 bÂ²)

= (3/4 aÂ² + 3bÂ² ) x 4( aÂ² â€“ 2/3 bÂ² )

=(3/4 aÂ² + 3bÂ² ) x (4aÂ² â€“ 8/3 bÂ² )

=3/4 aÂ²Â x (4aÂ² â€“ 8/3 bÂ² ) + 3bÂ² x (4aÂ² â€“ 8/3 bÂ² )

=3/4 aÂ²Â x 4aÂ² -3/4 aÂ²Â x 8/3 bÂ² + 3bÂ²Â x 4aÂ² â€“ 3bÂ² xÂ 8/3 bÂ²

=3 a4Â â€“ 2aÂ²bÂ²Â + 12 aÂ²Â bÂ² â€“ 8b4

= 3a4 + 10aÂ² bÂ² â€“ 8b4

2. Find the product.
(i) (5 â€“ 2x) (3 + x)
(ii) (x + 7y) (7x â€“ y)
(iii) (a2+ b) (a + b2)
(iv) (p2 â€“ q2) (2p + q)

Solution:

(i) (5 â€“ 2x) (3 + x)

= 5 (3 + x) â€“ 2x (3 + x)

=15 + 5x â€“ 6x â€“ 2x2
= 15 â€“ x -2 xÂ 2

(ii) (x + 7y) (7x â€“ y)

= x(7x-y) + 7y ( 7x-y)

=7x2Â â€“ xy + 49xy â€“ 7y2
= 7x2Â â€“ 7y2Â + 48xy

(iii) (a2+ b) (a + b2)

= a2Â  (a + b2) + b(a + b2)
= a3Â + a2Â b2Â + ab + b3
= a3Â + b3Â + a2Â b2Â + ab

(iv) (p2â€“ q2) (2p + q)

= p2 (2p + q) â€“ q2 (2p + q)

=2p3Â + p2q â€“ 2pq2Â â€“ q3
= 2p3Â â€“ q3Â + p2q â€“ 2pq2

3.Â Simplify.
(i) (x2â€“ 5) (x + 5) + 25
(ii) (a2+ 5) (b3+ 3) + 5

(iii)(t + s2)(t2 â€“ s)
(iv) (a + b) (c â€“ d) + (a â€“ b) (c + d) + 2 (ac + bd)
(v) (x + y)(2x + y) + (x + 2y)(x â€“ y)
(vi) (x + y)(x2â€“ xy + y2)
(vii) (1.5x â€“ 4y)(1.5x + 4y + 3) â€“ 4.5x + 12y
(viii) (a + b + c)(a + b â€“ c)

Solution :

(i) (x2â€“ 5) (x + 5) + 25

= x3Â + 5x2Â â€“ 5x â€“ 25 + 25
= x3 + 5x2Â â€“ 5x

(ii) (a2+ 5) (b3+ 3) + 5
= a2b3Â + 3a2Â + 5b3Â + 15 + 5
= a2b3Â + 5b3Â + 3a2Â + 20

(iii) (t + s2)(t2 â€“ s)

= t (t2 â€“ s) + s2(t2 â€“ s)

= t3 â€“ st + s2t2 â€“ s3

= t3 â€“ s3 â€“ st + s2t2

(iv) (a + b) (c â€“ d) + (a â€“ b) (c + d) + 2 (ac + bd)

= (a + b) (c â€“ d) + (a â€“ b) (c + d) + 2 (ac + bd)

=(ac â€“ ad + bc â€“ bd) + (ac + ad â€“ bc â€“ bd) + (2ac + 2bd)
= ac â€“ ad + bc â€“ bd + ac + ad â€“ bc â€“ bd + 2ac + 2bd
= 4ac

(v) (x + y)(2x + y) + (x + 2y)(x â€“ y)

= 2x2Â + xy + 2xy + y2Â + x2Â â€“ xy + 2xy â€“ 2y2
= 3x2Â + 4xy â€“ y2

(vi) (x + y)(x2â€“ xy + y2)

= x3Â â€“ x2y + xy2Â + x2y â€“ xy2Â + y3
= x3Â + y3

(vii) (1.5x â€“ 4y)(1.5x + 4y + 3) â€“ 4.5x + 12y

= 2.25x2Â + 6xy + 4.5x â€“ 6xy â€“ 16y2Â â€“ 12y â€“ 4.5x + 12y
= 2.25x2Â â€“ 16y2

(viii) (a + b + c)(a + b â€“ c)

= a2Â + ab â€“ ac + ab + b2Â â€“ bc + ac + bc â€“ c2
= a2Â + b2Â â€“ c2Â + 2ab

### Access Other Exercise Solutions of Class 8 Maths Chapter 9 Algebraic Expressions and Identities

Exercise 9.1 Solutions : 4 Questions (Short answers)

Exercise 9.2 Solutions : 5 Questions (Short answers)

Exercise 9.3 Solutions : 5 Questions (Short answers)

Exercise 9.5 Solutions : 8 Questions (Short answers)

### NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.4

Algebraic Expressions and Identities Exercise 9.4 explains about multiplying a binomial by a binomial, multiplying a binomial by a trinomial and simplification of the polynomials. For more practice, download the NCERT solutions and practice the questions and answers.