RBSE Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.4

Rajasthan Board RBSE Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.4 Textbook Exercise Questions and Answers.

Rajasthan Board RBSE Solutions for Class 8 Maths in Hindi Medium & English Medium are part of RBSE Solutions for Class 8. Students can also read RBSE Class 8 Maths Important Questions for exam preparation. Students can also go through RBSE Class 8 Maths Notes to understand and remember the concepts easily. Practicing the class 8 maths chapter 6 try these solutions will help students analyse their level of preparation.

RBSE Class 8 Maths Solutions Chapter 9 Algebraic Expressions and Identities Ex 9.4

Question 1.
Multiply the binomials
(i) (2x + 5) and (4x - 3)
(ii) (y - 8) and (3y - 4)
(iii) (2.5l - 0.5m) and (2.5l + 0.5m)
(iv) (a + 3b) and (x + 5)
(v) (2pq + 3q2) and (3pq - 2q2)
(vi) (\(\frac{3}{4}\)a2 + 3b2) and 4(a2 - \(\frac{2}{3}\)b2)
Answer:
(i) (2x + 5 ) x (4x - 3)
= 2x(4x - 3) + 5(4x - 3)
= 8x2 - 6x + 20x - 15
= 8x2 + 14x - 15

(ii) (y - 8) × (3y - 4)
= y(3y - 4) - 8(3y - 4)
= 3y2 - 4y - 24y + 32
= 3y2 - 28y + 32

RBSE Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.4

(iii) (2.5l - 0.5m) × (2.5l + 0.5m)
= 2.5l (2.5l + 0.5m) - 0.5m (2.5l + 0.5m)
= 6.25l2 + 1.25lm - 1.25ml - 0.25m2
= 6.25l2</sup. - 0.25m2 Ans. [∵ lm = ml]

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

(v) (2pq + 3q2) × (3pq - 2q2)
= 2pq(3pq - 2q2) + 3q2(3pq - 2q2)
= 6p2q2 - 4pq3 + 9pq3 - 6q4
= 6p2q2 + 5pq3 - 6q4

(vi) (\(\frac{3}{4}\)a2 + 3b2) × 4(a2 - \(\frac{2}{3}\)b2)
= (\(\frac{3}{4}\)a2 + 3b2) (4a2 - \(\frac{8}{3}\)b2)
= \(\frac{3}{4}\)a2(4a2 - \(\frac{8}{3}\)b2) + 3b2(4a2 - \(\frac{8}{3}\)b2)
= 3a4 - 2a2b2 + 12oa2b2 - 8b4
= 3a4 + 10a2b2 - 8b4

RBSE Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.4

Question 2.
Find the product
(i) (5 - 2x) (3 + x)
Answer:
(5 - 2x) (3 + x) = 5(3 + x) - 2x(3 + x)
= 15 + 5x - 6x - 2x2
= 15 - x - 2x2

(ii) (x + 7y) (7x - y)
Answer:
(x + 7y) (7x - y) = x(7x - y) + 7y(7x - y)
= 7x2 - xy + 49xy - 7y2
= 7x2 + 48xy - 7y2

(iii) (a2 + b) (a + b2)
Answer:
(a2 + b) (a + b2)
= a2(a + b2) + b(a + b2)
= a3 + a2b2 + ab + b3

(iv) (p2 - q2) (2p + q)
Answer:
(p2 - q2) (2p + q) = p2(2p + q) - q2(2p + q)
= 2p3 + p2q - 2pq2 - q3

Question 3.
Simplify
(i) (x2 - 5) (x + 5) + 25
(ii) (a2 + 5) (b3 + 3) + 5
(iii) (t + s2) (t2 - s)
(iv) (a + b) (c - d) + (a - b) (c + d) + 2(ac + bd)
(v) (x + y) (2x + y) + (x + 2y) (x - y)
(vi) (x + y) (x2 - xy + y2)
(vii) (1.5x - 4y) (1.5x + 4y + 3) - 4.5x + 12y
(viii) (a + b + c)(a + b - c)
Answer:
(i) (x2 - 5) (x + 5) + 25
= x2 (x + 5) - 5 (x + 5) + 25
= x3 + 5x2 - 5x - 25 + 25
= x2 + 5x2 - 5x

RBSE Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.4

(ii) (a2 + 5) (b3 + 3) + 5
= a2(b3 + 3) + 5 (b3 + 3) + 5
= a2b3 + 3a2 + 5b3 +15 + 5
= a2b3 + 3a2 + 5b3 + 20

(iii) (t + s2) (t2 - s) = t(t2 - s) + s2(t2 - s)
= t3 - ts + s2t2 - s3

(iv) (a + b) (c - d) + (a - b) (c + d) + 2 (ac + bd)
= a(c - d) + b(c - d) + a(c + d) - b(c + d) + 2ac + 2bd
= ac - ad + bc - bd + ac + ad - bc - bd + 2ac + 2bd
= (1 + 1 + 2) ac + (- 1 + 1 )ad + (1 - l)bc + (- 1 - 1 + 2) bd
= 4ac + (0) ad + (0) (bc) + (0) bd
= 4ac + 0 + 0 = 4ac

(v) (x + y) (2x + y) + (x + 2y) (x - y)
= x(2x + y) + y(2x + y) + x(x - y) + 2y(x - y)
= 2x2 + xy + 2xy + y2 + x2 - xy + 2xy - 2y2
= (2 + 1)x2 + (1 + 2 - 1 + 2)xy + (1 - 2)y2
= 3x2 + 4xy - y2

(vi) (x + y) (x2 - xy + y2)
= x(x2 - xy + y2) + y(x2 - xy + y2)
= x3 - x2y + xy2 + x2y - xy2 + y3
= x3 + (-1 + 1 )x2y + (1 - 1) xy2 + y3
= x3 + (0)x2y + (0) (xy2) + y3
= x3 + y3

(vii) (1.5x - 4y) (1.5x + 4y + 3) - 4.5x + 12y
= 1.5x(1.5x + 4y + 3) - 4y(1.5x + 4y + 3) - 4.5x + 12y
= 1.5x × 1.5x + 1.5x × 4y + 1.5x × 3 - 4y × 1.5x - 4y × 4y - 4y × 3 - 4.5x + 12y
= 2.25x2 + 6xy + 4.5x - 6xy - 16y2 - 12y - 4.5x + 12y
= 2.25x2 + (6 - 6)xy + (4.5 - 4.5)x - 16y2 + (- 12 + 12 )y
= 2.25x2 + (0)xy + (0)x - 16y2 + (0)y
= 2.25x2 + 0 + 0 - 16y2 + 0
= 2.25x2 - 16y2

RBSE Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.4

(viii) (a + b + c)(a + b - c)
= a (a + b - c) + b (a + b - c) + c ( a + b - c )
= a2 + ab - ac + ab + b2 - bc + ac + bc - c2
= a2 + b2 - c2 + 2ab  

Bhagya
Last Updated on May 19, 2022, 12:25 p.m.
Published May 19, 2022