# NCERT Solutions for class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.3

NCERT Solutions has been carefully compiled and developed keeping into consideration the latest syllabus. CBSE Class 8 Maths, Chapter 9 Exercise 9.3, exercise questions and answers helps students to understand multiplication of the two polynomials as well as simplification of expression at particular values. NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.3 are prepared using step by step approach and aim to improve problem-solving skills.

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## Exercise 9.3 Page No: 146

1. Carry out the multiplication of the expressions in each of the following pairs.
(i) 4p, q + r
(ii) ab, a â€“ b
(iii) a + b, 7aÂ²bÂ²
(iv) a2 â€“ 9, 4a
(v) pq + qr + rp, 0

Solution:

(i)4p(q + r) = 4pq + 4pr

(ii)ab(a â€“ b) = a2 b â€“ a b2

(iii)(a + b) (7a2b2) = 7a3b2Â + 7a2b3

(iv) (a2Â â€“ 9)(4a) = 4a3Â â€“ 36a

(v) (pq + qr + rp)Â Ã—Â 0 = 0 ( Anything multiplied by zero is zero )

2. Complete the table.

Solution:

 First expression Second expression Product (i) a b + c + d a(b+c+d) = aÃ—b + aÃ—c + aÃ—d = ab + ac + ad (ii) x + y â€“ 5 5xy 5 xy (x + y â€“ 5) = 5 xy x x + 5 xy x y â€“ 5 xy x 5 = 5 x2y + 5 xy2 â€“ 25xy (iii) p 6p2 â€“ 7p + 5 p (6 p 2-7 p +5) = pÃ— 6 p2 â€“ pÃ— 7 p + pÃ—5 = 6 p3 â€“ 7 p2 + 5 p (iv) 4 p2 q2 p2Â â€“ q2 4p2Â q2Â x (p2 â€“Â q2 ) =4 p4 q2 â€“ 4p2 q4 (v) a + b + c abc abc(a + b + c) = abc Ã— a + abc Ã— b + abc Ã— c = a2bc + ab2c + abc2

3.Â Find the product.
i) a2Â x (2a22) x (4a26)
ii) (2/3 xy) Ã—(-9/10 x2y2)

(iii) (-10/3 pq3/) Ã— (6/5 p3q)
(iv)Â  ( x)Â Ã—Â (x2)Â Ã—Â (x3)Â Ã—Â (x4)

Solution:

i) a2Â x (2a22) x (4a26) = (2 Ã— 4) ( a2 Ã— a22 Ã— a26 ) = 8 Ã— a2 + 22 + 26Â = 8a50

ii) (2xy/3) Ã—(-9x2y2/10)

=(2/3 Ã— -9/10 ) ( x Ã— x2 Ã— y Ã— y2 )
= (-3/5 x3y3)

iii) (-10pq3/3) Ã—(6p3q/5)

= ( -10/3 Ã— 6/5 ) (p Ã— p3 Ã— q3 Ã— q)
= (-4p4q4)

iv)Â Â ( x)Â xÂ (x2)Â xÂ (x3)Â xÂ (x4)

= x1 + 2 + 3 + 4Â
=Â  x10

4. (a) Simplify 3x (4x â€“ 5) + 3 and find its values for (i) x = 3 (ii) x =1/2

(b) SimplifyÂ a (a2+ a + 1) + 5Â and find its value for (i)Â a = 0, (ii)Â a = 1Â (iii)Â a = â€“ 1.

Solution:

(a) 3x (4x â€“ 5) + 3

=3x ( 4x) â€“ 3x( 5) +3

=12x2Â â€“ 15x + 3

(i) Putting x=3 in the equation we gets
12x2Â â€“ 15x + 3 =12(32) â€“ 15 (3) +3

= 108 â€“ 45 + 3 = 66

(ii) Putting x=1/2 in the equation we get

12x2Â â€“ 15x + 3 = 12 (1/2)2 â€“ 15 (1/2) + 3

=12 (1/4) â€“ 15/2 +3

= 3 â€“ 15/2 + 3

= 6- 15/2

= (12- 15 ) /2

= -3/2

(b) a(a2 +a +1)+5

=a x a2 + a x a + a x 1 + 5
=a3+a2+a+ 5

(i) putting a= 0 in the equation we get
03+02+0+5=5

(ii) putting a=1 in the equation we get
13Â + 12Â + 1+5 = 1 + 1 + 1+5 = 8

(iii) Putting a = -1 in the equation we get
(-1)3+(-1)2Â + (-1)+5 = -1 + 1 â€“ 1+5 = 4

5. (a) Add:Â p ( p â€“ q), q ( q â€“ r) and r ( r â€“ p)
(b) Add:Â 2x (z â€“ x â€“ y)Â andÂ 2y (z â€“ y â€“ x)
(c) Subtract:Â 3l (l â€“ 4 m + 5 n)Â fromÂ 4l ( 10 n â€“ 3 m + 2 l )
(d) Subtract:Â 3a (a + b + c ) â€“ 2 b (a â€“ b + c) Â fromÂ 4c ( â€“ a + b + c )

Solution:

a) p ( p â€“ q) + q ( q â€“ r) + r ( r â€“ p)

= (p2Â â€“ pq) + (q2Â â€“ qr) + (r2Â â€“ pr)
= p2Â + q2Â + r2Â â€“ pq â€“ qr â€“ pr

b) 2x (z â€“ x â€“ y)Â +Â 2y (z â€“ y â€“ x)

= (2xz â€“ 2x2Â â€“ 2xy) + (2yz â€“ 2y2Â â€“ 2xy)
= 2xz â€“ 4xy + 2yz â€“ 2x2Â â€“ 2y2

c) 4l ( 10 n â€“ 3 m + 2 l ) â€“ 3l (l â€“ 4 m + 5 n)
=(40ln â€“ 12lm + 8l2) â€“ (3l2Â â€“ 12lm + 15ln)
= 40ln â€“ 12lm + 8l2Â â€“ 3l2Â +12lm -15 ln
= 25 ln + 5l2

d) 4c ( â€“ a + b + c ) â€“ (3a (a + b + c ) â€“ 2 b (a â€“ b + c))

= (-4ac + 4bc + 4c2) â€“ (3a2Â + 3ab + 3ac â€“ ( 2ab â€“ 2b2 + 2bc ))

=-4ac + 4bc + 4c2 â€“ (3a2Â + 3ab + 3ac â€“ 2ab + 2b2 â€“ 2bc)

= -4ac + 4bc + 4c2Â â€“ 3a2Â â€“ 3ab â€“ 3ac +2ab â€“ 2b2 + 2bc
= -7ac + 6bc + 4c2Â â€“ 3a2Â â€“ ab â€“ 2b2

### 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 9.4 Solutions : 3 Questions (Short answers)

Exercise 9.5 Solutions : 8 Questions (Short answers)

### NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.3

Algebraic Expressions and Identities Exercise 9.3 is about multiply a monomial by a binomial, multiply a monomial by a trinomial and simplification of the expressions and their values for given points. Practice exercise problems and complete your homework on time.