In this page we have NCERT Solutions for Algebraic Expressions and Identities Class 8 Mathematics Chapter 9 for
Exercise 9.4 . Hope you like them and do not forget to like , social share
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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)
Answer:
Let ( a+b) (c+d) to be done
then
( a+b) (c+d)= a(c+d) + b( c+d)
=a x c+a x d+b x c+b x d
We will use the same concept in all the question below
i)
(2x + 5)(4x - 3)
=
2x x
4x -
2x x 3 +
5 x
4x -
5 x
3
=
8x² - 6x + 20x -15
=
8x² + 14x -15
ii) ( y - 8)(3y - 4)
= y
x 3y - 4y - 8
x 3y + 32
= 3y
2 - 4y - 24y + 32
= 3y
2 - 28y + 32
iii) (2.5l
- 0.5m)(2.5l + 0.5)
Using (a+b)(a-b) = a
2 - b
2
We get = 6.25l
2 - 0.25m
2
iv) ax + 5a + 3bx + 15b
v) 2pq
x 3pq - 2pq
x 2q
2 + 3q
2 x 3pq - 3q
2 x 2q
2
= 6p
2q
2 - 4pq
3 + 9pq
3 - 6q
4
= 6p
2q
2 - 5pq
3 - 6p
4
Question 2
Find the product.
(i) (5 – 2x) (3 + x)
(ii) (x + 7y) (7x – y)
iii) (a
2+ b) (a + b
2)
(iv) (p
2– q
2) (2p + q)
Answer:
i) 15 + 5x - 6x - 2x
2
= 15 - x - x
2
ii) 7x
2 - xy + 49xy - 7y
2
= 7x
2 - 7y
2 + 48xy
iii) a
2 x a + a
2 x b + a x b + b
3
= a
3 + a
2b + ab + b
3
= a
3 + b
3 + a
2b + ab
iv) 2p
3 + p
2q - 2pq
2 - q
3
= 2p
3 - q
3 + p
2q - 2pq
2
Question 3
Simplify.
(i) (x
2– 5) (x + 5) + 25
(ii) (a
2+ 5) (b
3+ 3) + 5
(iii) (a + b) (c – d) + (a – b) (c + d) + 2 (ac + bd)
(iv) (x + y)(2x + y) + (x + 2y)(x – y)
(v) (x + y)(x
2– xy + y
2)
(vi) (1.5x – 4y)(1.5x + 4y + 3) – 4.5x + 12y
(vii) (a + b + c)(a + b – c)
Answer:
i) x
3 + 5x
2 - 5x - 25 + 25
= x3 + 5x
2 -5x
ii) a
2b
3 + 3a
2 + 5b
3 + 15 + 5
= a
2b
3 + 5b
3 + 3a
2 + 20
iii) (ac - ad + bc - bd) + (ac + ad - bc - bd) + (2ac + 2bd)
= ac - ad + bc - bd + ac + ad - bc - bd + 2ac + 2bd
= 4ac
iv) 2x
2 + xy + 2xy + y
2 + x
2 - xy + 2xy - 2y
2
= 3x
2 + 4xy - y
2
v) x
3 - x
2y + xy
2 + x
2y - xy
2 + y
3
= x
3 + y
3
vi) 2.25x
2 + 6xy + 4.5x - 6xy - 16y
2 - 12y - 4.5x + 12y
= 2.25x
2 - 16y
2
vii) a
2 + ab - ac + ab + b
2 - bc + ac + bc - c
2
= a
2 + b
2 - c
2 + 2ab
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