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NCERT Solutions Class 8 Mathematics Solutions for Exercise 9.4 in Chapter 9 - Algebraic Expressions and Identities
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Q2) Find the product:
(i) (5 - 2x)(3 + x)
(ii) (x + 7y)(7x - y)
(iii) \left(a^2+b\right)\left(a+b^2\right)
(iv) \left(p^2-q^2\right)\left(2p+q\right)
Solution:
(i) \left(5-2x\right)\left(3+x\right)
= 5\times\left(3+x\right)-2x\left(3+x\right)\
= 5\times3+5\times x-2x\times3-2x\times x
= 15+5x-6x-2x^2
= 15-x-2x^2
(ii) \left(x+7y\right)\left(7x-y\right)
= x\left(7x-y\right)+7y\times\left(7x-y\right)
= x\times7x-x\times y+7y\times7x-7y\times y
= 7x^2-xy+49xy-7y^2
= 7x^2+48xy-7y^2
(iii) \left(a^2+b\right)\left(a+b^2\right)
= a^2\times\left(a+b^2\right)+b\times\left(a+b^2\right)
= a^2\times a+a^2\times b^2+b\times a+b\times b^2
= a^3+a^2b^2+ab+b^3
(iv) \left(p^2-q^2\right)\left(2p+q\right)
= p^2\times\left(2p+q\right)-q^2\left(2p+q\right)
= p^2\times2p+p^2\times q-q^2\times q
= 2p^3+p^2q-2pq^2-q^3
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