Question

"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)

Class 8 Algebraic Expressions and Identities Page 148"

Answer 1

Algebraic expressions:

A combination of constants and variables connected by any or all of the four fundamental operations +, -,×,÷ is called an algebraic expression

Multiplication of algebraic expression:

The product of two factors with like signs is positive and the product of two factors with unlike signs is negative.

Multiplication of a binomial  and the binomial:

 

 Let  ( a+b)&  (c+d) are two Binomials. By using distributive law of multiplatinum over addition twice, we may find their product

( a+b)× (c+d)

= a(c+d) + b( c+d)
=(a ×  c+a ×  d)+(b ×  c+b × d)

= ac+ad+bc+bd

This method is known as the horizontal method.

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Solution:

i) (5-2x)(3+x)

5(3+x)-2x(3+x)

15 + 5x - 6x - 2x²

= 15 - x - 2x²

ii)(x+7y)(7x-y)

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

 7x² - xy + 49xy - 7y²

= 7x²- 7y²+ 48xy

iii) (a²+b)(a+b²)

a²(a+b²)+ b(a+b²)

a² x a + a² x b² + a x b +b× b²

= a³ + a²b²+ab+b³

iv)  (p²-q²)(2p+q)

p²(2p+q)- q²(2p+q)

2p³+ p²q - 2pq² - q³

= 2p³- q³ + p²q - 2pq²

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Hope this will help you....