Q7 of 65 Page 139

Let us factorize the following algebraic expressions:

a3 + 3a2b + 3ab2 + b3 – 8

Given,


a3 + 3a2b + 3ab2 + b3 – 8


= (a + b)3 – (2)3


We know, a3 – b3 = (a – b)(a2 + ab + b2)


= (a + b – 2) [(a + b)2 + 2(a + b) + 22]


We know, (a + b)2 = a2 + 2ab + b2


= (a + b – 2) [a2 + 2ab + b2 + 2a + 2b + 4]


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