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Question

Factorize each of the following expressions:
(a+b)38(ab)3


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Solution

Given: (a+b)38(ab)3

(a+b)38(ab)3
=(a+b)3[2(ab)]3
=[(a+b)2(ab)][(a+b)2+(a+b)×2(ab)+(2(ab))2]

[x3y3=(xy)(x2+xy+y2)]

=(a+b2a+2b)[a2+2ab+b2+2a22b2+4(a22ab+b2)]
=(a+3b)(7a26ab+3b2)

Hence, (a+b)38(ab)3
=(a+3b)(7a26ab+3b2).




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