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Question

Factorise :

(a + b)3 - 8

My attempt

= (a + b)3 - (2)3

= (a + b - 2) {(a + b)2 ​​​​​+ (2)2 + 2(a + b)}

What should I do not?

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Solution

You just expand the last term that is
(a+b-2)(a²+2ab+b²+4+2a+2b)

So whole ans is

(a + b)3 - (2)3

= (a + b - 2) {(a + b)2 ​​​​​+ (2)2 + 2(a + b)}

=(a+b-2)(a²+b²+2ab+2a+2b+4)


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