8.(i) Factorise the following:

   (i) 8a^3 + b^3 + 12a^2 b + 6ab^2

Answers (1)
R Riya

We can rewrite   8a^3 + b^3 + 12a^2 b + 6ab^2  as

\Rightarrow 8a^3 + b^3 + 12a^2 b + 6ab^2 = (2a)^3+(b)^3+3.(2a)^2.b+3.2a.(b)^2

We will use identity

(x+y)^3=x^3+y^3+3x^2y+3xy^2

Here,  x=2a \ \ and \ \ y= b

Therefore, 

8a^3 + b^3 + 12a^2 b + 6ab^2 = (2a+b)^3

                                                   =(2a+b)(2a+b)(2a+b)

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