8.(ii)  Factorise the following:

   (ii)    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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