8.(iv)  Factorise the following:

   (iv)    64a^3 - 27b^3 - 144a^2 b + 108ab^2

Answers (1)
R Riya

We can rewrite   64a^3 - 27b^3 - 144a^2 b + 108ab^2  as

\Rightarrow 64a^3 - 27b^3 - 144a^2 b + 108ab^2 = (4a)^3-(3b)^3-3.(4a)^2.3b+3.4a.(3b)^2

We will use identity

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

Here,  x=4a \ \ and \ \ y= 3b

Therefore, 

64a^3 - 27b^3 - 144a^2 b + 108ab^2=(4a-3b)^2

                                                                  =(4a-3b)(4a-3b)(4a-3b)

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