8.(iii) Factorise the following:

    (iii)   27 - 125a^ 3 - 135a + 225a^2

Answers (1)
R Riya

We can rewrite   27 - 125a^ 3 - 135a + 225a^2  as

\Rightarrow 27 - 125a^ 3 - 135a + 225a^2^{} = (3)^3-(25a)^3-3.(3)^2.5a+3.3.(5a)^2

We will use identity

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

Here,  x=3 \ \ and \ \ y= 5a

Therefore, 

27 - 125a^ 3 - 135a + 225a^2 = (3-5a)^3

                                                          =(3-5a)(3-5a)(3-5a)

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