Question

Factorise:

`a^3/27 + 8/b^3`

Answer 1

Given expression is `a^3/27 + 8/b^3`,

It can be written in the form of perfect cubes as,

`(a/3)^3 + (2/b)^3`

Now, by using the identity x³ + y³ = x + yx² – xy + y², we get

`(a/3)^3 + (2/b)^3 = (a/3 + 2/b)[(a/3)^2 - a/3 xx 2/b + (2/b)^2]`

= `(a/3 + 2/b)(a^2/9 - (2a)/(3b) + 4/b^2)`

Hence, the factors of `(a/3)^3 + (2/b)^3` are `(a/3 + 2/b)(a^2/9 - (2a)/(3b) + 4/b^2)`.