Question

How do you factor `2a^3-16`?

Answer 1

The factor 2 is common to both the terms in the expression

`2a^3-16 = 2(a^3 - 8)`

`= 2(a^3 - 2^3)`

We know that `color(blue)(x^3 - y^3 = (x-y)(x^2 + xy +y^2)`
( Difference of Cubes Identity )

Hence `2(a^3 - 2^3) = 2(a-2)(a^2+2a+2^2)`

`= color(green)(2(a-2)(a^2+2a+4)`