Question

How do you factor `8x^3 - 216`?

Answer 1

`8(x-3)(x^2+3x+9)`

Explanation:

First step is to 'take out' a common factor of 8.

`rArr8(x^3-27)........ (A)`

now `x^3-27" is a " color(blue)"difference of cubes"` and is factorised as shown.

`color(red)(|bar(ul(color(white)(a/a)color(black)(a^3-b^3=(a-b)(a^2+ab+b^2))color(white)(a/a)|)))`

`x^3=(x)^3" and " 27=(3)^3`

hence a = x and b = 3

`rArrx^3-27=(x-3)(x^2+3x+3^2)=(x-3)(x^2+3x+9)`

Substituting this back into (A)

`rArr8x^3-216=8(x-3)(x^2+3x+9)`