Question

How do you factor `216u^3 - v^3`?

Answer 1

`(6u-v)(36u^2+6uv+v^2)`

Explanation:

This is a `color(blue)"difference of cubes"`

and in general is factorised as follows.

`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)|)))`

here `216u^3=(6u)^3rArra=6u`

and `v^3=(v)^3rArrb=v`

`rArr216u^3-v^3=(6u-v)(36u^2+6uv+v^2)`