How do you factor 216u^3 - v^3216u3v3?

1 Answer
May 24, 2016

(6u-v)(36u^2+6uv+v^2)(6uv)(36u2+6uv+v2)

Explanation:

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