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

1 Answer
May 24, 2016

Answer:

#(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)#