Question

How do you factor `64v^3-125`?

Answer 1

`(4v-5)(16v^2+20v+25)`

Explanation:

This is a `color(blue)"difference of cubes"` and , in general, factorises as.

`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)|)))........ (A)`

Now `64v^3=(4v)^3" and " 125=(5)^3`

`rArra=4v" and " b=5`

substitute into (A)

`rArr64v^3-125=(4v-5)(16v^2+20v+25)`