Question

How do you factor `z^3 - 125`?

Answer 1

`(z-5)(z^2+5z+25)`

Explanation:

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

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

`"here " (z)^3=z^3" and " (5)^3=125`

`rArra=z" and " b=5`

`rArrz^3-125=(z-5)(z^2+5z+25)`