Question

How do you factor `8t^3 -27`?

Answer 1

`(2t-3)(4t^2+6t+9)`

Explanation:

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

`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 `8t^3=(2t)^3rArra=2t`

and `27=(3)^3rArrb=3`

Substitute these into the right side gives.

`8t^3-27=(2t-3)(4t^2+6t+9)`