Question

How do you factor completely `10r^3s^2 + 25r^2s^2 – 15r^2s^3`?

Answer 1

`10r^3s^2+25r^2s^2-15r^2s^3 = 5r^2s^2(2r+5-3s)`

Explanation:

Given:

`10r^3s^2+25r^2s^2-15r^2s^3`

Note that all of the terms are divisible by `5`, `r^2` and `s^2`, so by `5r^2s^2`.

So we can separate that out as a factor:

`10r^3s^2+25r^2s^2-15r^2s^3 = 5r^2s^2(2r+5-3s)`

The remaining factor is already linear, so will not factor any further.