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

May 15, 2017

$10 {r}^{3} {s}^{2} + 25 {r}^{2} {s}^{2} - 15 {r}^{2} {s}^{3} = 5 {r}^{2} {s}^{2} \left(2 r + 5 - 3 s\right)$

Explanation:

Given:

$10 {r}^{3} {s}^{2} + 25 {r}^{2} {s}^{2} - 15 {r}^{2} {s}^{3}$

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

So we can separate that out as a factor:

$10 {r}^{3} {s}^{2} + 25 {r}^{2} {s}^{2} - 15 {r}^{2} {s}^{3} = 5 {r}^{2} {s}^{2} \left(2 r + 5 - 3 s\right)$

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