# How do you factor p^3r^5-p^2r?

Mar 27, 2017

${p}^{2} r \left(p {r}^{4} - 1\right)$

#### Explanation:

${p}^{3} {r}^{5} - {p}^{2} r$ is the same as $p \cdot p \cdot p \cdot r \cdot r \cdot r \cdot r \cdot r - p \cdot p \cdot r$.

To see what you can factor out, find what is common in both terms. Both terms have p and r, but the maximum number that they share can be factored out.

so ${p}^{2}$ and $r$ can be factored out.

when you remove two p's from the first term, there is one p left.
when you remove one r from the first term, there are four r's left.
when you remove two p's and one r from the second term, there is nothing left. However, you must put 1 there as a place holder (not 0, because when you distribute anything multiplied by 0 is 0).

So the answer is ${p}^{2} r \left(p {r}^{4} - 1\right)$