# How do you factor by grouping r(p^2 + 5) - s(p^2 + 5)?

Mar 14, 2018

The factored expression is $\left(r - s\right) \left({p}^{2} + 5\right)$.

#### Explanation:

Imagine that the $\left({p}^{2} + 5\right)$ terms are their own variable. It might actually be easier to do that for a few steps.

Substitute out $\left({p}^{2} + 5\right)$ for $u$. Then, we can factor like we already know how to:

$\textcolor{w h i t e}{=} r \left({p}^{2} + 5\right) - s \left({p}^{2} + 5\right)$

$= r u - s u$

$= \left(r - s\right) \cdot u$

Now, put back in $\left({p}^{2} + 5\right)$ for $u$ (don't forget the paretheses):

$\textcolor{w h i t e}{=} \left(r - s\right) \cdot u$

$= \left(r - s\right) \left({p}^{2} + 5\right)$

That's how you factor by grouping. Hope this helped!