# How do you factor the polynomials rp-9r+9p-81?

Aug 20, 2017

$\left(r + 9\right) \left(p - 9\right)$

#### Explanation:

To factor, you need to find like terms. The like terms in this expression are 9, p, and r. If you notice how the expression is written, you see that r is a common in the first two terms. 9 is common in the second two terms. Let's factor out r from the first two terms and 9 from the second two terms.

$r p - 9 r + 9 p - 81 \to$

$r \left(p - 9\right) + 9 \left(p - 9\right)$

Now we have $\left(p - 9\right)$ as the common term. We can factor out $\left(p - 9\right)$ to get the factored form of the whole expression.

$r \left(p - 9\right) + 9 \left(p - 9\right) \to$

$\left(p - 9\right) \left(r + 9\right)$ OR $\left(r + 9\right) \left(p - 9\right)$

If you want to check your answer, you can FOIL it or plug in two random numbers for r and p.