# How do you factor -9a^2-9a?

Nov 24, 2015

$- 9 a \left(a + 1\right)$

#### Explanation:

What is a common factor of the equation?
First lets look at $9$

The two numbers $- 9$ and $- 9$ both have a common factor of $- 9$, so we can take out a $- 9$ by dividing the equation by $- 9$ and placing it on the outside of the brackets.

Factoring out -9

$- 9 \left(\frac{\cancel{- 9} {a}^{2}}{\cancel{- 9}} + \frac{\cancel{- 9} a}{\cancel{- 9}}\right)$

New equation: $- 9 \left({a}^{2} + a\right)$

Now lets look at $a$

The common factor of ${a}^{2}$ and $a$ is $a$. Take out $a$ by dividing the inside of the brackets by $a$ and placing it on the outside

Factoring out the a
$- 9 a \left(\frac{{a}^{\cancel{2}}}{\cancel{a}} + \frac{\cancel{a}}{\cancel{a}}\right)$
New equation: $- 9 a \left(a + 1\right)$

Note: Keep in mind that $\frac{a}{a}$ is $1$, not zero, because $\frac{1}{1}$ is not zero either, so we have to keep a $1$ after cancelling out $\frac{a}{a}$.