# How do you multiply (a-9)^2?

Feb 19, 2017

There are two ways to expand this. The first way is to use this rule:

${\left(x \pm y\right)}^{2} = {x}^{2} \pm 2 x y + {y}^{2}$

Substituting $a$ for $x$ and $9$ for $b$ from our problem gives:

${\left(a - 9\right)}^{2} = {a}^{2} - 2 a 9 + {9}^{2} = {a}^{2} - 18 a + 81$

The second way is to first rewrite this expression as:

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

Then, to multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{a} - \textcolor{red}{9}\right) \left(\textcolor{b l u e}{a} - \textcolor{b l u e}{9}\right)$ becomes:

$\left(\textcolor{red}{a} \times \textcolor{b l u e}{a}\right) - \left(\textcolor{red}{a} \times \textcolor{b l u e}{9}\right) - \left(\textcolor{red}{9} \times \textcolor{b l u e}{a}\right) + \left(\textcolor{red}{9} \times \textcolor{b l u e}{9}\right)$

${a}^{2} - 9 a - 9 a + 81$

We can now combine like terms:

${a}^{2} + \left(- 9 - 9\right) a + 81$

${a}^{2} - 18 a + 81$