# How do you find the product of (a+5)(a-6)?

Apr 28, 2018

${a}^{2} - a - 30$

#### Explanation:

To solve this, we expand/distribute using FOIL:

As you can see in this image, the first thing we do is multiply the $\textcolor{s t e e l b l u e}{\text{firsts}}$:
$a \cdot a = {a}^{2}$

Then the $\textcolor{p u r p \le}{\text{outers}}$:
$a \cdot - 6 = - 6 a$

Then the $\textcolor{p e r u}{\text{inners}}$:
$5 \cdot a = 5 a$

and finally the $\textcolor{o l i v e \mathrm{dr} a b}{\text{lasts}}$:
$5 \cdot - 6 = - 30$

Now combine them all together:
${a}^{2} - 6 a + 5 a - 30$

We can still simplify the like terms. Let's color-code them:
${a}^{2} \quad \textcolor{red}{- \quad 6 a \quad + \quad 5 a} \quad - \quad 30$

Combine like terms and get the final answer:
${a}^{2} - a - 30$

Hope this helps!

Jun 30, 2018

${a}^{2} - a - 30$

#### Explanation:

$\textcolor{b l u e}{\left(a + 5\right)} \textcolor{g r e e n}{\left(a - 6\right)}$

Multiply everything in the right brackets (green) by everything in the left brackets (blue).

$\textcolor{g r e e n}{\textcolor{b l u e}{a} \left(a - 6\right) \textcolor{w h i t e}{\text{ddd}} \textcolor{b l u e}{+ 5} \left(a - 6\right)}$

Notice that the + sign followed the 5

${a}^{2} - 6 a \textcolor{w h i t e}{\text{dd}} + 5 a - 30$

but $- 6 a + 5 a$ is the same as $- a$ giving.

${a}^{2} - a - 30$