# How do you find the product of (x + 8)^2?

Apr 30, 2017

See the solution process below:

#### Explanation:

The first way is to use this rule:

${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

Substituting $x$ for $a$ and $8$ for $b$ gives:

${\left(x + 8\right)}^{2} = {x}^{2} + 2 x 8 + {8}^{2} = {x}^{2} + 16 x + 64$

We can also use this process to reach the same answer. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{x} + \textcolor{red}{8}\right) \left(\textcolor{b l u e}{x} + \textcolor{b l u e}{8}\right)$ becomes:

$\left(\textcolor{red}{x} \times \textcolor{b l u e}{x}\right) + \left(\textcolor{red}{x} \times \textcolor{b l u e}{8}\right) + \left(\textcolor{red}{8} \times \textcolor{b l u e}{x}\right) + \left(\textcolor{red}{8} \times \textcolor{b l u e}{8}\right)$

${x}^{2} + 8 x + 8 x + 64$

We can now combine like terms:

${x}^{2} + \left(8 + 8\right) x + 64$

${x}^{2} + 16 x + 64$