# How do you find the product of (x + 7)² ?

May 27, 2017

FOIL

#### Explanation:

FOIL stands for First Outside Inside Last

${\left(x + 7\right)}^{2}$

This can be rewritten as:

$\left(x + 7\right) \left(x + 7\right)$

Multiply the first terms in each expression.

$\left(\textcolor{b l u e}{x} + 7\right) \left(\textcolor{b l u e}{x} + 7\right)$

$\textcolor{b l u e}{x \cdot x = {x}^{2}}$

Now we move to outside . multiply the outside terms of each expression.

$\left(\textcolor{\mathmr{and} a n \ge}{{x}^{2}} + 7\right) \left({x}^{2} + \textcolor{\mathmr{and} a n \ge}{7}\right)$

$\textcolor{\mathmr{and} a n \ge}{{x}^{2} \cdot 7 = 7 {x}^{2}}$

Next up are the inside terms. Multiply these from each expression.

$\left({x}^{2} + \left(\textcolor{g r e e n}{7}\right)\right) \left(\textcolor{g r e e n}{{x}^{2}} + 7\right)$

color(green)(7 * x^2 = 7x^2

Finally, we have the last terms. Multiply the last terms from each expression.

$\left({x}^{2} + \textcolor{red}{7}\right) \left({x}^{2} + \textcolor{red}{7}\right)$

color(red)(7*7 = 49

Now combine all of the solutions that we have come up with.

$\textcolor{b l u e}{{x}^{2}} + \textcolor{\mathmr{and} a n \ge}{7 {x}^{2}} + \textcolor{g r e e n}{7 {x}^{2}} + \textcolor{red}{49}$

Combine the like terms in between.

${x}^{2} + 14 x + 49$