# Use FOIL to solve the problem (x-2)(x+2) last ?

Feb 9, 2018

(x-2)(x+2)

1) Do x times x = ${x}^{2}$
2) Do x times 2 = $2 x$
3) Do -2 times x = $- 2 x$
4) Do -2 times 2 = -4

5) Put all of those terms in order
${x}^{2} + 2 x - 2 x - 4$

6) Add or subtract like terms
${x}^{2} - 4$

Feb 9, 2018

This is a different format but is still foil

${x}^{2} - {2}^{2}$

#### Explanation:

$\textcolor{p u r p \le}{\text{Answering the question}}$

$\textcolor{b l u e}{\left(x - 2\right)} \textcolor{g r e e n}{\left(x + 2\right)}$

Multiply everything inside the right brackets by everything in the left.

$\textcolor{g r e e n}{\textcolor{b l u e}{x} \left(x + 2\right) \textcolor{w h i t e}{\text{ddd}} \textcolor{b l u e}{- 2} \left(x + 2\right)}$

color(green)(x^2+2xcolor(white)("d")color(white)("ddd")-2x-4

$\textcolor{w h i t e}{\text{dddddd}} \textcolor{g r e e n}{{x}^{2} - 4}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{p u r p \le}{\text{Foot note}}$

What follows is really worth committing to memory. It shows up a lot!

$\textcolor{red}{\text{The above of "x^2-4" is the same as } {x}^{2} - {2}^{2}}$

Compare this

$\textcolor{red}{{x}^{2} - {2}^{2}}$
$\textcolor{p u r p \le}{{a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right) \leftarrow \text{ Commit to memory}}$