# How do you simplify (x+2)+(x-2)(2x+1)?

Sep 11, 2015

$\left(x + 2\right) + \left(x - 2\right) \left(2 x + 1\right) = 2 {x}^{2} - 2 x$

#### Explanation:

To solve:
$\left(x + 2\right) + \left(x - 2\right) \left(2 x + 1\right)$,
first multiply the two binomials on the right.

We can use the FOIL method here:

Mulitply the first terms:
$x \cdot 2 x = \textcolor{b l u e}{2 {x}^{2}}$

Multiply the outer terms:
$x \cdot 1 = \textcolor{b l u e}{x}$

Multiply the inner terms:
$- 2 \cdot 2 x = \textcolor{b l u e}{- 4 x}$

Multiply the last terms:
$- 2 \cdot 1 = \textcolor{b l u e}{- 2}$

$2 {x}^{2} + x - 4 x - 2$
$= 2 {x}^{2} - 3 x - 2$

This means that
$\left(x - 2\right) \left(2 x + 1\right) = 2 {x}^{2} - 3 x - 2$

Now we can use this to simplify the original problem:

$\left(x + 2\right) + \left(x - 2\right) \left(2 x + 1\right)$
$= x + 2 + 2 {x}^{2} - 3 x - 2$
$\textcolor{b l u e}{= 2 {x}^{2} - 2 x}$

Sep 11, 2015

$2 {x}^{2} - 2 x$
$\textcolor{w h i t e}{\text{XX}}$or
$2 x \left(x - 1\right)$

#### Explanation:

$\textcolor{red}{\left(x - 2\right) \left(2 x + 1\right)}$
$\textcolor{w h i t e}{\text{XXX}} = \textcolor{red}{x \left(2 x + 1\right) - 2 \left(2 x + 1\right)}$
$\textcolor{w h i t e}{\text{XXX}} = \textcolor{red}{2 {x}^{2} + x - 4 x - 2}$
$\textcolor{w h i t e}{\text{XXX}} = \textcolor{red}{2 {x}^{2} - 3 x - 2}$

So
$\textcolor{b l u e}{\left(x + 2\right)} + \textcolor{red}{\left(x - 2\right) \left(2 x + 1\right)}$
$\textcolor{w h i t e}{\text{XXX}} = \textcolor{b l u e}{x + 2} + \textcolor{red}{2 {x}^{2} - 3 x - 2}$
$\textcolor{w h i t e}{\text{XXX}} = 2 {x}^{2} - 2 x$