# How do you expand (-x-2)^2 ?

Apr 18, 2018

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

#### Explanation:

Factor out the negative signs
$= \left(- x - 2\right) \left(- x - 2\right)$
$= - \left(x + 2\right) \times - \left(x + 2\right)$
$= {\left(x + 2\right)}^{2}$

Either by binomial expansion or distribution it will become
$= \left(x + 2\right) \left(x + 2\right)$
$= \left(x \cdot x + 2 \cdot x + 2 \cdot x + 2 \cdot 2\right)$
$= \left({x}^{2} + 2 x + 2 x + 4\right)$
$= \left({x}^{2} + 4 x + 4\right)$

Apr 18, 2018

${x}^{2} + 4 x + 4$

#### Explanation:

Let's rewrite this:

$\left(- x - 2\right) \left(- x - 2\right)$

From here we need to distribute

( color(green)(-x) color(brown)(-2) )( color(orange)(-x) color(purple)(-2) )#

$\left(\textcolor{g r e e n}{- x} \times \textcolor{\mathmr{and} a n \ge}{- x}\right) + \left(\textcolor{g r e e n}{- x} \times \textcolor{p u r p \le}{- 2}\right) + \left(\textcolor{b r o w n}{- 2} \times \textcolor{\mathmr{and} a n \ge}{- x}\right) + \left(\textcolor{b r o w n}{- 2} \times \textcolor{p u r p \le}{- 2}\right)$

${x}^{2} + 2 x + 2 x + 4$

${x}^{2} + 4 x + 4$

To check our work, let's graph the original function and what we got

graph{y=(-x-2)(-x-2)}

graph{y=x^2 +4x + 4}

They match! Nice work