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

2 Answers
Hailin W.
Apr 18, 2018

(x+2)^2

Explanation:

Factor out the negative signs
=(-x-2)(-x-2)
=-(x+2)xx -(x+2)
=(x+2)^2

Either by binomial expansion or distribution it will become
=(x+2)(x+2)
=(x*x+2*x+2*x+2*2)
=(x^2+2x+2x+4)
=(x^2+4x+4)

Rachel
Apr 18, 2018

x^2 +4x + 4

Explanation:

Let's rewrite this:

(-x-2)(-x-2)

From here we need to distribute

![www.mathgrafitti.net](useruploads.socratic.org)

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

( color(green)(-x) xx color(orange)(-x) ) + ( color(green)(-x) xx color(purple)(-2) ) + ( color(brown)(-2) xx color(orange)(-x) ) + ( color(brown)(-2) xx color(purple)(-2) )

x^2 + 2x + 2x +4

x^2 +4x + 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

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