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

#( 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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