Question

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

Answer 1

`(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)`

Answer 2

`x^2 +4x + 4`

Explanation:

Let's rewrite this:

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

From here we need to distribute

#( 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