How do you expand ${(- x - 2)}^{2}$ $(-x-2)^2$ ?

Question

How do you expand ${(- x - 2)}^{2}$ $(-x-2)^2$ ?

2 Answers

Impact of this question

18336 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-18T14:36:13

${(x + 2)}^{2}$ $(x+2)^2$

Explanation:

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

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

Answer 2 · 2018-04-18T14:38:41

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

Explanation:

Let's rewrite this:

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

From here we need to distribute

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

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

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

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

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

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

Science

Math

Humanities

... and beyond

How do you expand ${(- x - 2)}^{2}$ $(-x-2)^2$ ?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you expand (−x−2)2(-x-2)^2 ?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

How do you expand ${(- x - 2)}^{2}$ $(-x-2)^2$ ?