Answer:
[tex]x^3+8=(x+2)(x^2-2x+4)[/tex]
So if they meant [tex]x^3+8[/tex] then the answer is:
[tex](x+2)(x^2-2x+4)[/tex].
The choice this corresponds to is A.
Step-by-step explanation:
The sum of cubes formula for factoring or expanding:
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
You have I'm assuming they meant:
[tex]x^3+8[/tex].
Compare [tex]x^3+8[/tex] to [tex]a^3+b^3[/tex].
You should see in place of [tex]a[/tex] you have [tex]x[/tex].
You should also see in place of [tex]b[/tex] you have [tex]2[/tex].
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
[tex]x^3+8[/tex]
[tex]x^3+2^3[/tex]
[tex]x^3+2^3=(x+2)(x^2-2x+2^2)[/tex]
[tex]x^3+8=(x+2)(x^2-2x+4)[/tex]
Let's check it for fun.
So we are going to use the distributive property.
We are going to distribute all the terms in the first ( ) to all the terms in the second ( ).
[tex]x(x^2-2x+4)[/tex] + [tex]2(x^2-2x+4)[/tex]
[tex]x^3-2x^2+4x[/tex] + [tex]2x^2-4x+8[/tex]
Combine like terms:
[tex]x^3-2x^2+2x^2+4x-4x+8[/tex]
Simplify the grouping of like terms:
[tex]x^3+0x^2+0x+8[/tex]
0 times anything is 0:
[tex]x^3+8[/tex]
