Question

How would the expression x2 +8 be rewritten using Sum of Cubes?

Answer 1

Answer:

$x^3+8=(x+2)(x^2-2x+4)$

So if they meant $x^3+8$ then the answer is:

$(x+2)(x^2-2x+4)$.

The choice this corresponds to is A.

Step-by-step explanation:

The sum of cubes formula for factoring or expanding:

$a^3+b^3=(a+b)(a^2-ab+b^2)$

You have I'm assuming they meant:

$x^3+8$.

Compare $x^3+8$ to $a^3+b^3$.

You should see in place of $a$ you have $x$.

You should also see in place of $b$ you have $2$.

$a^3+b^3=(a+b)(a^2-ab+b^2)$

$x^3+8$

$x^3+2^3$

$x^3+2^3=(x+2)(x^2-2x+2^2)$

$x^3+8=(x+2)(x^2-2x+4)$

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 ( ).

$x(x^2-2x+4)$   +   $2(x^2-2x+4)$

$x^3-2x^2+4x$   + $2x^2-4x+8$

Combine like terms:

$x^3-2x^2+2x^2+4x-4x+8$

Simplify the grouping of like terms:

$x^3+0x^2+0x+8$

0 times anything is 0:

$x^3+8$