Question

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

A. (x+ 2)(x2 - 2x+4)
B. (x+2)(x2–2x - 4)
C. (x+2)(x2+2x-4)
D. (x-2)(2-2x+4)

Answer 1

`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.

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`