Question

The expression x3 – 64 can be written as (x)3 – (4)3. What is the factorization of x3 – 64?

a3 – b3 = (a – b)(a2 + ab + b2)
(x – 4)(x2 + 4x + 8)
(x – 4)(x2 + 4x + 16)
(x – 64)(x2 + 64x + 16)
(x – 64)(x2 + 64x + 4,096)

Answer 1

by factoring x^3-64 put you should get the second option as your answer

(x-4)(x^2+4x+16)

Answer 2

`(x-4)(x^2+4x+16)`

Explanation:

We have
`x^(3)-64=x^3-4^3` And we know that:
`a^3-b^3=(a-b)(a^2+ab+b^2)`. In our case we have that
`a=x` and
`b=4`, then we can eliminate the two last options. And we have:

`x^3-4^3=(x-4)(x^2+x4+4^2)=(x-4)(x^2+4x+16)`

Then the correct factorization is the second option.