Question

Factor completely.

x^6 − 27

Answer 1

`(x^(2)-3)(x^(4)+3x^(2)+9)`

Explanation:

we know that

A difference of cubes can be factored like this

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

In this problem we have

`x^(6)-27`

we know that

`x^(6)=(x^(2))^(3)`

and

`27=(3)^(3)`

Let

`a=x^(2)`

`b=3`

substitute

`(x^(2))^(3)-(3)^(3)=(x^(2)-3)(x^(4)+3x^(2)+9)`