Question

Factor completely.

x^6 − 27

Answer 1

Answer:

$(x^{2}-3)(x^{4}+3x^{2}+9)$

Step-by-step 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

$(x^{2})^{3}-(3)^{3}=(x^{2}-3)(x^{4}+3x^{2}+9)$