Question

How do you factor `x^6-4`?

Answer 1

`x^6 -4 = (x^3 +2)(x^3-2)`

Explanation:

Both terms are perfect squares and they are being subtracted.

We have the difference of squares which is factored as :

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

`x^6 -4 = (x^3 +2)(x^3-2)`

Note that `6` is not a square, but a base with an even index is a square.

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