Question

How do you factor completely `2x^2 - 32`?

Answer 1

`2x^2-32=2(x-4)(x+4)`

Explanation:

Separate out the common scalar factor `2` then use the difference of squares identity:

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

with `a=x` and `b=4` as follows:

`2x^2-32=2(x^2-16)=2(x^2-4^2)=2(x-4)(x+4)`