Question

How do you factor completely `2x^2-8`?

Answer 1

`color(brown)(2 * (x+ 2) * (x - 2)`

Explanation:

`2x^2 - 8 = 2x^2 - (2*2*2) = 2x^2 - (2 * 4)`

`x@^2 - 4` is in the form `a^2 - b^2 = (a+b) * (a - b)`

`:. => 2 * (x^2 - 4) = 2 * (x+ 2) * (x - 2)`

Answer 2

`2(x-2)(x+2)`

Explanation:

`"take out a "color(blue)"common factor of 2"`

`rArr2(x^2-4)`

`x^2-4larrcolor(blue)"is a difference of squares"`

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

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

`rArr2x^2-8=2(x-2)(x+2)`