Question

Help please #12 Solve using factoring

Answer 1

(R-2)x(r+2) that what I think it is

Answer 2

You have to use the sum/difference formula

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

In your case, $r^2-4$ is a difference of squares, so it can be factored with the sum and difference of the roots:

$r^2-4 = (r+2)(r-2)$

So, we have

$r^2-4 = 0 \iff (r+2)(r-2) = 0$

A multiplication is zero if and only if one of the factors is zero, so we have

$(r+2)(r-2) = 0 \iff r+2=0\ \lor\ r-2=0 \iff r=-2\ \lor\ r=2$