Answer
3(r$^2$+4)(r+2)(r-2)
Work Step by Step
3r$^2$-48
3(r$^4$-16)
Inside the parentheses is a difference of squares. If a represents the square root of the first term and b is the square root of the second term, then the factorization is (a+b)(a-b).
$\sqrt {r^4}$=r$^2$ and
$\sqrt {16}$=4. So the factorization is
3(r$^2$+4)(r$^2$-4).
Inside the second set of parentheses is yet another difference of squares, it is factored the same way.
$\sqrt {r^2}$=r and
$\sqrt {4}$=2. So the factorization is
3(r$^2$+4)(r+2)(r-2).
