Question

Select the expression that is equivalent to the given polynomial.

Answer 1

Observe that $16r^4$ is the square of $4r^2$, and 625 is the square of 25.

So, your expression is a difference of squares, and as such we can rewrite it as

$16r^4-625=(4r^2+25)(4r^2-25)$

Now again, $4r^2$ is the square of $2r$, and 25 is the square of 5. So, we have a sum and a difference of squares.

But if we think of 25 as $-(5i)^2$, we have again the difference of two squares, so we have

$4r^2+25=(2r+5i)(2r-5i)$

$4r^2-25=(2r+5)(2r-5)$