Answer
$x^{2}$$y$ - 16$y$ + 32 - 2$x^{2}$
= ($x^{2}$$y$ - 16$y$) - (2$x^{2}$ - 32)
= $y$($x^{2}$ - 16) - 2($x^{2}$ - 16)
= ($x^{2}$ - 16)($y$ - 2)
= ($x$ + 4)($x$ - 4)($y$ - 2)
Work Step by Step
This polynomial must be factored. First, we start by grouping the four terms into groups of two, as seen in step 2. We factor out the y in the first group and the 2 in the second group in step 3. In step 4, we can simplify the first group by factoring '(x^2-16)' into '(x+4)(x-4)' by using the formula 'A^2 - B^2 = (A+B)(A-B)'. Thus, the final answer is (x+4)(x-4)(y-2).
