# How do you factor x^2y^2 - 17xy^2 + 72y^2?

May 24, 2015

Notice that all of the terms are multiples of ${y}^{2}$.

Also notice that $72 = 8 \times 9$, while $17 = 8 + 9$.

So:

${x}^{2} {y}^{2} - 17 x {y}^{2} + 72 {y}^{2}$

$= {y}^{2} \left({x}^{2} - 17 x + 72\right)$

$= {y}^{2} \left(x - 8\right) \left(x - 9\right)$