# How do you factor p^2q^2-12pq+36?

Apr 14, 2017

${p}^{2} {q}^{2} - 12 p q + 36 = \left(p q - 6\right) \left(p q - 6\right)$

#### Explanation:

Given: ${p}^{2} {q}^{2} - 12 p q + 36$

This can be factored directly when we treat $p q$ as a single variable that can be broken down later into two terms when their relationship is defined. To answer the question, solve for $p q$.

Looking at the expression, we see there will be two sets of brackets because of the ${p}^{2} {q}^{2}$ and there will be two $-$ signs due to the $+ 36$ and the $- 12$.

${p}^{2} {q}^{2} - 12 p q + 36 = \left(p q - 6\right) \left(p q - 6\right)$