# How do you factor (9a+3b-c)^2-(3a-2b+c)^2 ?

Apr 22, 2018

${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

#### Explanation:

Using that will give you $\left(6 a + 5 b - 2 c\right) \left(12 a + b\right)$

Apr 22, 2018

Using the difference of two squares, we get $\left(12 a + b\right) \left(6 a + 5 b - 2 c\right)$.

#### Explanation:

In general the difference of two squares factors easily:

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

${\left(9 a + 3 b - c\right)}^{2} - {\left(3 a - 2 b + c\right)}^{2}$

$= \left(9 a + 3 b - c + 3 a - 2 b + c\right) \left(9 a + 3 b - c - 3 a + 2 b - c\right)$

$= \left(9 a + 3 b - c + 3 a - 2 b + c\right) \left(9 a + 3 b - c - 3 a + 2 b - c\right)$

$= \left(12 a + b\right) \left(6 a + 5 b - 2 c\right)$