# How do you factor (4y-2)^2-(3y)^2?

Jun 27, 2015

This is a difference of squares:

${\left(4 y - 2\right)}^{2} - {\left(3 y\right)}^{2}$

$= \left(\left(4 y - 2\right) - 3 y\right) \left(\left(4 y - 2\right) + 3 y\right)$

$= \left(y - 2\right) \left(7 y - 2\right)$

#### Explanation:

For any $a$ and $b$, we have ${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

Let $a = 4 y - 2$ and $b = 3 y$

Then

${\left(4 y - 2\right)}^{2} - {\left(3 y\right)}^{2}$

$= {a}^{2} - {b}^{2}$

$= \left(a - b\right) \left(a + b\right)$

$= \left(\left(4 y - 2\right) - 3 y\right) \left(\left(4 y - 2\right) + 3 y\right)$

$= \left(y - 2\right) \left(7 y - 2\right)$