How do you factor (a+b)^2-4b^2?

Jan 4, 2016

Use the difference of squares identity to find:

${\left(a + b\right)}^{2} - 4 {b}^{2} = \left(a - b\right) \left(a + 3 b\right)$

Explanation:

The difference of squares identity can be written:

${A}^{2} - {B}^{2} = \left(A - B\right) \left(A + B\right)$

Use this with $A = a + b$ and $B = 2 b$ as follows:

${\left(a + b\right)}^{2} - 4 {b}^{2}$

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

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

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