# How do you factor (x-3)^2(2x+1)^3+(x-3)^3(2x+1)^2?

Feb 7, 2017

${\left(x - 3\right)}^{2} {\left(2 x + 1\right)}^{3} + {\left(x - 3\right)}^{3} {\left(2 x + 1\right)}^{2} = {\left(x - 3\right)}^{2} {\left(2 x + 1\right)}^{2} \left(3 x - 2\right)$

#### Explanation:

Both of the two expressions are divisible by ${\left(x - 3\right)}^{2} {\left(2 x + 1\right)}^{2}$, so separate that out, then resolve the remaining terms:

${\left(x - 3\right)}^{2} {\left(2 x + 1\right)}^{3} + {\left(x - 3\right)}^{3} {\left(2 x + 1\right)}^{2}$

$= {\left(x - 3\right)}^{2} {\left(2 x + 1\right)}^{2} \left(\left(2 x + 1\right) + \left(x - 3\right)\right)$

$= {\left(x - 3\right)}^{2} {\left(2 x + 1\right)}^{2} \left(3 x - 2\right)$