# How do you factor 15a^2b^2-20ab^2+10ab^3?

Nov 16, 2015

$15 {a}^{2} {b}^{2} - 20 a {b}^{2} + 10 a {b}^{3} = 5 a {b}^{2} \left(3 a - 4 + 2 b\right)$
Looking at each of the terms, we can see that $15$, $20$, and $10$ have the greatest common divisor of $5$. Additionally, the highest shared power of $a$ between terms is ${a}^{1}$ and the highest shared power of $b$ is ${b}^{2}$.
Thus we know that they all have a common factor of $5 a {b}^{2}$. Factoring this out gives us
$15 {a}^{2} {b}^{2} - 20 a {b}^{2} + 10 a {b}^{3} = 5 a {b}^{2} \left(3 a - 4 + 2 b\right)$