# How do you factor ab - a^4b?

##### 1 Answer
Apr 13, 2015

$a b - {a}^{4} b$

$a b$ is common to both the terms here. So the expression can be written as

$a b \cdot \left(1 - {a}^{3}\right)$

$= a b \cdot \left({1}^{3} - {a}^{3}\right)$

We know that color(blue)(x^3 - y^3 = (x - y)*(z^2 + xy + y ^2)

$= a b \cdot \left(1 - a\right) \left({1}^{2} + \left(1 \cdot a\right) + {a}^{2}\right)$

$= a b \cdot \left(1 - a\right) \left({1}^{2} + \left(1 \cdot a\right) + {a}^{2}\right)$

$= a b \cdot \left(1 - a\right) \left(1 + a + {a}^{2}\right)$

As none of the factors can be factorised further, we can say that  color(green)(ab*(1 - a)(1+a+a^2) is the final factorised form of $a b - {a}^{4} b$