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

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Answer 1 · 2015-04-13T10:27:38

$ab - a^4b$

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

$ab*(1 - a^3)$

$= ab*(1^3 - a^3)$

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

$= ab*(1 - a)(1^2+(1*a)+a^2)$

$= ab*(1 - a)(1+a+a^2)$

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 $ab - a^4b$

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