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#