How do you factor #x^(3a) y^a - y^(3a) x^a#?

1 Answer
Alan P.
Jun 3, 2015

Decompose the terms of #x^(3a)y^a - y^(3a)x^a#
as
#= x^(2a)*x^a*y^a - x^a*y^a*y^(2a)#
#color(white)("XXXX")#now we can see an obvious common term #x^ay^a #=(x^ay^a)(x^(2a)-y^(2a))#

#=(x^ay^a)((x^a)^2 -(y^a)^2)#
#color(white)("XXXX")#the second term is the difference of squares, so
#=(x^ay^a)((x^a+y^a)(x^a-y^a)#

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