How do you factor #3x^4 y - 24xy^4#?

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1 Answer
Jim H
Apr 10, 2015

First remove the common factot (s). Then see whether you're finished.

#3x^4y-24xy^4 = 3xy (x^3-8 y^3)#

We're not finished because 8 is a cube, so #8y^3= (2y)^3# and we can factor the difference of cubes: #a^3-b^3 =(a-b)(a^2+ab+b^2)#

So we get
#3x^4y-24xy^4=3xy (x^3-8y^3)= 3xy (x-2y)(x^2+2xy+4y^2)#

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