Question

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

Answer 1

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)`