Question

How do you factor `a^3b^3 - 8x^6y^9`?

Answer 1

This is a difference of cubes:

`a^3b^3 - 8x^6y^9`

`=(ab)^3 - (2x^2y^3)^3`

`=((ab)-(2x^2y^3))((ab)^2+(ab)(2x^2y^3)+(2x^2y^3)^2)`

`=(ab-2x^2y^3)(a^2b^2+2abx^2y^3+4x^4y^6)`

using the identity `A^3-B^3 = (A-B)(A^2+AB+B^2)`