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

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Answer 1 · 2015-05-28T22:07:42

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 $A^3-B^3 = (A-B)(A^2+AB+B^2)$

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