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

1 Answer

May 28, 2015

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)#

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