How do you factor #x^3y^3 + z^3#?

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Answer 1 · 2015-07-22T07:39:48

Use sum of cubes identity to find:

#x^3y^3+z^3 = (xy+z)(x^2y^2-xyz+z^2)#

Use the sum of cubes identity:

#a^3+b^3=(a+b)(a^2-ab+b^2)#

with #a=xy# and #b=z# as follows:

#x^3y^3+z^3#

#=(xy)^3+z^3#

#=((xy)+z)((xy)^2-(xy)z+z^2)#

#=(xy+z)(x^2y^2-xyz+z^2)#