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

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Answer 1 · 2016-02-07T17:37:54

Answer is: #(xy + z)(x^2 y^2 - xyz + z^2)#.

You can check by multiplying it out.

Notice that each term is a perfect cube: #x^3 y^3 = (xy)^3#.

So we have a sum of cubes, and the factoring formula is:

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

So we use #a = xy# and #b = z# to get:

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

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

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

check by multiplying it out to make sure!

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