How do you factor the expression $x^{3} y^{3} + z^{3}$ $x^3y^3 + z^3$ ?

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Answer 1 · 2016-02-07T17:37:54

Answer is: $(x y + z) (x^{2} y^{2} - x y z + z^{2})$ $(xy + z)(x^2 y^2 - xyz + z^2)$ .

You can check by multiplying it out.

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

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

$a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ $a^3 + b^3 = (a+b)(a^2-ab+b^2)$

So we use $a = x y$ $a = xy$ and $b = z$ $b = z$ to get:

$x^{3} y^{3} + z^{3} = {(x y)}^{3} + z^{3}$ $x^3 y^3 + z^3 = (xy)^3 + z^3$

$= ((x y) + z) ({(x y)}^{2} - (x y) z + z^{2})$ $= ((xy) +z)((xy)^2-(xy)z+z^2)$

$= (x y + z) (x^{2} y^{2} - x y z + z^{2})$ $=(xy + z)(x^2 y^2 - xyz + z^2)$ .

check by multiplying it out to make sure!

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How do you factor the expression x^3y^3 + z^3x3y3+z3x^3y^3 + z^3?