What is ((x-y)^3+z^3)/((x-y)+z) ?

The solution to ((x-y)^3+z^3)/((x-y)+z) is (x-y)^2-z(x-y)+z^2

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simplify ((x-y)^3+z^3)/((x-y)+z)

simplify

\frac{( x - y ) ^{3} + z ^{3}}{( x - y ) + z}

(x - y)^{2} - z (x - y) + z^{2}

Solution steps

\frac{( x - y ) ^{3} + z ^{3}}{( x - y ) + z}

Remove parentheses:

(a) = a

= \frac{( x - y ) ^{3} + z ^{3}}{x - y + z}

Factor

(x - y)^{3} + z^{3} : (x - y + z) ((x - y)^{2} - z (x - y) + z^{2})

= \frac{( x - y + z ) ( ( x - y ) ^{2} - z ( x - y ) + z ^{2} )}{x - y + z}

Cancel the common factor:

x - y + z

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

- 2 x^{3} + 2 x^{2} + 12 x

12 x + 18 y - 24 z

\frac{1}{6 2}

\frac{4}{3} π 9^{3}

\frac{9}{16} - \frac{3}{16}

What is ((x-y)^3+z^3)/((x-y)+z) ?
The solution to ((x-y)^3+z^3)/((x-y)+z) is (x-y)^2-z(x-y)+z^2