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

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

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

simplify

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

x^{2} - x y + y^{2}

Solution steps

\frac{x ^{3} + y ^{3}}{x + y}

Apply Sum of Cubes Formula:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

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

Cancel the common factor:

x + y

= x^{2} - x y + y^{2}

- 8 \div \frac{1}{4}

\frac{14}{88}

2 + 1

\frac{14}{13}