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 Difference 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}

- \frac{1}{x} \cdot \frac{1}{x}

(4 x^{3} - 7 y^{2})^{2}

7 \cdot 28

(- sin (x))^{2} + (cos (x))^{2}

- \frac{3}{2} \cdot (- \frac{2}{3})