What is (a^3-b^3)/(a-b) ?

The solution to (a^3-b^3)/(a-b) is a^2+ab+b^2

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simplify (a^3-b^3)/(a-b)

simplify

\frac{a ^{3} - b ^{3}}{a - b}

a^{2} + ab + b^{2}

Solution steps

\frac{a ^{3} - b ^{3}}{a - b}

Apply Difference of Cubes Formula:

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

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

= \frac{( a - b ) ( a ^{2} + ab + b ^{2} )}{a - b}

Cancel the common factor:

a - b

= a^{2} + ab + b^{2}

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