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

The solution to (x^3-a^3)/(x-a) is x^2+xa+a^2

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

simplify

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

x^{2} + x a + a^{2}

Solution steps

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

Apply Difference of Cubes Formula:

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

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

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

Cancel the common factor:

x - a

= x^{2} + x a + a^{2}

x^{4} x^{5}

2 (3 x + 4) - 3 (x - 2)

\frac{( 12 x ^{2} + 29 x + 15 )}{( 4 x + 3 )}

\frac{3}{5} \times \frac{2}{3}

2 x - 5 x^{2}