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

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

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

simplify

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

\frac{b ^{2} + ba + a ^{2}}{3}

Solution steps

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

Apply Difference of Cubes Formula:

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

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

= \frac{( b - a ) ( b ^{2} + ba + a ^{2} )}{3 ( b - a )}

Cancel the common factor:

b - a

= \frac{b ^{2} + ba + a ^{2}}{3}

(3 x - y)^{5}

x^{3} - 6 x + 9

x^{3} - 6 x + 5

25 \cdot 25 \cdot 25

\frac{2}{5} \times \frac{7}{2}

What is (b^3-a^3)/(3(b-a)) ?
The solution to (b^3-a^3)/(3(b-a)) is (b^2+ba+a^2)/3