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

The solution to (a+b)^3-(a-b)^3 is 6a^2b+2b^3

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

simplify

(a + b)^{3} - (a - b)^{3}

6 a^{2} b + 2 b^{3}

Solution steps

(a + b)^{3} - (a - b)^{3}

Expand

(a + b)^{3} : a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

Expand

- (a - b)^{3} : - a^{3} + 3 a^{2} b - 3 a b^{2} + b^{3}

= a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} - a^{3} + 3 a^{2} b - 3 a b^{2} + b^{3}

Group like terms

= a^{3} - a^{3} + 3 a^{2} b + 3 a^{2} b + 3 a b^{2} - 3 a b^{2} + b^{3} + b^{3}

Add similar elements:

a^{3} - a^{3} = 0

= 3 a^{2} b + 3 a^{2} b + 3 a b^{2} - 3 a b^{2} + b^{3} + b^{3}

Add similar elements:

3 a^{2} b + 3 a^{2} b = 6 a^{2} b

= 6 a^{2} b + 3 a b^{2} - 3 a b^{2} + b^{3} + b^{3}

Add similar elements:

3 a b^{2} - 3 a b^{2} = 0

= 6 a^{2} b + b^{3} + b^{3}

Add similar elements:

b^{3} + b^{3} = 2 b^{3}

= 6 a^{2} b + 2 b^{3}

\frac{x ^{p^{2}}}{x ^{q^{2}}}

\frac{18}{- 2}

125 t^{3} + d^{3}

\frac{18}{28}

\frac{15}{11} \div \frac{4}{5}