What is expand (N(N+1)(2N+1))/6 ?

The solution to expand (N(N+1)(2N+1))/6 is (N^3)/3+(N^2)/2+N/6

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expand (N(N+1)(2N+1))/6

expand

\frac{N ( N + 1 ) ( 2 N + 1 )}{6}

\frac{N ^{3}}{3} + \frac{N ^{2}}{2} + \frac{N}{6}

Solution steps

\frac{N ( N + 1 ) ( 2 N + 1 )}{6}

Expand

N (N + 1) (2 N + 1) : 2 N^{3} + 3 N^{2} + N

= \frac{2 N ^{3} + 3 N ^{2} + N}{6}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{2 N ^{3} + 3 N ^{2} + N}{6} = \frac{2 N ^{3}}{6} + \frac{3 N ^{2}}{6} + \frac{N}{6}

= \frac{2 N ^{3}}{6} + \frac{3 N ^{2}}{6} + \frac{N}{6}

Cancel

\frac{2 N ^{3}}{6} : \frac{N ^{3}}{3}

= \frac{N ^{3}}{3} + \frac{3 N ^{2}}{6} + \frac{N}{6}

Cancel

\frac{3 N ^{2}}{6} : \frac{N ^{2}}{2}

= \frac{N ^{3}}{3} + \frac{N ^{2}}{2} + \frac{N}{6}

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What is expand (N(N+1)(2N+1))/6 ?
The solution to expand (N(N+1)(2N+1))/6 is (N^3)/3+(N^2)/2+N/6