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

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

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

expand

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

\frac{n ^{2}}{3} + \frac{n}{2} + \frac{1}{6}

Solution steps

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

Expand

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

= \frac{2 n ^{2} + 3 n + 1}{6}

Apply the fraction rule:

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

\frac{2 n ^{2} + 3 n + 1}{6} = \frac{2 n ^{2}}{6} + \frac{3 n}{6} + \frac{1}{6}

= \frac{2 n ^{2}}{6} + \frac{3 n}{6} + \frac{1}{6}

Cancel

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

= \frac{n ^{2}}{3} + \frac{3 n}{6} + \frac{1}{6}

Cancel

\frac{3 n}{6} : \frac{n}{2}

= \frac{n ^{2}}{3} + \frac{n}{2} + \frac{1}{6}

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