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

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

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

expand

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

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

Solution steps

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

Expand

(2 n + 1) (n + 1) n : 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}

2 (2 + 2)

\frac{1}{( s + 1 ) ( s ^{2} + 4 s + 25 )}

(- 4 e^{x} + 8 e) (- 2 e^{x} + e + 2)

\frac{1}{5 ( 35 - 10 x )}

\frac{k ( s + 5 )}{s ( s + 1 ) ( s + 10 )}

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