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

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

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

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Cancel

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

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

Cancel

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

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

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\frac{( a - x ) ^{4}}{4}

4 (3 cos (t) + 1) - (3 sin (t) + 3)^{2} sin (3 cos (t) + 1)

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