What is expand (k(k+1)(k+2))/3 ?

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

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expand (k(k+1)(k+2))/3

expand

\frac{k ( k + 1 ) ( k + 2 )}{3}

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

Solution steps

\frac{k ( k + 1 ) ( k + 2 )}{3}

Expand

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{3}{3} = 1

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

\frac{( s + 3 ) ( s + 4 )}{( s + 2 ) ( s + 5 ) ( s + 6 )}

2 (\frac{x}{x + 3} + \frac{5}{x})

\frac{- 11 s + 188}{1780 ( s ^{2} - 8 s + 80 )}

\frac{( 1 - x ) ( 4 - x )}{x}

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

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