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

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

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

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Cancel

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

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

Cancel

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

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

\frac{- x ^{2} + 1}{( x ^{2} - x + 1 ) ^{2}}

(x - 2 + 3) (x - 2 - 3)

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

\frac{k ^{2} ( k + 1 ) ^{2}}{4}

(x + 3 - 2) (x + 3 + 2)

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