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

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

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

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

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

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

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

Cancel

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

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

Cancel

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

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

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