What is expand (n^2-n)/2*(n+2)/3 ?

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

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expand (n^2-n)/2*(n+2)/3

expand

\frac{n ^{2} - n}{2} \cdot \frac{n + 2}{3}

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

Solution steps

\frac{n ^{2} - n}{2} \cdot \frac{n + 2}{3}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{( n ^{2} - n ) ( n + 2 )}{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{( n ^{2} - n ) ( n + 2 )}{6}

Expand

(n^{2} - n) (n + 2) : n^{3} + n^{2} - 2 n

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

Apply the fraction rule:

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

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

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

Cancel

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

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

1 + (x^{2} + 1)

\frac{6}{( x + h ) ^{2}}

(x^{2} + y^{2} + 1) d x - 2 x y d y

\frac{2 ( 5 x ^{2} - 3 x + 2 )}{x - 4}

\frac{( n + 1 )}{π ( n + 2 )}

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