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Popular >

expand (n(n-1)^2)/2

Solution

expand

\frac{n ( n - 1 ) ^{2}}{2}

Solution

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

Solution steps

\frac{n ( n - 1 ) ^{2}}{2}

(n - 1)^{2} = n^{2} - 2 n + 1

= \frac{n ( n ^{2} - 2 n + 1 )}{2}

Expand

n (n^{2} - 2 n + 1) : n^{3} - 2 n^{2} + n

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{2}{2} = 1

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

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Frequently Asked Questions (FAQ)

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