What is expand ((n-r)((n-r)-1))/2 ?

The solution to expand ((n-r)((n-r)-1))/2 is -nr+(r^2)/2+r/2+(n^2)/2-n/2

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

expand

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

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

Solution steps

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

Remove parentheses:

(a) = a

= \frac{( n - r ) ( n - r - 1 )}{2}

Expand

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{2}{2} = 1

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

\frac{1}{2 ( s + 0.2 )}

(e^{- x} + x) (e^{- x} - x)

\frac{3 ^{7}}{3 ^{5}}

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

\frac{g ( 5 - t )}{2}

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