展开 ((r+s)((r+s)-1))/2

解答

展开

\frac{( r + s ) ( ( r + s ) - 1 )}{2}

rs + \frac{r ^{2}}{2} - \frac{r}{2} + \frac{s ^{2}}{2} - \frac{s}{2}

求解步骤

\frac{( r + s ) ( ( r + s ) - 1 )}{2}

去除括号:

(a) = a

= \frac{( r + s ) ( r + s - 1 )}{2}

乘开

(r + s) (r + s - 1) : 2 rs + r^{2} - r + s^{2} - s

= \frac{2 rs + r ^{2} - r + s ^{2} - s}{2}

使用分式法则:

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

\frac{2 rs + r ^{2} - r + s ^{2} - s}{2} = \frac{2 rs}{2} + \frac{r ^{2}}{2} - \frac{r}{2} + \frac{s ^{2}}{2} - \frac{s}{2}

= \frac{2 rs}{2} + \frac{r ^{2}}{2} - \frac{r}{2} + \frac{s ^{2}}{2} - \frac{s}{2}

数字相除:

\frac{2}{2} = 1

= rs + \frac{r ^{2}}{2} - \frac{r}{2} + \frac{s ^{2}}{2} - \frac{s}{2}

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