What is expand (r(2+r))/2 ?

The solution to expand (r(2+r))/2 is (r^2)/2+r

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expand (r(2+r))/2

expand

\frac{r ( 2 + r )}{2}

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

Solution steps

\frac{r ( 2 + r )}{2}

Expand

r (2 + r) : 2 r + r^{2}

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{2}{2} = 1

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

Rewrite in standard form

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

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