What is expand ((4-r^2)^2)/2 ?

The solution to expand ((4-r^2)^2)/2 is (r^4)/2-4r^2+8

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expand ((4-r^2)^2)/2

expand

\frac{( 4 - r ^{2} ) ^{2}}{2}

\frac{r ^{4}}{2} - 4 r^{2} + 8

Solution steps

\frac{( 4 - r ^{2} ) ^{2}}{2}

(4 - r^{2})^{2} = 16 - 8 r^{2} + r^{4}

= \frac{16 - 8 r ^{2} + r ^{4}}{2}

Apply the fraction rule:

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

\frac{16 - 8 r ^{2} + r ^{4}}{2} = \frac{16}{2} - \frac{8 r ^{2}}{2} + \frac{r ^{4}}{2}

= \frac{16}{2} - \frac{8 r ^{2}}{2} + \frac{r ^{4}}{2}

Divide the numbers:

\frac{16}{2} = 8

= 8 - \frac{8 r ^{2}}{2} + \frac{r ^{4}}{2}

Divide the numbers:

\frac{8}{2} = 4

= 8 - 4 r^{2} + \frac{r ^{4}}{2}

Rewrite in standard form

= \frac{r ^{4}}{2} - 4 r^{2} + 8

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What is expand ((4-r^2)^2)/2 ?
The solution to expand ((4-r^2)^2)/2 is (r^4)/2-4r^2+8