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

The solution to expand (r*(4r^2sin^2(θ)-r^4))/2 is 2r^3sin^2(θ)-(r^5)/2

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expand (r*(4r^2sin^2(θ)-r^4))/2

expand

\frac{r \cdot ( 4 r ^{2} sin ^{2} ( θ ) - r ^{4} )}{2}

2 r^{3} sin^{2} (θ) - \frac{r ^{5}}{2}

Solution steps

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

Expand

r (4 r^{2} sin^{2} (θ) - r^{4}) : 4 r^{3} sin^{2} (θ) - r^{5}

= \frac{4 r ^{3} sin ^{2} ( θ ) - r ^{5}}{2}

Apply the fraction rule:

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

\frac{4 r ^{3} sin ^{2} ( θ ) - r ^{5}}{2} = \frac{4 r ^{3} sin ^{2} ( θ )}{2} - \frac{r ^{5}}{2}

= \frac{4 r ^{3} sin ^{2} ( θ )}{2} - \frac{r ^{5}}{2}

Divide the numbers:

\frac{4}{2} = 2

= 2 r^{3} sin^{2} (θ) - \frac{r ^{5}}{2}

5 (7 - x = 31 - x)

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What is expand (r*(4r^2sin^2(θ)-r^4))/2 ?
The solution to expand (r*(4r^2sin^2(θ)-r^4))/2 is 2r^3sin^2(θ)-(r^5)/2