What is expand (x(16-x)^2)/(64) ?

The solution to expand (x(16-x)^2)/(64) is (x^3}{64}-\frac{x^2)/2+4x

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expand (x(16-x)^2)/(64)

expand

\frac{x ( 16 - x ) ^{2}}{64}

\frac{x ^{3}}{64} - \frac{x ^{2}}{2} + 4 x

Solution steps

\frac{x ( 16 - x ) ^{2}}{64}

(16 - x)^{2} = 256 - 32 x + x^{2}

= \frac{x ( x ^{2} - 32 x + 256 )}{64}

Expand

x (256 - 32 x + x^{2}) : 256 x - 32 x^{2} + x^{3}

= \frac{256 x - 32 x ^{2} + x ^{3}}{64}

Apply the fraction rule:

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

\frac{256 x - 32 x ^{2} + x ^{3}}{64} = \frac{256 x}{64} - \frac{32 x ^{2}}{64} + \frac{x ^{3}}{64}

= \frac{256 x}{64} - \frac{32 x ^{2}}{64} + \frac{x ^{3}}{64}

Divide the numbers:

\frac{256}{64} = 4

= 4 x - \frac{32 x ^{2}}{64} + \frac{x ^{3}}{64}

Cancel

\frac{32 x ^{2}}{64} : \frac{x ^{2}}{2}

= 4 x - \frac{x ^{2}}{2} + \frac{x ^{3}}{64}

Rewrite in standard form

= \frac{x ^{3}}{64} - \frac{x ^{2}}{2} + 4 x

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What is expand (x(16-x)^2)/(64) ?
The solution to expand (x(16-x)^2)/(64) is (x^3}{64}-\frac{x^2)/2+4x