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

The solution to expand (x(2-x)^2)/2 is (x^3)/2-2x^2+2x

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

expand

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

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

Solution steps

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

(2 - x)^{2} = 4 - 4 x + x^{2}

= \frac{x ( x ^{2} - 4 x + 4 )}{2}

Expand

x (4 - 4 x + x^{2}) : 4 x - 4 x^{2} + x^{3}

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{4}{2} = 2

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

Rewrite in standard form

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

(1 - 4 (x))^{2} - (x)

(x + \frac{3}{x})^{9}

\frac{( x - 1 ) ^{2}}{4}

\frac{\partial}{\partial x} ((z) (e^{z} - x yz))

(8 + 6 i)^{4}

What is expand (x(2-x)^2)/2 ?
The solution to expand (x(2-x)^2)/2 is (x^3)/2-2x^2+2x