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

The solution to expand (x(2-x)^4)/4 is (x^5)/4-2x^4+6x^3-8x^2+4x

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

expand

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

\frac{x ^{5}}{4} - 2 x^{4} + 6 x^{3} - 8 x^{2} + 4 x

Solution steps

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

(2 - x)^{4} = 16 - 32 x + 24 x^{2} - 8 x^{3} + x^{4}

= \frac{x ( x ^{4} - 8 x ^{3} + 24 x ^{2} - 32 x + 16 )}{4}

Expand

x (16 - 32 x + 24 x^{2} - 8 x^{3} + x^{4}) : 16 x - 32 x^{2} + 24 x^{3} - 8 x^{4} + x^{5}

= \frac{16 x - 32 x ^{2} + 24 x ^{3} - 8 x ^{4} + x ^{5}}{4}

Apply the fraction rule:

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

\frac{16 x - 32 x ^{2} + 24 x ^{3} - 8 x ^{4} + x ^{5}}{4} = \frac{16 x}{4} - \frac{32 x ^{2}}{4} + \frac{24 x ^{3}}{4} - \frac{8 x ^{4}}{4} + \frac{x ^{5}}{4}

= \frac{16 x}{4} - \frac{32 x ^{2}}{4} + \frac{24 x ^{3}}{4} - \frac{8 x ^{4}}{4} + \frac{x ^{5}}{4}

\frac{16 x}{4} = 4 x

\frac{32 x ^{2}}{4} = 8 x^{2}

\frac{24 x ^{3}}{4} = 6 x^{3}

\frac{8 x ^{4}}{4} = 2 x^{4}

= 4 x - 8 x^{2} + 6 x^{3} - 2 x^{4} + \frac{x ^{5}}{4}

Rewrite in standard form

= \frac{x ^{5}}{4} - 2 x^{4} + 6 x^{3} - 8 x^{2} + 4 x

(x + sin (x) - 1)^{2}

(2 x) (3 x + 1 + 1)

(- \frac{1}{2} e^{t} + \frac{3}{2} e^{- t}) \cdot (4 e^{t} + e^{- t})

\frac{3}{( s + 1 ) ( s + 2 ) ^{2}}

sin (\frac{( 2 x - 1 ) π}{2})

What is expand (x(2-x)^4)/4 ?
The solution to expand (x(2-x)^4)/4 is (x^5)/4-2x^4+6x^3-8x^2+4x