What is expand ((8-x)^5)/(40) ?

The solution to expand ((8-x)^5)/(40) is -(x^5)/(40)+x^4-16x^3+128x^2-512x+4096/5

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expand ((8-x)^5)/(40)

expand

\frac{( 8 - x ) ^{5}}{40}

- \frac{x ^{5}}{40} + x^{4} - 16 x^{3} + 128 x^{2} - 512 x + \frac{4096}{5}

Solution steps

\frac{( 8 - x ) ^{5}}{40}

(8 - x)^{5} = 32768 - 20480 x + 5120 x^{2} - 640 x^{3} + 40 x^{4} - x^{5}

= \frac{32768 - 20480 x + 5120 x ^{2} - 640 x ^{3} + 40 x ^{4} - x ^{5}}{40}

Apply the fraction rule:

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

\frac{32768 - 20480 x + 5120 x ^{2} - 640 x ^{3} + 40 x ^{4} - x ^{5}}{40} = \frac{32768}{40} - \frac{20480 x}{40} + \frac{5120 x ^{2}}{40} - \frac{640 x ^{3}}{40} + \frac{40 x ^{4}}{40} - \frac{x ^{5}}{40}

= \frac{32768}{40} - \frac{20480 x}{40} + \frac{5120 x ^{2}}{40} - \frac{640 x ^{3}}{40} + \frac{40 x ^{4}}{40} - \frac{x ^{5}}{40}

\frac{32768}{40} = \frac{4096}{5}

\frac{20480 x}{40} = 512 x

\frac{5120 x ^{2}}{40} = 128 x^{2}

\frac{640 x ^{3}}{40} = 16 x^{3}

\frac{40 x ^{4}}{40} = x^{4}

= \frac{4096}{5} - 512 x + 128 x^{2} - 16 x^{3} + x^{4} - \frac{x ^{5}}{40}

Rewrite in standard form

= - \frac{x ^{5}}{40} + x^{4} - 16 x^{3} + 128 x^{2} - 512 x + \frac{4096}{5}

2 e^{- x^{2} - y^{2}} x - 2 e^{- x^{2} - y^{2}} x (x^{2} + 2 y^{2})

\frac{a + b}{( a + b ) ^{2} - 1}

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

\frac{- 3 s - 5}{2 ( s + 1 ) ( s + 4 ) ( s + 3 )}

\frac{3}{x + 5} + \frac{7}{x - 2}

What is expand ((8-x)^5)/(40) ?
The solution to expand ((8-x)^5)/(40) is -(x^5)/(40)+x^4-16x^3+128x^2-512x+4096/5