What is expand (2x(8-x)^3)/3 ?

The solution to expand (2x(8-x)^3)/3 is -(2x^4)/3+16x^3-128x^2+(1024x)/3

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expand (2x(8-x)^3)/3

expand

\frac{2 x ( 8 - x ) ^{3}}{3}

- \frac{2 x ^{4}}{3} + 16 x^{3} - 128 x^{2} + \frac{1024 x}{3}

Solution steps

\frac{2 x ( 8 - x ) ^{3}}{3}

(8 - x)^{3} = 512 - 192 x + 24 x^{2} - x^{3}

= \frac{2 x ( - x ^{3} + 24 x ^{2} - 192 x + 512 )}{3}

Expand

2 x (512 - 192 x + 24 x^{2} - x^{3}) : 1024 x - 384 x^{2} + 48 x^{3} - 2 x^{4}

= \frac{1024 x - 384 x ^{2} + 48 x ^{3} - 2 x ^{4}}{3}

Apply the fraction rule:

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

\frac{1024 x - 384 x ^{2} + 48 x ^{3} - 2 x ^{4}}{3} = \frac{1024 x}{3} - \frac{384 x ^{2}}{3} + \frac{48 x ^{3}}{3} - \frac{2 x ^{4}}{3}

= \frac{1024 x}{3} - \frac{384 x ^{2}}{3} + \frac{48 x ^{3}}{3} - \frac{2 x ^{4}}{3}

Divide the numbers:

\frac{384}{3} = 128

= \frac{1024 x}{3} - 128 x^{2} + \frac{48 x ^{3}}{3} - \frac{2 x ^{4}}{3}

Divide the numbers:

\frac{48}{3} = 16

= \frac{1024 x}{3} - 128 x^{2} + 16 x^{3} - \frac{2 x ^{4}}{3}

Rewrite in standard form

= - \frac{2 x ^{4}}{3} + 16 x^{3} - 128 x^{2} + \frac{1024 x}{3}

\frac{4 x ^{3}}{( x ^{2} - 1 ) ^{2}}

\frac{18 x ^{3}}{( z - 0.5 ) ( z - 0.8 ) ^{2}}

x (x - \frac{π}{2})

(k + 1) \cdot (k + 1)!

\frac{x}{2 ( x ^{2} + 1 )}

What is expand (2x(8-x)^3)/3 ?
The solution to expand (2x(8-x)^3)/3 is -(2x^4)/3+16x^3-128x^2+(1024x)/3