What is expand (2x(6-2x)^3)/3 ?

The solution to expand (2x(6-2x)^3)/3 is -(16x^4)/3+48x^3-144x^2+144x

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expand (2x(6-2x)^3)/3

expand

\frac{2 x ( 6 - 2 x ) ^{3}}{3}

- \frac{16 x ^{4}}{3} + 48 x^{3} - 144 x^{2} + 144 x

Solution steps

\frac{2 x ( 6 - 2 x ) ^{3}}{3}

(6 - 2 x)^{3} = 216 - 216 x + 72 x^{2} - 8 x^{3}

= \frac{2 x ( - 8 x ^{3} + 72 x ^{2} - 216 x + 216 )}{3}

Expand

2 x (216 - 216 x + 72 x^{2} - 8 x^{3}) : 432 x - 432 x^{2} + 144 x^{3} - 16 x^{4}

= \frac{432 x - 432 x ^{2} + 144 x ^{3} - 16 x ^{4}}{3}

Apply the fraction rule:

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

\frac{432 x - 432 x ^{2} + 144 x ^{3} - 16 x ^{4}}{3} = \frac{432 x}{3} - \frac{432 x ^{2}}{3} + \frac{144 x ^{3}}{3} - \frac{16 x ^{4}}{3}

= \frac{432 x}{3} - \frac{432 x ^{2}}{3} + \frac{144 x ^{3}}{3} - \frac{16 x ^{4}}{3}

Divide the numbers:

\frac{432}{3} = 144

= 144 x - 144 x^{2} + \frac{144 x ^{3}}{3} - \frac{16 x ^{4}}{3}

Divide the numbers:

\frac{144}{3} = 48

= 144 x - 144 x^{2} + 48 x^{3} - \frac{16 x ^{4}}{3}

Rewrite in standard form

= - \frac{16 x ^{4}}{3} + 48 x^{3} - 144 x^{2} + 144 x

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What is expand (2x(6-2x)^3)/3 ?
The solution to expand (2x(6-2x)^3)/3 is -(16x^4)/3+48x^3-144x^2+144x