What is expand ((12-x)^3)/3 ?

The solution to expand ((12-x)^3)/3 is -(x^3)/3+12x^2-144x+576

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expand ((12-x)^3)/3

expand

\frac{( 12 - x ) ^{3}}{3}

- \frac{x ^{3}}{3} + 12 x^{2} - 144 x + 576

Solution steps

\frac{( 12 - x ) ^{3}}{3}

(12 - x)^{3} = 1728 - 432 x + 36 x^{2} - x^{3}

= \frac{1728 - 432 x + 36 x ^{2} - x ^{3}}{3}

Apply the fraction rule:

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

\frac{1728 - 432 x + 36 x ^{2} - x ^{3}}{3} = \frac{1728}{3} - \frac{432 x}{3} + \frac{36 x ^{2}}{3} - \frac{x ^{3}}{3}

= \frac{1728}{3} - \frac{432 x}{3} + \frac{36 x ^{2}}{3} - \frac{x ^{3}}{3}

Divide the numbers:

\frac{1728}{3} = 576

= 576 - \frac{432 x}{3} + \frac{36 x ^{2}}{3} - \frac{x ^{3}}{3}

Divide the numbers:

\frac{432}{3} = 144

= 576 - 144 x + \frac{36 x ^{2}}{3} - \frac{x ^{3}}{3}

Divide the numbers:

\frac{36}{3} = 12

= 576 - 144 x + 12 x^{2} - \frac{x ^{3}}{3}

Rewrite in standard form

= - \frac{x ^{3}}{3} + 12 x^{2} - 144 x + 576

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What is expand ((12-x)^3)/3 ?
The solution to expand ((12-x)^3)/3 is -(x^3)/3+12x^2-144x+576