What is expand (2(-8x^3+72x^2-216x+216))/(27) ?

The solution to expand (2(-8x^3+72x^2-216x+216))/(27) is -(16x^3}{27}+\frac{16x^2)/3-16x+16

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expand (2(-8x^3+72x^2-216x+216))/(27)

expand

\frac{2 ( - 8 x ^{3} + 72 x ^{2} - 216 x + 216 )}{27}

- \frac{16 x ^{3}}{27} + \frac{16 x ^{2}}{3} - 16 x + 16

Solution steps

\frac{2 ( - 8 x ^{3} + 72 x ^{2} - 216 x + 216 )}{27}

Expand

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

= \frac{- 16 x ^{3} + 144 x ^{2} - 432 x + 432}{27}

Apply the fraction rule:

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

\frac{- 16 x ^{3} + 144 x ^{2} - 432 x + 432}{27} = - \frac{16 x ^{3}}{27} + \frac{144 x ^{2}}{27} - \frac{432 x}{27} + \frac{432}{27}

= - \frac{16 x ^{3}}{27} + \frac{144 x ^{2}}{27} - \frac{432 x}{27} + \frac{432}{27}

Cancel

\frac{144 x ^{2}}{27} : \frac{16 x ^{2}}{3}

= - \frac{16 x ^{3}}{27} + \frac{16 x ^{2}}{3} - \frac{432 x}{27} + \frac{432}{27}

Divide the numbers:

\frac{432}{27} = 16

= - \frac{16 x ^{3}}{27} + \frac{16 x ^{2}}{3} - 16 x + 16

x e^{x} (x e^{x} - 1)

(3 e^{5 t} - 2 e^{4 t}) (15 e^{5 t} - 8 e^{4 t})

\frac{x ^{2} ( - \frac{x}{2} + 4 ) ^{4}}{32}

\frac{f ( x + h ) - 8 x + 2}{h}

What is expand (2(-8x^3+72x^2-216x+216))/(27) ?
The solution to expand (2(-8x^3+72x^2-216x+216))/(27) is -(16x^3}{27}+\frac{16x^2)/3-16x+16