What is expand-(2x(x+1)^2)/3 ?

The solution to expand-(2x(x+1)^2)/3 is -(2x^3)/3-(4x^2)/3-(2x)/3

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expand-(2x(x+1)^2)/3

expand

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

- \frac{2 x ^{3}}{3} - \frac{4 x ^{2}}{3} - \frac{2 x}{3}

Solution steps

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

(x + 1)^{2} = x^{2} + 2 x + 1

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

Expand

2 x (x^{2} + 2 x + 1) : 2 x^{3} + 4 x^{2} + 2 x

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

Apply the fraction rule:

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

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

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

Remove parentheses:

(a) = a

= - \frac{2 x ^{3}}{3} - \frac{4 x ^{2}}{3} - \frac{2 x}{3}

3 - sin (2 x^{2} - 3 x - 1) (4 x - 3)

(3 x^{2} + 3 y^{2} \frac{d y}{d x}) (x^{2} + y^{2})

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What is expand-(2x(x+1)^2)/3 ?
The solution to expand-(2x(x+1)^2)/3 is -(2x^3)/3-(4x^2)/3-(2x)/3