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Popular >

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

Solution

expand

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

Solution

\frac{x ^{3}}{2} + 2 x^{2} + 2 x

Solution steps

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

(- x - 2)^{2} = x^{2} + 4 x + 4

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

Expand

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{4}{2} = 2

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

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Frequently Asked Questions (FAQ)

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