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

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

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

expand

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

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

Solution steps

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

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{4}{2} = 2

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

Rewrite in standard form

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

[8 (a + b) + 6 (- z - y)] [8 (a + b) + 6 (y + z)]

4 (3 - 1)

e^{x} (x - 1)

2 (\frac{- u - 3}{49} + \frac{1}{7})

16 (s + s^{'})^{12}

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