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

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

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

expand

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

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

Solution steps

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

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{4}{2} = 2

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

Rewrite in standard form

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

\frac{5 x ^{2} - 36 x + 48}{x ( x - 4 ) ^{2}}

\frac{x ^{2} ( x + 1 ) ^{3}}{( x - 2 ) ^{2} ( x - 4 ) ^{4}}

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

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

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