What is expand ((u-1)/2)^2 ?

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

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expand ((u-1)/2)^2

expand

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

\frac{u ^{2}}{4} - \frac{u}{2} + \frac{1}{4}

Solution steps

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( u - 1 ) ^{2}}{2 ^{2}}

(u - 1)^{2} = u^{2} - 2 u + 1

= \frac{u ^{2} - 2 u + 1}{2 ^{2}}

2^{2} = 4

= \frac{u ^{2} - 2 u + 1}{4}

Apply the fraction rule:

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

\frac{u ^{2} - 2 u + 1}{4} = \frac{u ^{2}}{4} - \frac{2 u}{4} + \frac{1}{4}

= \frac{u ^{2}}{4} - \frac{2 u}{4} + \frac{1}{4}

Cancel

\frac{2 u}{4} : \frac{u}{2}

= \frac{u ^{2}}{4} - \frac{u}{2} + \frac{1}{4}

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