What is expand ((2+x)^2)/4 ?

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

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expand ((2+x)^2)/4

expand

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

\frac{x ^{2}}{4} + x + 1

Solution steps

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

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

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

Apply the fraction rule:

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

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

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

Apply rule

\frac{a}{a} = 1

\frac{4}{4} = 1

= 1 + \frac{4 x}{4} + \frac{x ^{2}}{4}

Divide the numbers:

\frac{4}{4} = 1

= 1 + x + \frac{x ^{2}}{4}

Rewrite in standard form

= \frac{x ^{2}}{4} + x + 1

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