What is expand ((5+c)/2)^2 ?

The solution to expand ((5+c)/2)^2 is 25/4+(5c)/2+(c^2)/4

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expand ((5+c)/2)^2

expand

(\frac{5 + c}{2})^{2}

\frac{25}{4} + \frac{5 c}{2} + \frac{c ^{2}}{4}

Solution steps

(\frac{5 + c}{2})^{2}

Apply exponent rule:

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

= \frac{( 5 + c ) ^{2}}{2 ^{2}}

(5 + c)^{2} = 25 + 10 c + c^{2}

= \frac{25 + 10 c + c ^{2}}{2 ^{2}}

2^{2} = 4

= \frac{25 + 10 c + c ^{2}}{4}

Apply the fraction rule:

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

\frac{25 + 10 c + c ^{2}}{4} = \frac{25}{4} + \frac{10 c}{4} + \frac{c ^{2}}{4}

= \frac{25}{4} + \frac{10 c}{4} + \frac{c ^{2}}{4}

Cancel

\frac{10 c}{4} : \frac{5 c}{2}

= \frac{25}{4} + \frac{5 c}{2} + \frac{c ^{2}}{4}

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What is expand ((5+c)/2)^2 ?
The solution to expand ((5+c)/2)^2 is 25/4+(5c)/2+(c^2)/4