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

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

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

expand

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

\frac{a ^{3}}{4} + 2 a + \frac{4}{a}

Solution steps

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

(a^{2} + 4)^{2} = a^{4} + 8 a^{2} + 16

= \frac{a ^{4} + 8 a ^{2} + 16}{4 a}

Apply the fraction rule:

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

\frac{a ^{4} + 8 a ^{2} + 16}{4 a} = \frac{a ^{4}}{4 a} + \frac{8 a ^{2}}{4 a} + \frac{16}{4 a}

= \frac{a ^{4}}{4 a} + \frac{8 a ^{2}}{4 a} + \frac{16}{4 a}

Cancel

\frac{a ^{4}}{4 a} : \frac{a ^{3}}{4}

= \frac{a ^{3}}{4} + \frac{8 a ^{2}}{4 a} + \frac{16}{4 a}

Cancel

\frac{8 a ^{2}}{4 a} : 2 a

= \frac{a ^{3}}{4} + 2 a + \frac{16}{4 a}

Divide the numbers:

\frac{16}{4} = 4

= \frac{a ^{3}}{4} + 2 a + \frac{4}{a}

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