What is expand (2+(2k)/n)^2 ?

The solution to expand (2+(2k)/n)^2 is (4n^2+8kn+4k^2)/(n^2)

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expand (2+(2k)/n)^2

expand

(2 + \frac{2 k}{n})^{2}

\frac{4 n ^{2} + 8 kn + 4 k ^{2}}{n ^{2}}

Solution steps

(2 + \frac{2 k}{n})^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(2 + \frac{2 k}{n})^{2} = 2^{2} + 2 \cdot 2 \cdot \frac{2 k}{n} + (\frac{2 k}{n})^{2}

= 2^{2} + 2 \cdot 2 \cdot \frac{2 k}{n} + (\frac{2 k}{n})^{2}

Simplify

2^{2} + 2 \cdot 2 \cdot \frac{2 k}{n} + (\frac{2 k}{n})^{2} : \frac{4 n ^{2} + 8 kn + 4 k ^{2}}{n ^{2}}

= \frac{4 n ^{2} + 8 kn + 4 k ^{2}}{n ^{2}}

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

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What is expand (2+(2k)/n)^2 ?
The solution to expand (2+(2k)/n)^2 is (4n^2+8kn+4k^2)/(n^2)