What is expand (e^{2x}+7/(e^{5x)})^2 ?

The solution to expand (e^{2x}+7/(e^{5x)})^2 is e^{4x}+(14)/(e^{3x)}+(49)/(e^{10x)}

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expand (e^{2x}+7/(e^{5x)})^2

expand

(e^{2 x} + \frac{7}{e ^{5 x}})^{2}

e^{4 x} + \frac{14}{e ^{3 x}} + \frac{49}{e ^{10 x}}

Solution steps

(e^{2 x} + \frac{7}{e ^{5 x}})^{2}

Apply Perfect Square Formula:

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

a = e^{2 x}, b = \frac{7}{e ^{5 x}}

= (e^{2 x})^{2} + 2 e^{2 x} \frac{7}{e ^{5 x}} + (\frac{7}{e ^{5 x}})^{2}

Simplify

(e^{2 x})^{2} + 2 e^{2 x} \frac{7}{e ^{5 x}} + (\frac{7}{e ^{5 x}})^{2} : e^{4 x} + \frac{14}{e ^{3 x}} + \frac{49}{e ^{10 x}}

= e^{4 x} + \frac{14}{e ^{3 x}} + \frac{49}{e ^{10 x}}

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4 x 2 - 2 x x

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I n (\frac{7 x ^{5}}{y ^{3}})

What is expand (e^{2x}+7/(e^{5x)})^2 ?
The solution to expand (e^{2x}+7/(e^{5x)})^2 is e^{4x}+(14)/(e^{3x)}+(49)/(e^{10x)}