What is expand (e^t+e^{5t})^2 ?

The solution to expand (e^t+e^{5t})^2 is e^{2t}+2e^{6t}+e^{10t}

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expand (e^t+e^{5t})^2

expand

(e^{t} + e^{5 t})^{2}

e^{2 t} + 2 e^{6 t} + e^{10 t}

Solution steps

(e^{t} + e^{5 t})^{2}

Apply Perfect Square Formula:

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

a = e^{t}, b = e^{5 t}

= (e^{t})^{2} + 2 e^{t} e^{5 t} + (e^{5 t})^{2}

Simplify

(e^{t})^{2} + 2 e^{t} e^{5 t} + (e^{5 t})^{2} : e^{2 t} + 2 e^{6 t} + e^{10 t}

= e^{2 t} + 2 e^{6 t} + e^{10 t}

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What is expand (e^t+e^{5t})^2 ?
The solution to expand (e^t+e^{5t})^2 is e^{2t}+2e^{6t}+e^{10t}