What is expand (e^t+e^tt)^2 ?

The solution to expand (e^t+e^tt)^2 is e^{2t}+2e^{2t}t+e^{2t}t^2

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expand (e^t+e^tt)^2

expand

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

e^{2 t} + 2 e^{2 t} t + e^{2 t} t^{2}

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

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