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

The solution to expand t(e^t+e^{2t})^2 is e^{2t}t+2e^{3t}t+e^{4t}t

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

expand

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

e^{2 t} t + 2 e^{3 t} t + e^{4 t} t

Solution steps

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

(e^{t} + e^{2 t})^{2} = e^{2 t} + 2 e^{3 t} + e^{4 t}

= t (e^{2 t} + 2 e^{3 t} + e^{4 t})

Distribute parentheses

= t e^{2 t} + t \cdot 2 e^{3 t} + t e^{4 t}

= e^{2 t} t + 2 e^{3 t} t + e^{4 t} t

(2 x + 1)^{2}

(1 + e^{x})^{2}

\frac{- x ^{2} + 4}{( x ^{2} + 4 ) ^{2}}

\frac{1}{s ^{2} ( s ^{2} + a ^{2} )}

(x - \frac{1}{x})^{8}

What is expand t(e^t+e^{2t})^2 ?
The solution to expand t(e^t+e^{2t})^2 is e^{2t}t+2e^{3t}t+e^{4t}t