What is expand t(e^t+e^{4t})^2 ?

The solution to expand t(e^t+e^{4t})^2 is e^{2t}t+2e^{5t}t+e^{8t}t

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expand t(e^t+e^{4t})^2

expand

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

e^{2 t} t + 2 e^{5 t} t + e^{8 t} t

Solution steps

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

(e^{t} + e^{4 t})^{2} = e^{2 t} + 2 e^{5 t} + e^{8 t}

= t (e^{2 t} + 2 e^{5 t} + e^{8 t})

Distribute parentheses

= t e^{2 t} + t \cdot 2 e^{5 t} + t e^{8 t}

= e^{2 t} t + 2 e^{5 t} t + e^{8 t} t

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

\frac{8 y + 6}{( 4 y - 9 ) ( y + 2 )}

sin (x) cos (x) (- csc (x) + sec (x))

What is expand t(e^t+e^{4t})^2 ?
The solution to expand t(e^t+e^{4t})^2 is e^{2t}t+2e^{5t}t+e^{8t}t