What is expand e^{3t}(t+cos(t))^2 ?

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

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expand e^{3t}(t+cos(t))^2

expand

e^{3 t} (t + cos (t))^{2}

e^{3 t} t^{2} + 2 e^{3 t} t cos (t) + e^{3 t} cos^{2} (t)

Solution steps

e^{3 t} (t + cos (t))^{2}

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

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

Distribute parentheses

= e^{3 t} t^{2} + e^{3 t} \cdot 2 t cos (t) + e^{3 t} cos^{2} (t)

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

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