What is expand t(e^{-3t}-t^2+1) ?

The solution to expand t(e^{-3t}-t^2+1) is e^{-3t}t-t^3+t

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expand t(e^{-3t}-t^2+1)

expand

t (e^{- 3 t} - t^{2} + 1)

e^{- 3 t} t - t^{3} + t

Solution steps

t (e^{- 3 t} - t^{2} + 1)

Distribute parentheses

= t e^{- 3 t} + t (- t^{2}) + t \cdot 1

Apply minus-plus rules

+ (- a) = - a

= e^{- 3 t} t - t^{2} t + 1 \cdot t

Simplify

e^{- 3 t} t - t^{2} t + 1 \cdot t : e^{- 3 t} t - t^{3} + t

= e^{- 3 t} t - t^{3} + t

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What is expand t(e^{-3t}-t^2+1) ?
The solution to expand t(e^{-3t}-t^2+1) is e^{-3t}t-t^3+t