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

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b - c) = ab - a c

a = (- (3 + 2 e^{2 t})), b = t, c = e^{2 t}

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

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

Simplify

t (- (3 + 2 e^{2 t})) - e^{2 t} (- (3 + 2 e^{2 t})) : - 3 t - 2 e^{2 t} t + 3 e^{2 t} + 2 e^{4 t}

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

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