What is expand ((sin(t))^2-2(e^t))(e^t) ?

The solution to expand ((sin(t))^2-2(e^t))(e^t) is e^tsin^2(t)-2e^{2t}

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expand ((sin(t))^2-2(e^t))(e^t)

expand

((sin (t))^{2} - 2 (e^{t})) (e^{t})

e^{t} sin^{2} (t) - 2 e^{2 t}

Solution steps

((sin (t))^{2} - 2 (e^{t})) (e^{t})

= (e^{t}) ((sin (t))^{2} - 2 (e^{t}))

Apply the distributive law:

a (b - c) = ab - a c

a = (e^{t}), b = (sin (t))^{2}, c = 2 (e^{t})

= (e^{t}) (sin (t))^{2} - (e^{t}) \cdot 2 (e^{t})

= (sin (t))^{2} (e^{t}) - 2 (e^{t}) (e^{t})

Simplify

(sin (t))^{2} (e^{t}) - 2 (e^{t}) (e^{t}) : e^{t} sin^{2} (t) - 2 e^{2 t}

= e^{t} sin^{2} (t) - 2 e^{2 t}

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What is expand ((sin(t))^2-2(e^t))(e^t) ?
The solution to expand ((sin(t))^2-2(e^t))(e^t) is e^tsin^2(t)-2e^{2t}