What is expand (e^t)(e^{-t}-te^{-t}) ?

The solution to expand (e^t)(e^{-t}-te^{-t}) is 1-t

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expand (e^t)(e^{-t}-te^{-t})

expand

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

1 - t

Solution steps

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

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

Apply the distributive law:

a (b - c) = ab - a c

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

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

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

Simplify

e^{- t} (e^{t}) - e^{- t} t (e^{t}) : 1 - t

= 1 - t

(\frac{d y}{d x} + y = e^{x}) e^{x}

lo g_{3} (27)

\frac{( 2 x ^{2} - 4 ) x}{( x + 2 ) ( 10 x ^{2} + 4 x - 5 )}

\frac{( 1 + 3 x ) ( 1 + 7 x )}{( 7 - 9 x ) ( 2 - x )}

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