What is expand (-3e^{-t})(-5e^{4t}+e^{-2t}) ?

The solution to expand (-3e^{-t})(-5e^{4t}+e^{-2t}) is 15e^{3t}-3e^{-3t}

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expand (-3e^{-t})(-5e^{4t}+e^{-2t})

expand

(- 3 e^{- t}) (- 5 e^{4 t} + e^{- 2 t})

15 e^{3 t} - 3 e^{- 3 t}

Solution steps

(- 3 e^{- t}) (- 5 e^{4 t} + e^{- 2 t})

Apply the distributive law:

a (b + c) = ab + a c

a = (- 3 e^{- t}), b = - 5 e^{4 t}, c = e^{- 2 t}

= (- 3 e^{- t}) (- 5 e^{4 t}) + (- 3 e^{- t}) e^{- 2 t}

Apply minus-plus rules

+ (- a) = - a

= - 5 e^{4 t} (- 3 e^{- t}) + e^{- 2 t} (- 3 e^{- t})

Simplify

- 5 e^{4 t} (- 3 e^{- t}) + e^{- 2 t} (- 3 e^{- t}) : 15 e^{3 t} - 3 e^{- 3 t}

= 15 e^{3 t} - 3 e^{- 3 t}

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

2^{3}

(a + b - ab) (c + d - c d) (e + f - e f)

2^{8}

4 π (- r^{2} + 4)

What is expand (-3e^{-t})(-5e^{4t}+e^{-2t}) ?
The solution to expand (-3e^{-t})(-5e^{4t}+e^{-2t}) is 15e^{3t}-3e^{-3t}