What is expand (1-e^t+3e^{-4t})*cos(3t) ?

The solution to expand (1-e^t+3e^{-4t})*cos(3t) is cos(3t)-e^tcos(3t)+3e^{-4t}cos(3t)

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expand (1-e^t+3e^{-4t})*cos(3t)

expand

(1 - e^{t} + 3 e^{- 4 t}) \cdot cos (3 t)

cos (3 t) - e^{t} cos (3 t) + 3 e^{- 4 t} cos (3 t)

Solution steps

(1 - e^{t} + 3 e^{- 4 t}) cos (3 t)

= cos (3 t) (1 - e^{t} + 3 e^{- 4 t})

Distribute parentheses

= cos (3 t) \cdot 1 + cos (3 t) (- e^{t}) + cos (3 t) \cdot 3 e^{- 4 t}

Apply minus-plus rules

+ (- a) = - a

= 1 \cdot cos (3 t) - e^{t} cos (3 t) + 3 e^{- 4 t} cos (3 t)

Multiply:

1 \cdot cos (3 t) = cos (3 t)

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

\frac{500 0 _{0}}{( 1 + 5 ) ^{0}}

3 x (2 x + 2)

\frac{( 10 + 2 x ) \frac{d}{d t} ( ( x ) 10 )}{7 + x}

- 9 (2) - 1

(3.5 + e^{- x})^{2}

What is expand (1-e^t+3e^{-4t})*cos(3t) ?
The solution to expand (1-e^t+3e^{-4t})*cos(3t) is cos(3t)-e^tcos(3t)+3e^{-4t}cos(3t)