What is expand (1-e^t+3e^{-4t})cos(5t) ?

The solution to expand (1-e^t+3e^{-4t})cos(5t) is cos(5t)-e^tcos(5t)+3e^{-4t}cos(5t)

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expand (1-e^t+3e^{-4t})cos(5t)

expand

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

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

Solution steps

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

= cos (5 t) (1 - e^{t} + 3 e^{- 4 t})

Distribute parentheses

= cos (5 t) \cdot 1 + cos (5 t) (- e^{t}) + cos (5 t) \cdot 3 e^{- 4 t}

Apply minus-plus rules

+ (- a) = - a

= 1 \cdot cos (5 t) - e^{t} cos (5 t) + 3 e^{- 4 t} cos (5 t)

Multiply:

1 \cdot cos (5 t) = cos (5 t)

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

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

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

F (0, - 2)

(sin (x) + cos (2 x))^{2}

What is expand (1-e^t+3e^{-4t})cos(5t) ?
The solution to expand (1-e^t+3e^{-4t})cos(5t) is cos(5t)-e^tcos(5t)+3e^{-4t}cos(5t)