What is expand 2t(45cos(3t)+16e^{-4t}-8sin(2t)) ?

The solution to expand 2t(45cos(3t)+16e^{-4t}-8sin(2t)) is 90tcos(3t)+32e^{-4t}t-16tsin(2t)

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expand 2t(45cos(3t)+16e^{-4t}-8sin(2t))

expand

2 t (45 cos (3 t) + 16 e^{- 4 t} - 8 sin (2 t))

90 t cos (3 t) + 32 e^{- 4 t} t - 16 t sin (2 t)

Solution steps

2 t (45 cos (3 t) + 16 e^{- 4 t} - 8 sin (2 t))

Distribute parentheses

= 2 t \cdot 45 cos (3 t) + 2 t \cdot 16 e^{- 4 t} + 2 t (- 8 sin (2 t))

Apply minus-plus rules

+ (- a) = - a

= 2 \cdot 45 t cos (3 t) + 2 \cdot 16 e^{- 4 t} t - 2 \cdot 8 t sin (2 t)

Simplify

2 \cdot 45 t cos (3 t) + 2 \cdot 16 e^{- 4 t} t - 2 \cdot 8 t sin (2 t) : 90 t cos (3 t) + 32 e^{- 4 t} t - 16 t sin (2 t)

= 90 t cos (3 t) + 32 e^{- 4 t} t - 16 t sin (2 t)

30 (\frac{1}{3} sin (3 x) - \frac{1}{2} cos (2 x) + \frac{1}{5} e^{5 x} + C)

(6 x y^{2} + 2 y) d x + (3 x^{2} y + 6 y^{2}) d y

\frac{2 k}{( ( 2 j w + 1 ) ( j w + 1 ) ( j w + 2 ) )}

\frac{6 x ^{2}}{( x - 1 ) ^{4}}

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

What is expand 2t(45cos(3t)+16e^{-4t}-8sin(2t)) ?
The solution to expand 2t(45cos(3t)+16e^{-4t}-8sin(2t)) is 90tcos(3t)+32e^{-4t}t-16tsin(2t)