What is expand-e^{3x}(12sin(2x)-5cos(2x)) ?

The solution to expand-e^{3x}(12sin(2x)-5cos(2x)) is -12e^{3x}sin(2x)+5e^{3x}cos(2x)

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expand-e^{3x}(12sin(2x)-5cos(2x))

expand

- e^{3 x} (12 sin (2 x) - 5 cos (2 x))

- 12 e^{3 x} sin (2 x) + 5 e^{3 x} cos (2 x)

Solution steps

- e^{3 x} (12 sin (2 x) - 5 cos (2 x))

Apply the distributive law:

a (b - c) = ab - a c

a = - e^{3 x}, b = 12 sin (2 x), c = 5 cos (2 x)

= - e^{3 x} \cdot 12 sin (2 x) - (- e^{3 x}) \cdot 5 cos (2 x)

Apply minus-plus rules

- (- a) = a

= - 12 e^{3 x} sin (2 x) + 5 e^{3 x} cos (2 x)

(3 + j) (2 - j)

tan (x) (1 + cot^{3} (x)) + cot (x) (1 + tan^{3} (x)) + 2

\frac{6 x}{( x ^{2} + 1 ) ^{2}}

\frac{1}{( a + b ) ^{2}}

(x - \frac{3}{x})^{5}

What is expand-e^{3x}(12sin(2x)-5cos(2x)) ?
The solution to expand-e^{3x}(12sin(2x)-5cos(2x)) is -12e^{3x}sin(2x)+5e^{3x}cos(2x)