What is expand (e^xsin(2x))(e^xcos(2x)+2e^xsin(2x)) ?

The solution to expand (e^xsin(2x))(e^xcos(2x)+2e^xsin(2x)) is e^{2x}cos(2x)sin(2x)+2e^{2x}sin^2(2x)

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expand (e^xsin(2x))(e^xcos(2x)+2e^xsin(2x))

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

a = (e^{x} sin (2 x)), b = e^{x} cos (2 x), c = 2 e^{x} sin (2 x)

= (e^{x} sin (2 x)) e^{x} cos (2 x) + (e^{x} sin (2 x)) \cdot 2 e^{x} sin (2 x)

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

Simplify

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

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

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

\frac{( R ^{2} C s + 2 R ) C s}{RC s + 1} - 1 - RC s

(- \frac{1}{6} - e^{3 x}) 4

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

\frac{2 ^{n - 1}}{n ^{2} ( n + 1 )}

What is expand (e^xsin(2x))(e^xcos(2x)+2e^xsin(2x)) ?
The solution to expand (e^xsin(2x))(e^xcos(2x)+2e^xsin(2x)) is e^{2x}cos(2x)sin(2x)+2e^{2x}sin^2(2x)