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

Simplify

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

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

m (m - n)

(x + 3) 4 (x - 2 + 7) (x + 2 - 7)

(\frac{x}{3} + 3 y) (\frac{x}{4} + 2 y)

\frac{2 x}{( x - 3 ) ^{4} - y ^{4}}

(4) (- 4) (- 8) (- 12) (- 16) (- 20)

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