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

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

Apply minus-plus rules

+ (- a) = - a

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

Simplify

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

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

(3 y - 5 i)^{2}

(e^{iπ x} + e^{- iπ x})^{2}

\frac{x}{x - x - 6} - \frac{1}{x + 2} - \frac{2}{x - 3}

(- 3 a cos^{2} (t) + sin (t))^{2}

(a + 4 b) (a - 2 b)

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