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

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b - c) = ab - a c

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

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

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

Simplify

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

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

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

(z^{2} + cos (z)) (2 z - sin (z))

\frac{7 x}{( x + 6 ) ^{2}}

2 (1 + \frac{2 k}{n})

(2 y - 3) d y

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