What is expand (-e^tsin(t)+e^tcos(t))(2e^tcos(t)) ?

The solution to expand (-e^tsin(t)+e^tcos(t))(2e^tcos(t)) is -2e^{2t}sin(t)cos(t)+2e^{2t}cos^2(t)

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expand (-e^tsin(t)+e^tcos(t))(2e^tcos(t))

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

Apply minus-plus rules

+ (- a) = - a

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

Simplify

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

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

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

\frac{d}{d x} ((f (x)) (9 x^{2} + 11 x + 2))

(4 + 32) (- 3 + 5)

(8 x^{2} - 16 x + 16) e^{x}

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

What is expand (-e^tsin(t)+e^tcos(t))(2e^tcos(t)) ?
The solution to expand (-e^tsin(t)+e^tcos(t))(2e^tcos(t)) is -2e^{2t}sin(t)cos(t)+2e^{2t}cos^2(t)