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

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

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

expand

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

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

Solution steps

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

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

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

Simplify

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

(a - bi)^{2}

lo g_{10} (x^{5} y^{- 4})

(1 - cos^{2} (x))^{2}

\frac{x ( 2 x ^{2} - 5 )}{2 y ( y ^{2} - 2 )}

- \frac{2 ( 3 5 - 5 )}{5} + 1

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