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

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

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

expand

2 e^{t} cos (t) \cdot (e^{t} cos (t) + e^{t} sin (t))

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

Solution steps

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

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

Simplify

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

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

\frac{8 x ^{2} + 36 x + 47}{( 3 x - 1 ) ( x + 2 ) ( 2 x + 3 )}

(x - 5) (3 x + 4) - (2 x - 4)^{'} (3 x + 7)^{'}

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

- \frac{16 x}{( x ^{2} + 4 ) ( - x ^{2} + 4 )}

\frac{5 ( 10 a + 11 b )}{9}

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