en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand e^xcos(2x)*(e^xsin(2x)+2e^xcos(2x))

Solution

expand

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

Solution

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

Simplify

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

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

Popular Examples

simplify cos(x)*\delta(x-3pi)simplify

cos (x) \cdot δ (x - 3 π)

expand (p(1+r)+b(1+f))/(q(p+b))expand

\frac{p ( 1 + r ) + b ( 1 + f )}{q ( p + b )}

expand (-5)/((2.5-2)^2)expand

\frac{- 5}{( 2.5 - 2 ) ^{2}}

expand (x((2x+5)^{3/2}-(-2x+5)^{3/2}))/3 expand

\frac{x ( ( 2 x + 5 ) ^{\frac{3}{2}} - ( - 2 x + 5 ) ^{\frac{3}{2}} )}{3}

expand 4/((s+3)^2(s^2+7s+10))expand

\frac{4}{( s + 3 ) ^{2} ( s ^{2} + 7 s + 10 )}

Frequently Asked Questions (FAQ)

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