What is expand (xe^{x/2}-2e^{x/2})e^x ?

The solution to expand (xe^{x/2}-2e^{x/2})e^x is e^{(3x)/2}x-2e^{(3x)/2}

Popular >

expand (xe^{x/2}-2e^{x/2})e^x

expand

(x e^{\frac{x}{2}} - 2 e^{\frac{x}{2}}) e^{x}

e^{\frac{3 x}{2}} x - 2 e^{\frac{3 x}{2}}

Solution steps

(x e^{\frac{x}{2}} - 2 e^{\frac{x}{2}}) e^{x}

= e^{x} (e^{\frac{x}{2}} x - 2 e^{\frac{x}{2}})

Apply the distributive law:

a (b - c) = ab - a c

a = e^{x}, b = x e^{\frac{x}{2}}, c = 2 e^{\frac{x}{2}}

= e^{x} x e^{\frac{x}{2}} - e^{x} \cdot 2 e^{\frac{x}{2}}

= e^{\frac{x}{2}} e^{x} x - 2 e^{\frac{x}{2}} e^{x}

Simplify

e^{\frac{x}{2}} e^{x} x - 2 e^{\frac{x}{2}} e^{x} : e^{\frac{3 x}{2}} x - 2 e^{\frac{3 x}{2}}

= e^{\frac{3 x}{2}} x - 2 e^{\frac{3 x}{2}}

\frac{( s \cdot ( s + 0.5 ) \cdot ( s + 1 ) \cdot ( s ^{2} + 0.4 s + 4 ) )}{s + 4}

86 (68.8 s + \frac{10 s + 2057600}{s})

cos (x) (cos (y) - 1) - sin (x) sin (y)

x^{2} \cdot sin (u s) (x + y^{2})

(\frac{3}{2 x ^{3}} - 6 y) (\frac{3}{2 x ^{3}} + 6 y)

What is expand (xe^{x/2}-2e^{x/2})e^x ?
The solution to expand (xe^{x/2}-2e^{x/2})e^x is e^{(3x)/2}x-2e^{(3x)/2}