What is expand y^2e^y(1+2/y)sin(x) ?

The solution to expand y^2e^y(1+2/y)sin(x) is e^yy^2sin(x)+2e^yysin(x)

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expand y^2e^y(1+2/y)sin(x)

expand

y^{2} e^{y} (1 + \frac{2}{y}) sin (x)

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

Solution steps

y^{2} e^{y} (1 + \frac{2}{y}) sin (x)

= e^{y} y^{2} sin (x) (1 + \frac{2}{y})

Apply the distributive law:

a (b + c) = ab + a c

a = y^{2} e^{y} sin (x), b = 1, c = \frac{2}{y}

= y^{2} e^{y} sin (x) \cdot 1 + y^{2} e^{y} sin (x) \frac{2}{y}

= 1 \cdot e^{y} y^{2} sin (x) + e^{y} \frac{2}{y} y^{2} sin (x)

Simplify

1 \cdot e^{y} y^{2} sin (x) + e^{y} \frac{2}{y} y^{2} sin (x) : e^{y} y^{2} sin (x) + 2 e^{y} y sin (x)

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

\frac{4}{( 4 - x ) ^{3}}

(sec^{2} (x) + 1)^{2}

\frac{10 ( 1229 - 2 )}{49}

\frac{- e ^{ik} ( ik - 1 ) + e ^{- ik} ( - ik - 1 )}{k ^{2}}

(t - 2)^{3} e^{3 t}

What is expand y^2e^y(1+2/y)sin(x) ?
The solution to expand y^2e^y(1+2/y)sin(x) is e^yy^2sin(x)+2e^yysin(x)