展开 (x^2+y^2e^{x/y})y

解答

展开

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

x^{2} y + e^{\frac{x}{y}} y^{3}

求解步骤

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

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

使用分配律:

a (b + c) = ab + a c

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

= y x^{2} + y y^{2} e^{\frac{x}{y}}

= x^{2} y + e^{\frac{x}{y}} y^{2} y

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

= x^{2} y + e^{\frac{x}{y}} y^{3}

e x p an d \frac{2 x ^{2} + 9 x + 7}{( x + 2 ) ( x + 3 ) ( x + 4 )}

e x p an d (y + x^{2} + y^{2}) d x

e x p an d (4 y - e^{y} sin (x)) + i (4 y - e^{y} sin (x) + c)

e x p an d \frac{( x ^{2} - 3 x - 4 ) ( x + 1 )}{( x - 1 ) ( x ^{2} + 2 x - 3 )}

e x p an d \frac{( y - 3 ) ^{2}}{4}