What is expand (x^2z+e^{y/x})(2z^2y-xy^2) ?

The solution to expand (x^2z+e^{y/x})(2z^2y-xy^2) is 2x^2z^3y-x^3zy^2+2e^{y/x}z^2y-e^{y/x}xy^2

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expand (x^2z+e^{y/x})(2z^2y-xy^2)

expand

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

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

Solution steps

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

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

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

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

Apply minus-plus rules

+ (- a) = - a

= 2 x^{2} z^{2} zy - x^{2} x z y^{2} + 2 e^{\frac{y}{x}} z^{2} y - e^{\frac{y}{x}} x y^{2}

Simplify

2 x^{2} z^{2} zy - x^{2} x z y^{2} + 2 e^{\frac{y}{x}} z^{2} y - e^{\frac{y}{x}} x y^{2} : 2 x^{2} z^{3} y - x^{3} z y^{2} + 2 e^{\frac{y}{x}} z^{2} y - e^{\frac{y}{x}} x y^{2}

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

\frac{( s + 1 )}{[ ( s + 3 ) ( s + 5 ) ]}

(5 - 3)^{2}

(2 e^{y} - \frac{1}{8} e^{- y})^{2}

\frac{3 ( 14 + 106 )}{4}

x sin (y) d y + (x^{3} - 2 x^{2} cos (y) + cos (y)) d x

What is expand (x^2z+e^{y/x})(2z^2y-xy^2) ?
The solution to expand (x^2z+e^{y/x})(2z^2y-xy^2) is 2x^2z^3y-x^3zy^2+2e^{y/x}z^2y-e^{y/x}xy^2