What is expand (1-ye^{xy})*(e^{-xy}+x) ?

The solution to expand (1-ye^{xy})*(e^{-xy}+x) is e^{-yx}+x-y-e^{yx}yx

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expand (1-ye^{xy})*(e^{-xy}+x)

expand

(1 - y e^{x y}) \cdot (e^{- x y} + x)

e^{- y x} + x - y - e^{y x} y x

Solution steps

(1 - y e^{x y}) (e^{- x y} + x)

= (1 - e^{y x} y) (e^{- y x} + x)

Apply FOIL method:

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

a = 1, b = - y e^{x y}, c = e^{- x y}, d = x

= 1 \cdot e^{- x y} + 1 \cdot x + (- y e^{x y}) e^{- x y} + (- y e^{x y}) x

Apply minus-plus rules

+ (- a) = - a

= 1 \cdot e^{- y x} + 1 \cdot x - e^{y x} e^{- y x} y - e^{y x} y x

Simplify

1 \cdot e^{- y x} + 1 \cdot x - e^{y x} e^{- y x} y - e^{y x} y x : e^{- y x} + x - y - e^{y x} y x

= e^{- y x} + x - y - e^{y x} y x

\frac{5 e ^{- x}}{x ( x + 1 )}

\frac{3 x + 2}{x ( x + 1 ) ^{2}}

(\frac{z - 1}{z T})^{2}

(e^{j θ} + e^{- j θ})^{3}

(2 e^{- 4 t} - 2)^{3}

What is expand (1-ye^{xy})*(e^{-xy}+x) ?
The solution to expand (1-ye^{xy})*(e^{-xy}+x) is e^{-yx}+x-y-e^{yx}yx