What is expand (-1+e^{-0.02y})(e^{-0.1x}-1) ?

The solution to expand (-1+e^{-0.02y})(e^{-0.1x}-1) is -e^{-0.1x}+1+e^{-0.02y-0.1x}-e^{-0.02y}

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expand (-1+e^{-0.02y})(e^{-0.1x}-1)

expand

(- 1 + e^{- 0.02 y}) (e^{- 0.1 x} - 1)

- e^{- 0.1 x} + 1 + e^{- 0.02 y - 0.1 x} - e^{- 0.02 y}

Solution steps

(- 1 + e^{- 0.02 y}) (e^{- 0.1 x} - 1)

Apply FOIL method:

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

a = - 1, b = e^{- 0.02 y}, c = e^{- 0.1 x}, d = - 1

= (- 1) e^{- 0.1 x} + (- 1) (- 1) + e^{- 0.02 y} e^{- 0.1 x} + e^{- 0.02 y} (- 1)

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= - 1 \cdot e^{- 0.1 x} + 1 \cdot 1 + e^{- 0.02 y} e^{- 0.1 x} - 1 \cdot e^{- 0.02 y}

Simplify

- 1 \cdot e^{- 0.1 x} + 1 \cdot 1 + e^{- 0.02 y} e^{- 0.1 x} - 1 \cdot e^{- 0.02 y} : - e^{- 0.1 x} + 1 + e^{- 0.02 y - 0.1 x} - e^{- 0.02 y}

= - e^{- 0.1 x} + 1 + e^{- 0.02 y - 0.1 x} - e^{- 0.02 y}

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What is expand (-1+e^{-0.02y})(e^{-0.1x}-1) ?
The solution to expand (-1+e^{-0.02y})(e^{-0.1x}-1) is -e^{-0.1x}+1+e^{-0.02y-0.1x}-e^{-0.02y}