What is expand (e^x-1)(e^x-2) ?

The solution to expand (e^x-1)(e^x-2) is e^{2x}-3e^x+2

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expand (e^x-1)(e^x-2)

expand

(e^{x} - 1) (e^{x} - 2)

e^{2 x} - 3 e^{x} + 2

Solution steps

(e^{x} - 1) (e^{x} - 2)

Apply FOIL method:

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

a = e^{x}, b = - 1, c = e^{x}, d = - 2

= e^{x} e^{x} + e^{x} (- 2) + (- 1) e^{x} + (- 1) (- 2)

Apply minus-plus rules

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

= e^{x} e^{x} - 2 e^{x} - 1 \cdot e^{x} + 1 \cdot 2

Simplify

e^{x} e^{x} - 2 e^{x} - 1 \cdot e^{x} + 1 \cdot 2 : e^{2 x} - 3 e^{x} + 2

= e^{2 x} - 3 e^{x} + 2

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What is expand (e^x-1)(e^x-2) ?
The solution to expand (e^x-1)(e^x-2) is e^{2x}-3e^x+2