What is expand (e^{2x}-4)(e^{-2x}-4) ?

The solution to expand (e^{2x}-4)(e^{-2x}-4) is -4e^{-2x}-4e^{2x}+17

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expand (e^{2x}-4)(e^{-2x}-4)

expand

(e^{2 x} - 4) (e^{- 2 x} - 4)

- 4 e^{- 2 x} - 4 e^{2 x} + 17

Solution steps

(e^{2 x} - 4) (e^{- 2 x} - 4)

Apply FOIL method:

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

a = e^{2 x}, b = - 4, c = e^{- 2 x}, d = - 4

= e^{2 x} e^{- 2 x} + e^{2 x} (- 4) + (- 4) e^{- 2 x} + (- 4) (- 4)

Apply minus-plus rules

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

= e^{2 x} e^{- 2 x} - 4 e^{2 x} - 4 e^{- 2 x} + 4 \cdot 4

Simplify

e^{2 x} e^{- 2 x} - 4 e^{2 x} - 4 e^{- 2 x} + 4 \cdot 4 : - 4 e^{- 2 x} - 4 e^{2 x} + 17

= - 4 e^{- 2 x} - 4 e^{2 x} + 17

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What is expand (e^{2x}-4)(e^{-2x}-4) ?
The solution to expand (e^{2x}-4)(e^{-2x}-4) is -4e^{-2x}-4e^{2x}+17