What is expand (e^{-2x}-e^{-3x})^2 ?

The solution to expand (e^{-2x}-e^{-3x})^2 is e^{-4x}-2e^{-5x}+e^{-6x}

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expand (e^{-2x}-e^{-3x})^2

expand

(e^{- 2 x} - e^{- 3 x})^{2}

e^{- 4 x} - 2 e^{- 5 x} + e^{- 6 x}

Solution steps

(e^{- 2 x} - e^{- 3 x})^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = e^{- 2 x}, b = e^{- 3 x}

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

Simplify

(e^{- 2 x})^{2} - 2 e^{- 2 x} e^{- 3 x} + (e^{- 3 x})^{2} : e^{- 4 x} - 2 e^{- 5 x} + e^{- 6 x}

= e^{- 4 x} - 2 e^{- 5 x} + e^{- 6 x}

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What is expand (e^{-2x}-e^{-3x})^2 ?
The solution to expand (e^{-2x}-e^{-3x})^2 is e^{-4x}-2e^{-5x}+e^{-6x}