What is expand (1-e^{-abc})^2 ?

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

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expand (1-e^{-abc})^2

expand

(1 - e^{- ab c})^{2}

1 - 2 e^{- ab c} + e^{- 2 ab c}

Solution steps

(1 - e^{- ab c})^{2}

Apply Perfect Square Formula:

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

a = 1, b = e^{- ab c}

= 1^{2} - 2 \cdot 1 \cdot e^{- ab c} + (e^{- ab c})^{2}

Simplify

1^{2} - 2 \cdot 1 \cdot e^{- ab c} + (e^{- ab c})^{2} : 1 - 2 e^{- ab c} + e^{- 2 ab c}

= 1 - 2 e^{- ab c} + e^{- 2 ab c}

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