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Popular >

factor (0.5(e^x-e^{-x}))^2

Solution

factor

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

Solution

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

Solution steps

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= 0. 5^{2} (e^{x} - e^{- x})^{2}

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

= 0. 5^{2} (e^{- x} (e^{x} + 1) (e^{x} - 1))^{2}

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

= 0. 5^{2} e^{- 2 x} (e^{x} + 1)^{2} (e^{x} - 1)^{2}

0. 5^{2} = 0.25

= 0.25 e^{- 2 x} (e^{x} + 1)^{2} (e^{x} - 1)^{2}

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Frequently Asked Questions (FAQ)

What is factor (0.5(e^x-e^{-x}))^2 ?
The solution to factor (0.5(e^x-e^{-x}))^2 is 0.25e^{-2x}(e^x+1)^2(e^x-1)^2