What is factor ae^{4x}-ae^{-4x} ?

The solution to factor ae^{4x}-ae^{-4x} is ae^{-4x}(e^{4x}+1)(e^{2x}+1)(e^x+1)(e^x-1)

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factor ae^{4x}-ae^{-4x}

factor

a e^{4 x} - a e^{- 4 x}

a e^{- 4 x} (e^{4 x} + 1) (e^{2 x} + 1) (e^{x} + 1) (e^{x} - 1)

Solution steps

a e^{4 x} - a e^{- 4 x}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

e^{4 x} = e^{- 4 x} e^{8 x}

= a e^{- 4 x} e^{8 x} - a e^{- 4 x}

Factor out common term

a e^{- 4 x}

= a e^{- 4 x} (e^{8 x} - 1)

Factor

e^{8 x} - 1 : (e^{4 x} + 1) (e^{2 x} + 1) (e^{x} + 1) (e^{x} - 1)

= a e^{- 4 x} (e^{x} + 1) (e^{x} - 1) (e^{4 x} + 1) (e^{2 x} + 1)

(x - 1)^{3} - 27

(3 x - 6 x^{3}) + 2

x^{2} - \frac{13}{6} x + 1

4^{n + 2} + 2^{2 n + 2}

e^{2} + 10 e + 16

What is factor ae^{4x}-ae^{-4x} ?
The solution to factor ae^{4x}-ae^{-4x} is ae^{-4x}(e^{4x}+1)(e^{2x}+1)(e^x+1)(e^x-1)