What is factor e^{-j^8z}-e^{j^8z} ?

The solution to factor e^{-j^8z}-e^{j^8z} is -e^{-j^8z}(e^{j^8z}+1)(e^{j^8z}-1)

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factor e^{-j^8z}-e^{j^8z}

factor

e^{- j^{8} z} - e^{j^{8} z}

- e^{- j^{8} z} (e^{j^{8} z} + 1) (e^{j^{8} z} - 1)

Solution steps

e^{- j^{8} z} - e^{j^{8} z}

Apply exponent rule:

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

e^{j^{8} z} = e^{- j^{8} z} e^{2 j^{8} z}

= e^{- j^{8} z} - e^{- j^{8} z} e^{2 j^{8} z}

Factor out common term

e^{- j^{8} z}

= e^{- j^{8} z} (1 - e^{2 j^{8} z})

Factor

- e^{2 j^{8} z} + 1 : - (e^{j^{8} z} + 1) (e^{j^{8} z} - 1)

= e^{- j^{8} z} (- (e^{j^{8} z} + 1) (e^{j^{8} z} - 1))

Refine

= - e^{- j^{8} z} (e^{j^{8} z} + 1) (e^{j^{8} z} - 1)

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What is factor e^{-j^8z}-e^{j^8z} ?
The solution to factor e^{-j^8z}-e^{j^8z} is -e^{-j^8z}(e^{j^8z}+1)(e^{j^8z}-1)