What is factor e^{x-4t}+e^{x+4t} ?

The solution to factor e^{x-4t}+e^{x+4t} is e^{-4t+x}(1+e^{8t})

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factor e^{x-4t}+e^{x+4t}

factor

e^{x - 4 t} + e^{x + 4 t}

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

Solution steps

e^{x - 4 t} + e^{x + 4 t}

Apply exponent rule:

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

= e^{x} e^{- 4 t} + e^{x} e^{4 t}

Apply exponent rule:

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

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

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

Factor out common term

e^{- 4 t} e^{x}

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

Refine

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

2 ab c - 3 ab - 4 x c + 6 x

(y + z)^{3} + 27

y^{2} + 0.4 y - 0.05

l {e^{3 t}}

What is factor e^{x-4t}+e^{x+4t} ?
The solution to factor e^{x-4t}+e^{x+4t} is e^{-4t+x}(1+e^{8t})