What is factor e^{x+y}+e^{x-y} ?

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

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factor e^{x+y}+e^{x-y}

factor

e^{x + y} + e^{x - y}

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

Solution steps

e^{x + y} + e^{x - y}

Apply exponent rule:

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

= e^{y} e^{x} + e^{x} e^{- y}

Apply exponent rule:

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

e^{y} = e^{- y} e^{2 y}

= e^{x} e^{- y} e^{2 y} + e^{x} e^{- y}

Factor out common term

e^{- y} e^{x}

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

Refine

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

sin^{2} (x) - sin (x) - 2

(tan (x^{3} + c))^{2}

e^{2} - 10 e + 9

ab - c d + a c - b d

ux + u y + 2 x + 2 y

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