What is factor ae^x+be^{-x}+ce^{3x} ?

The solution to factor ae^x+be^{-x}+ce^{3x} is e^{-x}(ae^{2x}+b+ce^{4x})

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factor ae^x+be^{-x}+ce^{3x}

factor

a e^{x} + b e^{- x} + c e^{3 x}

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

Solution steps

a e^{x} + b e^{- x} + c e^{3 x}

Apply exponent rule:

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

e^{x} = e^{- x} e^{2 x}, e^{3 x} = e^{- x} e^{4 x}

= a e^{- x} e^{2 x} + b e^{- x} + c e^{- x} e^{4 x}

Factor out common term

e^{- x}

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

1 - 1 - x^{2}

\frac{4 x}{12}

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

x + y + (- 1)

(x)^{3} + (x^{2} - x + 1)

What is factor ae^x+be^{-x}+ce^{3x} ?
The solution to factor ae^x+be^{-x}+ce^{3x} is e^{-x}(ae^{2x}+b+ce^{4x})