What is factor-3Ae^{-3x}+2Be^{2x}+4Ce^{4x} ?

The solution to factor-3Ae^{-3x}+2Be^{2x}+4Ce^{4x} is e^{-3x}(-3A+2Be^{5x}+4Ce^{7x})

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factor-3Ae^{-3x}+2Be^{2x}+4Ce^{4x}

factor

- 3 A e^{- 3 x} + 2 B e^{2 x} + 4 C e^{4 x}

e^{- 3 x} (- 3 A + 2 B e^{5 x} + 4 C e^{7 x})

Solution steps

- 3 A e^{- 3 x} + 2 B e^{2 x} + 4 C e^{4 x}

Apply exponent rule:

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

e^{2 x} = e^{- 3 x} e^{5 x}, e^{4 x} = e^{- 3 x} e^{7 x}

= - 3 A e^{- 3 x} + 2 B e^{- 3 x} e^{5 x} + 4 C e^{- 3 x} e^{7 x}

Factor out common term

e^{- 3 x}

= e^{- 3 x} (- 3 A + 2 B e^{5 x} + 4 C e^{7 x})

6 a^{3} - 10 a x - 5 b x^{2} + 3 a^{2} b x

2^{2^{5}} - 1

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

(a + b) - d

\frac{x ^{2} - 4}{x + 2}

What is factor-3Ae^{-3x}+2Be^{2x}+4Ce^{4x} ?
The solution to factor-3Ae^{-3x}+2Be^{2x}+4Ce^{4x} is e^{-3x}(-3A+2Be^{5x}+4Ce^{7x})