What is factor e^{-4t}u(-t)+4e^{-7t}u(t) ?

The solution to factor e^{-4t}u(-t)+4e^{-7t}u(t) is -e^{-7t}tu(e^{3t}-4)

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factor e^{-4t}u(-t)+4e^{-7t}u(t)

factor

e^{- 4 t} u (- t) + 4 e^{- 7 t} u (t)

- e^{- 7 t} t u (e^{3 t} - 4)

Solution steps

e^{- 4 t} u (- t) + 4 e^{- 7 t} u (t)

Apply exponent rule:

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

e^{- 4 t} = e^{- 7 t} e^{3 t}

= e^{- 7 t} e^{3 t} u (- t) + 4 e^{- 7 t} u t

Rewrite as

= u (- t) e^{- 7 t} e^{3 t} - 4 u (- t) e^{- 7 t}

Factor out common term

u (- t) e^{- 7 t}

= u (- t) e^{- 7 t} (e^{3 t} - 4)

Refine

= - e^{- 7 t} t u (e^{3 t} - 4)

x - (y - 1)^{4}

x^{35} + 45 x

(- 7 x^{9}) + 4 x^{2}

2 cos^{2} (x) - 9 cos (x) - 5

a^{2} + a^{0} - a^{- 2}

What is factor e^{-4t}u(-t)+4e^{-7t}u(t) ?
The solution to factor e^{-4t}u(-t)+4e^{-7t}u(t) is -e^{-7t}tu(e^{3t}-4)