What is expand e^{xt-t}*(Ue^{xt}-Uxt-U) ?

The solution to expand e^{xt-t}*(Ue^{xt}-Uxt-U) is e^{2xt-t}U-e^{xt-t}xtU-e^{xt-t}U

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expand e^{xt-t}*(Ue^{xt}-Uxt-U)

expand

e^{x t - t} \cdot (U e^{x t} - Ux t - U)

e^{2 x t - t} U - e^{x t - t} x t U - e^{x t - t} U

Solution steps

e^{x t - t} (U e^{x t} - Ux t - U)

= e^{x t - t} (e^{x t} U - x t U - U)

Distribute parentheses

= e^{x t - t} U e^{x t} + e^{x t - t} (- Ux t) + e^{x t - t} (- U)

Apply minus-plus rules

+ (- a) = - a

= e^{x t - t} e^{x t} U - e^{x t - t} x t U - e^{x t - t} U

e^{x t - t} e^{x t} U = e^{2 x t - t} U

= e^{2 x t - t} U - e^{x t - t} x t U - e^{x t - t} U

(6 e^{x} - e^{2 x} - 9) (- 3 2 e^{x} - 6 x + 5)

t (e^{- 3 t} + e^{- 2 t})

5 (- 8 + 3)

4 (2 x cos (2 t) - 2 y sin (2 t))

(7^{\frac{1}{3}} - 4^{\frac{1}{3}}) (7^{\frac{1}{3}} + 4^{\frac{1}{3}})

What is expand e^{xt-t}*(Ue^{xt}-Uxt-U) ?
The solution to expand e^{xt-t}*(Ue^{xt}-Uxt-U) is e^{2xt-t}U-e^{xt-t}xtU-e^{xt-t}U