What is expand [(t+1)^2+e^{t-2}]U(t-2) ?

The solution to expand [(t+1)^2+e^{t-2}]U(t-2) is -2e^{t-2}U+t^3U-3tU+e^{t-2}tU-2U

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expand [(t+1)^2+e^{t-2}]U(t-2)

expand

[(t + 1)^{2} + e^{t - 2}] U (t - 2)

- 2 e^{t - 2} U + t^{3} U - 3 t U + e^{t - 2} t U - 2 U

Solution steps

[(t + 1)^{2} + e^{t - 2}] U (t - 2)

= U [(t + 1)^{2} + e^{t - 2}] (t - 2)

Apply the distributive law:

a (b - c) = ab - a c

a = [(t + 1)^{2} + e^{t - 2}] U, b = t, c = 2

= [(t + 1)^{2} + e^{t - 2}] U t - [(t + 1)^{2} + e^{t - 2}] U \cdot 2

= t U [(t + 1)^{2} + e^{t - 2}] - 2 U [(t + 1)^{2} + e^{t - 2}]

Simplify

t U [(t + 1)^{2} + e^{t - 2}] - 2 U [(t + 1)^{2} + e^{t - 2}] : - 2 e^{t - 2} U + t^{3} U - 3 t U + e^{t - 2} t U - 2 U

= - 2 e^{t - 2} U + t^{3} U - 3 t U + e^{t - 2} t U - 2 U

(D + x) (D + 1) e^{x}

(1 + i)^{5}

(3 + i)^{26}

(e^{u} + e^{- u}) (e^{u} - e^{- u})

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

What is expand [(t+1)^2+e^{t-2}]U(t-2) ?
The solution to expand [(t+1)^2+e^{t-2}]U(t-2) is -2e^{t-2}U+t^3U-3tU+e^{t-2}tU-2U