What is expand e^{3(t-6)}U(t-6) ?

The solution to expand e^{3(t-6)}U(t-6) is e^{3t-18}tU-6e^{3t-18}U

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expand e^{3(t-6)}U(t-6)

expand

e^{3 (t - 6)} U (t - 6)

e^{3 t - 18} t U - 6 e^{3 t - 18} U

Solution steps

e^{3 (t - 6)} U (t - 6)

Apply the distributive law:

a (b - c) = ab - a c

a = e^{3 (t - 6)} U, b = t, c = 6

= e^{3 (t - 6)} U t - e^{3 (t - 6)} U \cdot 6

= e^{3 (t - 6)} t U - 6 e^{3 (t - 6)} U

Simplify

e^{3 (t - 6)} t U - 6 e^{3 (t - 6)} U : e^{3 t - 18} t U - 6 e^{3 t - 18} U

= e^{3 t - 18} t U - 6 e^{3 t - 18} U

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What is expand e^{3(t-6)}U(t-6) ?
The solution to expand e^{3(t-6)}U(t-6) is e^{3t-18}tU-6e^{3t-18}U