What is expand e^{8t}*t(f(t-8)\H(t-8)) ?

The solution to expand e^{8t}*t(f(t-8)\H(t-8)) is e^{8t}t^2f\H(t-8)-8e^{8t}tf\H(t-8)

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expand e^{8t}*t(f(t-8)\H(t-8))

expand

e^{8 t} \cdot t (f (t - 8) H (t - 8))

e^{8 t} t^{2} f H (t - 8) - 8 e^{8 t} t f H (t - 8)

Solution steps

e^{8 t} t (f (t - 8) H (t - 8))

Remove parentheses:

(a) = a

= e^{8 t} t f (t - 8) H (t - 8)

= e^{8 t} t f H (t - 8) (t - 8)

Apply the distributive law:

a (b - c) = ab - a c

a = e^{8 t} t f H (t - 8), b = t, c = 8

= e^{8 t} t f H (t - 8) t - e^{8 t} t f H (t - 8) \cdot 8

= e^{8 t} tt f H (t - 8) - 8 e^{8 t} t f H (t - 8)

e^{8 t} tt f H (t - 8) = e^{8 t} t^{2} f H (t - 8)

= e^{8 t} t^{2} f H (t - 8) - 8 e^{8 t} t f H (t - 8)

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What is expand e^{8t}*t(f(t-8)\H(t-8)) ?
The solution to expand e^{8t}*t(f(t-8)\H(t-8)) is e^{8t}t^2f\H(t-8)-8e^{8t}tf\H(t-8)