What is expand e^{2t}*t^2*U(t-3) ?

The solution to expand e^{2t}*t^2*U(t-3) is e^{2t}t^3U-3e^{2t}t^2U

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expand e^{2t}t^2U(t-3)

expand

e^{2 t} \cdot t^{2} \cdot U (t - 3)

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

Solution steps

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

Apply the distributive law:

a (b - c) = ab - a c

a = e^{2 t} t^{2} U, b = t, c = 3

= e^{2 t} t^{2} U t - e^{2 t} t^{2} U \cdot 3

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

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

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

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

(sec (x) - tan (x)) cot (x) - csc (x)

\frac{24}{( 1 0 ^{2} )}

ln (\frac{x - 92}{x})

\frac{( x + 11 )}{( x - 3 ) ( 2 x + 1 )}

What is expand e^{2t}*t^2*U(t-3) ?
The solution to expand e^{2t}*t^2*U(t-3) is e^{2t}t^3U-3e^{2t}t^2U