What is expand t^5e^{2t}d(t-2) ?

The solution to expand t^5e^{2t}d(t-2) is e^{2t}t^6d-2e^{2t}t^5d

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expand t^5e^{2t}d(t-2)

expand

t^{5} e^{2 t} d (t - 2)

e^{2 t} t^{6} d - 2 e^{2 t} t^{5} d

Solution steps

t^{5} e^{2 t} d (t - 2)

= e^{2 t} t^{5} d (t - 2)

Apply the distributive law:

a (b - c) = ab - a c

a = t^{5} e^{2 t} d, b = t, c = 2

= t^{5} e^{2 t} d t - t^{5} e^{2 t} d \cdot 2

= e^{2 t} t^{5} t d - 2 e^{2 t} t^{5} d

e^{2 t} t^{5} t d = e^{2 t} t^{6} d

= e^{2 t} t^{6} d - 2 e^{2 t} t^{5} d

\frac{- 2 x + h}{( x ^{2} ) ( x + h ) ^{2}}

e^{t^{2}} (4 t^{3} - 7 t^{2} + 9 t)

\frac{( y + 1 ) ( y + 8 )}{( y + 2 ) ( y - 6 )}

(x^{2} + 2 y) d y

a (4 x - 6 y = - 3)

What is expand t^5e^{2t}d(t-2) ?
The solution to expand t^5e^{2t}d(t-2) is e^{2t}t^6d-2e^{2t}t^5d