What is expand e^t*(6e^t-8te^t) ?

The solution to expand e^t*(6e^t-8te^t) is 6e^{2t}-8e^{2t}t

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expand e^t*(6e^t-8te^t)

expand

e^{t} \cdot (6 e^{t} - 8 t e^{t})

6 e^{2 t} - 8 e^{2 t} t

Solution steps

e^{t} (6 e^{t} - 8 t e^{t})

= e^{t} (6 e^{t} - 8 e^{t} t)

Apply the distributive law:

a (b - c) = ab - a c

a = e^{t}, b = 6 e^{t}, c = 8 t e^{t}

= e^{t} \cdot 6 e^{t} - e^{t} \cdot 8 t e^{t}

= 6 e^{t} e^{t} - 8 e^{t} e^{t} t

Simplify

6 e^{t} e^{t} - 8 e^{t} e^{t} t : 6 e^{2 t} - 8 e^{2 t} t

= 6 e^{2 t} - 8 e^{2 t} t

\frac{8 ( 2 x + 1 ) ( x + 1 )}{3 x ^{2}}

(x - 2 y = 6, 3) (x - 6 y = 18)

\frac{5 ( 11257 - 75 )}{64}

2 \frac{1}{4} (- 15.2)

(x + 1) d y - (3 y + (x + 1)^{4}) d x

What is expand e^t*(6e^t-8te^t) ?
The solution to expand e^t*(6e^t-8te^t) is 6e^{2t}-8e^{2t}t