What is expand (64+48t+12t^2+t^3)(e^t+te^t) ?

The solution to expand (64+48t+12t^2+t^3)(e^t+te^t) is 64e^t+112e^tt+60e^tt^2+13e^tt^3+e^tt^4

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expand (64+48t+12t^2+t^3)(e^t+te^t)

expand

(64 + 48 t + 12 t^{2} + t^{3}) (e^{t} + t e^{t})

64 e^{t} + 112 e^{t} t + 60 e^{t} t^{2} + 13 e^{t} t^{3} + e^{t} t^{4}

Solution steps

(64 + 48 t + 12 t^{2} + t^{3}) (e^{t} + t e^{t})

= (64 + 48 t + 12 t^{2} + t^{3}) (e^{t} + e^{t} t)

Distribute parentheses

= 64 e^{t} + 64 t e^{t} + 48 t e^{t} + 48 tt e^{t} + 12 t^{2} e^{t} + 12 t^{2} t e^{t} + t^{3} e^{t} + t^{3} t e^{t}

= 64 e^{t} + 64 e^{t} t + 48 e^{t} t + 48 e^{t} tt + 12 e^{t} t^{2} + 12 e^{t} t^{2} t + e^{t} t^{3} + e^{t} t^{3} t

Simplify

64 e^{t} + 64 e^{t} t + 48 e^{t} t + 48 e^{t} tt + 12 e^{t} t^{2} + 12 e^{t} t^{2} t + e^{t} t^{3} + e^{t} t^{3} t : 64 e^{t} + 112 e^{t} t + 60 e^{t} t^{2} + 13 e^{t} t^{3} + e^{t} t^{4}

= 64 e^{t} + 112 e^{t} t + 60 e^{t} t^{2} + 13 e^{t} t^{3} + e^{t} t^{4}

l im x \Rightarrow - 1 (3 x^{3} - 10) (x + 3)

(t + Δ t)^{2}

12 (A e^{4 x} + B e^{- 3 x})

\frac{3 ( 3 x + 2 ) ( x + 5 )}{( x - 1 ) ( x - 3 )}

e^{x} \cdot (x + 1)

What is expand (64+48t+12t^2+t^3)(e^t+te^t) ?
The solution to expand (64+48t+12t^2+t^3)(e^t+te^t) is 64e^t+112e^tt+60e^tt^2+13e^tt^3+e^tt^4