What is expand (10e^t+2)(t^4+1) ?

The solution to expand (10e^t+2)(t^4+1) is 10e^tt^4+10e^t+2t^4+2

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expand (10e^t+2)(t^4+1)

expand

(10 e^{t} + 2) (t^{4} + 1)

10 e^{t} t^{4} + 10 e^{t} + 2 t^{4} + 2

Solution steps

(10 e^{t} + 2) (t^{4} + 1)

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = 10 e^{t}, b = 2, c = t^{4}, d = 1

= 10 e^{t} t^{4} + 10 e^{t} \cdot 1 + 2 t^{4} + 2 \cdot 1

= 10 e^{t} t^{4} + 10 \cdot 1 \cdot e^{t} + 2 t^{4} + 2 \cdot 1

Simplify

10 e^{t} t^{4} + 10 \cdot 1 \cdot e^{t} + 2 t^{4} + 2 \cdot 1 : 10 e^{t} t^{4} + 10 e^{t} + 2 t^{4} + 2

= 10 e^{t} t^{4} + 10 e^{t} + 2 t^{4} + 2

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

\frac{4}{( s - 2 ) ( s ^{2} - 4 s - 4 )}

(0.25 + 0.75 e^{t})^{5}

\frac{( x + 1 ) y}{x}

(- 2, - 6) y (12, 18)

What is expand (10e^t+2)(t^4+1) ?
The solution to expand (10e^t+2)(t^4+1) is 10e^tt^4+10e^t+2t^4+2