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

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

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

expand

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

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

Solution steps

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

Apply FOIL method:

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

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

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

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

Simplify

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

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

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