What is expand (2t+3t^2)*(4e^{t^2-1}+10t^4) ?

The solution to expand (2t+3t^2)*(4e^{t^2-1}+10t^4) is 8e^{t^2-1}t+20t^5+12e^{t^2-1}t^2+30t^6

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expand (2t+3t^2)*(4e^{t^2-1}+10t^4)

expand

(2 t + 3 t^{2}) \cdot (4 e^{t^{2} - 1} + 10 t^{4})

8 e^{t^{2} - 1} t + 20 t^{5} + 12 e^{t^{2} - 1} t^{2} + 30 t^{6}

Solution steps

(2 t + 3 t^{2}) (4 e^{t^{2} - 1} + 10 t^{4})

Apply FOIL method:

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

a = 2 t, b = 3 t^{2}, c = 4 e^{t^{2} - 1}, d = 10 t^{4}

= 2 t \cdot 4 e^{t^{2} - 1} + 2 t \cdot 10 t^{4} + 3 t^{2} \cdot 4 e^{t^{2} - 1} + 3 t^{2} \cdot 10 t^{4}

= 2 \cdot 4 e^{t^{2} - 1} t + 2 \cdot 10 t^{4} t + 3 \cdot 4 e^{t^{2} - 1} t^{2} + 3 \cdot 10 t^{4} t^{2}

Simplify

2 \cdot 4 e^{t^{2} - 1} t + 2 \cdot 10 t^{4} t + 3 \cdot 4 e^{t^{2} - 1} t^{2} + 3 \cdot 10 t^{4} t^{2} : 8 e^{t^{2} - 1} t + 20 t^{5} + 12 e^{t^{2} - 1} t^{2} + 30 t^{6}

= 8 e^{t^{2} - 1} t + 20 t^{5} + 12 e^{t^{2} - 1} t^{2} + 30 t^{6}

49 π (19 e^{20} + 1)

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\frac{3 x ^{2} ( 9 - x ^{2} )}{( 7 - 5 x ) ( 5 x ^{2} - 6 )}

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

What is expand (2t+3t^2)*(4e^{t^2-1}+10t^4) ?
The solution to expand (2t+3t^2)*(4e^{t^2-1}+10t^4) is 8e^{t^2-1}t+20t^5+12e^{t^2-1}t^2+30t^6