What is expand 12e^{2t}*(3e^{2t}+6te^{2t}) ?

The solution to expand 12e^{2t}*(3e^{2t}+6te^{2t}) is 36e^{4t}+72e^{4t}t

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expand 12e^{2t}*(3e^{2t}+6te^{2t})

expand

12 e^{2 t} \cdot (3 e^{2 t} + 6 t e^{2 t})

36 e^{4 t} + 72 e^{4 t} t

Solution steps

12 e^{2 t} (3 e^{2 t} + 6 t e^{2 t})

= 12 e^{2 t} (3 e^{2 t} + 6 e^{2 t} t)

Apply the distributive law:

a (b + c) = ab + a c

a = 12 e^{2 t}, b = 3 e^{2 t}, c = 6 t e^{2 t}

= 12 e^{2 t} \cdot 3 e^{2 t} + 12 e^{2 t} \cdot 6 t e^{2 t}

= 12 \cdot 3 e^{2 t} e^{2 t} + 12 \cdot 6 e^{2 t} e^{2 t} t

Simplify

12 \cdot 3 e^{2 t} e^{2 t} + 12 \cdot 6 e^{2 t} e^{2 t} t : 36 e^{4 t} + 72 e^{4 t} t

= 36 e^{4 t} + 72 e^{4 t} t

\frac{1}{( s + 1 ) ( 2 s + 1 ) ( 3 s + 1 )}

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

\frac{1}{( ( a + h ) ^{2} + 1 )}

(1 - \frac{δ}{R})^{2}

\frac{4 x}{( x ^{2} + 1 ) ( x ^{2} + 2 x + 3 )}

What is expand 12e^{2t}*(3e^{2t}+6te^{2t}) ?
The solution to expand 12e^{2t}*(3e^{2t}+6te^{2t}) is 36e^{4t}+72e^{4t}t