What is expand 2e^{2t}(4e^{2t}+4te^{2t}) ?

The solution to expand 2e^{2t}(4e^{2t}+4te^{2t}) is 8e^{4t}+8e^{4t}t

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expand 2e^{2t}(4e^{2t}+4te^{2t})

expand

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

8 e^{4 t} + 8 e^{4 t} t

Solution steps

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

= 2 e^{2 t} (4 e^{2 t} + 4 e^{2 t} t)

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

Simplify

2 \cdot 4 e^{2 t} e^{2 t} + 2 \cdot 4 e^{2 t} e^{2 t} t : 8 e^{4 t} + 8 e^{4 t} t

= 8 e^{4 t} + 8 e^{4 t} t

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What is expand 2e^{2t}(4e^{2t}+4te^{2t}) ?
The solution to expand 2e^{2t}(4e^{2t}+4te^{2t}) is 8e^{4t}+8e^{4t}t