What is expand (9e^{3t})(18e^{3t}t+12e^{3t}) ?

The solution to expand (9e^{3t})(18e^{3t}t+12e^{3t}) is 162e^{6t}t+108e^{6t}

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expand (9e^{3t})(18e^{3t}t+12e^{3t})

expand

(9 e^{3 t}) (18 e^{3 t} t + 12 e^{3 t})

162 e^{6 t} t + 108 e^{6 t}

Solution steps

(9 e^{3 t}) (18 e^{3 t} t + 12 e^{3 t})

Apply the distributive law:

a (b + c) = ab + a c

a = (9 e^{3 t}), b = 18 e^{3 t} t, c = 12 e^{3 t}

= (9 e^{3 t}) \cdot 18 e^{3 t} t + (9 e^{3 t}) \cdot 12 e^{3 t}

= 18 e^{3 t} t (9 e^{3 t}) + 12 e^{3 t} (9 e^{3 t})

Simplify

18 e^{3 t} t (9 e^{3 t}) + 12 e^{3 t} (9 e^{3 t}) : 162 e^{6 t} t + 108 e^{6 t}

= 162 e^{6 t} t + 108 e^{6 t}

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What is expand (9e^{3t})(18e^{3t}t+12e^{3t}) ?
The solution to expand (9e^{3t})(18e^{3t}t+12e^{3t}) is 162e^{6t}t+108e^{6t}