What is expand (e^{3t}+3e^{3t}t)^2 ?

The solution to expand (e^{3t}+3e^{3t}t)^2 is e^{6t}+6e^{6t}t+9e^{6t}t^2

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expand (e^{3t}+3e^{3t}t)^2

expand

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

e^{6 t} + 6 e^{6 t} t + 9 e^{6 t} t^{2}

Solution steps

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

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = e^{3 t}, b = 3 e^{3 t} t

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

Simplify

(e^{3 t})^{2} + 2 e^{3 t} \cdot 3 e^{3 t} t + (3 e^{3 t} t)^{2} : e^{6 t} + 6 e^{6 t} t + 9 e^{6 t} t^{2}

= e^{6 t} + 6 e^{6 t} t + 9 e^{6 t} t^{2}

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What is expand (e^{3t}+3e^{3t}t)^2 ?
The solution to expand (e^{3t}+3e^{3t}t)^2 is e^{6t}+6e^{6t}t+9e^{6t}t^2