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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

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

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

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