What is expand (1+2e^{2t})^2 ?

The solution to expand (1+2e^{2t})^2 is 1+4e^{2t}+4e^{4t}

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expand (1+2e^{2t})^2

expand

(1 + 2 e^{2 t})^{2}

1 + 4 e^{2 t} + 4 e^{4 t}

Solution steps

(1 + 2 e^{2 t})^{2}

Apply Perfect Square Formula:

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

a = 1, b = 2 e^{2 t}

= 1^{2} + 2 \cdot 1 \cdot 2 e^{2 t} + (2 e^{2 t})^{2}

Simplify

1^{2} + 2 \cdot 1 \cdot 2 e^{2 t} + (2 e^{2 t})^{2} : 1 + 4 e^{2 t} + 4 e^{4 t}

= 1 + 4 e^{2 t} + 4 e^{4 t}

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What is expand (1+2e^{2t})^2 ?
The solution to expand (1+2e^{2t})^2 is 1+4e^{2t}+4e^{4t}