What is expand (sqrt(1+e^x)-1)^2 ?

The solution to expand (sqrt(1+e^x)-1)^2 is e^x+2-2sqrt(e^x+1)

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expand (sqrt(1+e^x)-1)^2

expand

(1 + e^{x} - 1)^{2}

e^{x} + 2 - 2 e^{x} + 1

Solution steps

(1 + e^{x} - 1)^{2}

Apply Perfect Square Formula:

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

a = 1 + e^{x}, b = 1

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

Simplify

(1 + e^{x})^{2} - 2 1 + e^{x} \cdot 1 + 1^{2} : e^{x} + 2 - 2 e^{x} + 1

= e^{x} + 2 - 2 e^{x} + 1

(sin (ln (2 x)) - cos (ln (2 x)))^{2}

\frac{7 + 1}{3}

(2 - 1)^{4}

4 (7 - 1)

(200 - \frac{q}{2}) q

What is expand (sqrt(1+e^x)-1)^2 ?
The solution to expand (sqrt(1+e^x)-1)^2 is e^x+2-2sqrt(e^x+1)