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

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

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

expand

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

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

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 e^{x} + 1 + 2

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

(\frac{( \frac{5 y - 3}{2} )}{2})^{2}

- \frac{2}{( x + 3 ) ^{2}}

(5 t + e^{- 2 t} cos (7 t)) u (t)

(x^{3} + \frac{3}{x})^{8}

\frac{10 x + 6}{( x - 3 ) ( x + 3 )}

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