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

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

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simplify (sqrt(x^2+1)+x)^2

simplify

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

2 - x^{2} (2 - x^{2})

(x - 2 i) (x + 2 i) (x - 3)^{2}

20000 (x - 5) e^{- \frac{x}{4} - 1}

- 3 a l e f t (- 2 a - 4)

(2 + 3)^{2}

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