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

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

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

simplify

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

(cos (4 t) + cos (3 t))^{2}

(1 - 3 y i)^{2}

3 (x + Δ x)

P (- 2, - 3) Q (3, 4)

(- e^{- t} cos (t) - e^{- t} sin (t))^{2}

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