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

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

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

simplify

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

\frac{5 x ^{2} + 20 x + 6}{x ( x + 1 ) ^{2}}

\frac{x + 3}{( x - 1 ) ( x ^{2} + 1 )}

(x + 2) (x^{2} - 4)

(3 x^{2} y - 6 x) d x + (x^{3} + 2 y) d y

(x - 1) \cdot e^{x}

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