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

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

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

simplify

(x - x - 1)^{2}

2 x - 2 x x - 1 - 1

Solution steps

(x - x - 1)^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

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

= 2 x - 2 x x - 1 - 1

(x - 13)^{2}

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

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

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

(4 x + \frac{1}{3}) (4 x - \frac{1}{2})

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