What is (sqrt(x+\sqrt{y)}-sqrt(x-\sqrt{y)})^2 ?

The solution to (sqrt(x+\sqrt{y)}-sqrt(x-\sqrt{y)})^2 is 2x-2sqrt(x+\sqrt{y)}sqrt(x-\sqrt{y)}

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simplify (sqrt(x+\sqrt{y)}-sqrt(x-\sqrt{y)})^2

simplify

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

2 x - 2 x + y x - y

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

= 2 x - 2 x + y x - y

(x^{2} - 2 x) f r a c e^{2 x} 2

tan (x) (tan (x) + 1)

(x + \frac{1}{x ^{2}})^{7}

(e^{3 x} + 3 e^{3 x} x) e^{3 x}

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

What is (sqrt(x+\sqrt{y)}-sqrt(x-\sqrt{y)})^2 ?
The solution to (sqrt(x+\sqrt{y)}-sqrt(x-\sqrt{y)})^2 is 2x-2sqrt(x+\sqrt{y)}sqrt(x-\sqrt{y)}