For positive x and y, which expression is equivalent to (x^1/2-y^1/2)^2?

a. x-y
b. x+2sqrt(xy)+y
c. x-2sqrt(xy)+y

I need all of the steps to get to the right answer.
Thanks

(√x - √y)^2

= x - 2√(xy) + y

To simplify the expression (x^1/2 - y^1/2)^2, we can use the properties of exponents and expand the expression.

Step 1: Rewrite the exponents as fractional exponents.

(x^1/2 - y^1/2)^2 = (sqrt(x) - sqrt(y))^2

Step 2: Expand the expression using the pattern (a - b)^2 = a^2 - 2ab + b^2.

(x^1/2 - y^1/2)^2 = (sqrt(x))^2 - 2(sqrt(x))(sqrt(y)) + (sqrt(y))^2

Step 3: Simplify each term.

(sqrt(x))^2 = x
(sqrt(y))^2 = y
2(sqrt(x))(sqrt(y)) = 2√(xy)

Therefore:

(x^1/2 - y^1/2)^2 = x - 2√(xy) + y

So, the correct expression equivalent to (x^1/2 - y^1/2)^2 is Option C: x - 2√(xy) + y.