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

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

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

simplify

(x - y - 1)^{2}

x - y - 2 x - y + 1

Solution steps

(x - y - 1)^{2}

Apply Perfect Square Formula:

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

(x - y - 1)^{2} = (x - y)^{2} - 2 x - y \cdot 1 + 1^{2}

= (x - y)^{2} - 2 x - y \cdot 1 + 1^{2}

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

- 2 x - y \cdot 1 = - 2 x - y

1^{2} = 1

= x - y - 2 x - y + 1

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