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

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

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simplify (sqrt(x+y)-sqrt(x-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

\frac{2 x ^{2} - 13 x + 22}{( x - 2 ) ^{2}}

\frac{12}{( s + 2 ) ^{2} ( s + 4 )}

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

4 (u v^{3} + w^{4}) (u + v e^{w})^{3}

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