We can solve this question using matching operations (see the video lesson below )

Given:
Quantity A: \(x^2+y^2\)
Quantity B: \((x+y)^2\)

Expand and simplify Quantity B:
Quantity A: \(x^2+y^2\)
Quantity B: \(x^2+ 2xy + y^2\)

Subtract \(x^2\) from both quantities:
Quantity A: \(y^2\)
Quantity B: \(2xy + y^2\)

Subtract \(y^2\) from both quantities:
Quantity A: \(0\)
Quantity B: \(2xy\)

Divide both quantities by \(2\) to get:
Quantity A: \(0\)
Quantity B: \(xy\)

Since it's given that \(xy<0\), the correct answer is A.

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