B) -(xy-1)+(12xy+x^2-4)-(xy+x^2-2)

To simplify the given expression, we need to combine like terms. Let's break it down step by step:<br /><br />Given expression:<br />\[ -(xy - 1) + (12xy + x^2 - 4) - (xy + x^2 - 2) \]<br /><br />First, distribute the negative sign in the first and third terms:<br />\[ -xy + 1 + 12xy + x^2 - 4 - xy - x^2 + 2 \]<br /><br />Next, combine like terms:<br />- Combine the \(xy\) terms: \(-xy + 12xy - xy = 10xy\)<br />- Combine the constant terms: \(1 - 4 + 2 = -1\)<br />- The \(x^2\) terms cancel each other out: \(x^2 - x^2 = 0\)<br /><br />So, the simplified expression is:<br />\[ 10xy - 1 \]<br /><br />Therefore, the answer is:<br />\[ 10xy - 1 \]