What is the simplified form of (6x^2-4xy+2y^2-3x^2+9xy-y^2)?

Correct answer: (3x^2+5xy+y^2)

The direct answer is option A: \(3x^2+5xy+y^2\). To simplify an algebraic expression, combine only like terms. Like terms have the same variables with the same powers. First combine the \(x^2\) terms: \(6x^2-3x^2=3x^2\). Next combine the \(xy\) terms: \(-4xy+9xy=5xy\). Finally combine the \(y^2\) terms: \(2y^2-y^2=y^2\). Therefore the result is \(3x^2+5xy+y^2\). Option A is correct because it contains all three correctly combined terms. Option B has \(9x^2\), but the coefficient should be 3. Option C has \(-13xy\), but \(-4+9=5\), not -13. Option D gives incorrect coefficients for several terms. Remember: collect identical variable parts separately; never combine \(x^2\), \(xy\), and \(y^2\) as though they were the same.