Simplify the given polynomial expression:
2. $\left(x^{2}-5 x+6\right)-\left(2 x^{2}-x-3\right)$

Answer

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Answer

$\boxed{-x^{2} - 4x + 9}$ is the final simplified form of the given polynomial expression.

Steps

Step 1 ：Distribute the negative sign to the terms in the second parentheses: $x^{2}-5x+6 - (2x^{2}-x-3)$ becomes $x^{2}-5x+6 -2x^{2}+x+3$.

Step 2 ：Combine like terms: $x^{2}-5x+6 -2x^{2}+x+3$ becomes $-x^{2} - 4x + 9$.

Step 3 ：$\boxed{-x^{2} - 4x + 9}$ is the final simplified form of the given polynomial expression.