Simplify the Expression: xy - 3x² + 2y² - 6x²

To solve this problem, we'll follow these steps:

• Step 1: Identify like terms.
• Step 2: Simplify the expression by combining like terms.

Let's simplify the given expression:
The expression is given as $x \times y - 3x \times x + 2y \times y - 6x^2$.

First, simplify each term:
- $x \times y$ remains $xy$.
- $3x \times x$ simplifies to $3x^2$.
- So, the expression becomes $xy - 3x^2 + 2y^2 - 6x^2$.

Next, combine like terms:
- Combine the $x^2$ terms: $-3x^2 - 6x^2 = -9x^2$.
- The $xy$ term and $2y^2$ term are unique and remain as they are.

This results in the simplified expression: $xy - 9x^2 + 2y^2$.

Upon comparing this simplification with the answer choices, the correct option is:

$xy - 9x^2 + 2y^2$

Therefore, the solution to the problem is $xy - 9x^2 + 2y^2$.