To simplify the expression -5x^2 + 3xy - 6y^2 + 4x^2 - xy + 2y^2, we can combine like terms by adding or subtracting the coefficients of the same variables. First, let's combine the x^2 terms. We have -5x^2 + 4x^2 = -x^2. Next, let's combine the xy terms. We have 3xy - xy = 2xy. Finally, let's combine the y^2 terms. We have -6y^2 + 2y^2 = -4y^2. Putting it all together, the simplified expression is -x^2 + 2xy - 4y^2. Here's an example to help illustrate the process: Let's say x = 2 and y = 3. Using the original expression, we have: -5(2^2) + 3(2)(3) - 6(3^2) + 4(2^2) - (2)(3) + 2(3^2) Simplifying each term, we get: -5(4) + 3(2)(3) - 6(9) + 4(4) - 6 + 18 -20 + 18 - 54 + 16 - 6 + 18 -28 Using the simplified expression, we have: -(2^2) + 2(2)(3) - 4(3^2) -4 + 12 - 36 -28 As you can see, both expressions give us the same result of -28.
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