Tính : (3x³-x²y+2xy+3)×(x²y-2xy-2)

To multiply these two polynomials, we can use the distributive property and combine like terms.

(3x³ - x²y + 2xy + 3) × (x²y - 2xy - 2)

First, let's multiply each term in the first polynomial by the second polynomial:

3x³ × (x²y - 2xy - 2) = 3x⁵y - 6x⁴y - 6x³
-x²y × (x²y - 2xy - 2) = -x⁴y² + 2x³y² + 2x²y
2xy × (x²y - 2xy - 2) = 2x³y² - 4x²y² - 4xy
3 × (x²y - 2xy - 2) = 3x²y - 6xy - 6

Now, let's combine like terms:

(3x⁵y - 6x⁴y - 6x³) + (-x⁴y² + 2x³y² + 2x²y) + (2x³y² - 4x²y² - 4xy) + (3x²y - 6xy - 6)

Simplifying further:

3x⁵y - 6x⁴y - 6x³ - x⁴y² + 2x³y² + 2x²y + 2x³y² - 4x²y² - 4xy + 3x²y - 6xy - 6

Combining like terms again:

3x⁵y - x⁴y² - 6x⁴y + 4x³y² - 4x²y² - 4xy + 3x²y - 12xy - 6

Therefore, the product of (3x³ - x²y + 2xy + 3) and (x²y - 2xy - 2) is:

3x⁵y - x⁴y² - 6x⁴y + 4x³y² - 4x²y² - 4xy + 3x²y - 12xy - 6