Add the following expressions:3x²y + 4x³y – xy² + x²y², 11x²y – x³y + 5x²y², 5x³y – x²y² + 7x²y – 3xy²

To add the given expressions, we combine like terms. Like terms are those that have the same variables and powers.

The given expressions are:

1. 3x²y + 4x³y – xy² + x²y²
2. 11x²y – x³y + 5x²y²
3. 5x³y – x²y² + 7x²y – 3xy²

First, let's identify the like terms across all three expressions:

• x²y terms: 3x²y, 11x²y, 7x²y
• x³y terms: 4x³y, -x³y, 5x³y
• x²y² terms: x²y², 5x²y², -x²y²
• xy² terms: -xy², -3xy²

Now, let's add these like terms together:

• x²y: 3x²y + 11x²y + 7x²y = 21x²y
• x³y: 4x³y - x³y + 5x³y = 8x³y
• x²y²: x²y² + 5x²y² - x²y² = 5x²y²
• xy²: -xy² - 3xy² = -4xy²

So, the sum of the given expressions is 21x²y + 8x³y + 5x²y² - 4xy².