Problem: Simplify the expression $5x^2 + 7x - 2x^2 + 9y + 8y^2 - 3x$. 1. Identify like terms. First, group like terms by variable and degree: $5x^2$ and $-2x^2$ are like terms; $7x$ and $-3x$ are like terms; $8y^2$ and $9y$ are terms in $y$ of different degrees. 2. Combine the $x^2$ terms. $5x^2 - 2x^2 = 3x^2$. 3. Combine the $x$ terms. $7x - 3x = 4x$. 4. Keep the $y$ terms. $8y^2$ and $9y$ cannot combine with $x$ terms, so they remain unchanged. 5. Write the simplified polynomial. Combine the results to get $3x^2 + 4x + 8y^2 + 9y$. Final answer: $3x^2 + 4x + 8y^2 + 9y$.