1. The problem is to understand the difference between adding and subtracting polynomials. 2. When adding polynomials, we combine like terms by adding their coefficients. For example, if we have $3x^2 + 2x$ and $5x^2 + 4$, we add the coefficients of like terms: $3x^2 + 5x^2 = 8x^2$ and $2x + 0 = 2x$, so the sum is $8x^2 + 2x + 4$. 3. When subtracting polynomials, we distribute the negative sign (which is equivalent to multiplying by $-1$) to each term of the polynomial being subtracted. For example, if we subtract $5x^2 + 4$ from $3x^2 + 2x$, we write it as $3x^2 + 2x - (5x^2 + 4)$. 4. Distributing the negative sign gives $3x^2 + 2x - 5x^2 - 4$. 5. Then, we combine like terms: $3x^2 - 5x^2 = -2x^2$, $2x$ remains, and $-4$ remains, so the result is $-2x^2 + 2x - 4$. 6. Therefore, the key difference is that subtraction requires distributing the negative sign to all terms of the polynomial being subtracted before combining like terms.