To solve the expression \((19x^2 + 9x + 16) - (5x^2 + 12x + 7)\), follow these steps:

1. Distribute the negative sign across the second polynomial:
   \[
   19x^2 + 9x + 16 - 5x^2 - 12x - 7
   \]

2. Combine like terms:
   - \(19x^2 - 5x^2 = 14x^2\)
   - \(9x - 12x = -3x\)
   - \(16 - 7 = 9\)

So, the simplified expression is:
\[
14x^2 - 3x + 9
\]

Would you like more details or have any questions?

Here are some related questions:
1. How would the expression change if the first polynomial had a different constant term?
2. What happens if you add instead of subtract these two polynomials?
3. How can you factor the simplified expression \(14x^2 - 3x + 9\)?
4. What if the coefficients of \(x^2\) in both polynomials were equal?
5. How do you solve the equation if \(14x^2 - 3x + 9 = 0\)?

**Tip:** When subtracting polynomials, always distribute the negative sign before combining like terms.

The query submitted by the user: (19x^2 + 9x + 16) - (5x^2 + 12x + 7)

Learn how to simplify the polynomial expression (19x^2 + 9x + 16) - (5x^2 + 12x + 7) with a detailed step-by-step solution. This problem covers key algebraic concepts, including the subtraction of polynomials and the distributive property. Suitable for students in Grades 8-10.

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