https://file.aiquickdraw.com/mathbot/file/1729821963295ffbb6xl6.jpg

The given expression is:

\[
-6x^2 + 4 + 7x^2 - 12 - 12x
\]

We will simplify this expression step by step:

### Step 1: Combine like terms
- Combine the \(x^2\) terms:
  \[
  -6x^2 + 7x^2 = (7 - 6)x^2 = x^2
  \]
- Combine the constant terms:
  \[
  4 - 12 = -8
  \]
- The \(x\) term remains as it is:
  \[
  -12x
  \]

### Step 2: Final simplified expression
After combining like terms, the expression becomes:
\[
x^2 - 12x - 8
\]

Would you like further details or have any questions about the steps? 

Here are 5 related questions you might explore:
1. How do you factor a quadratic expression like \(x^2 - 12x - 8\)?
2. What is the importance of combining like terms in polynomial expressions?
3. How can you solve for \(x\) in the equation \(x^2 - 12x - 8 = 0\)?
4. What are the key properties of quadratic functions and their graphs?
5. How does the degree of a polynomial affect its shape and behavior?

**Tip**: When simplifying algebraic expressions, always group terms by their powers to make the process easier.

Simplify the following expression: -6x^2 + 4 + 7x^2 - 12 - 12x

Learn how to simplify the polynomial expression -6x^2 + 4 + 7x^2 - 12 - 12x. This step-by-step solution covers key algebraic concepts like combining like terms, suitable for students in Grades 6-8.

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