https://file.aiquickdraw.com/mathbot/file/1726062035449nxasqwkg.jpg

The equation in the image is:

\[
(5 - 6y - 4y^2) - (-2y^2 + 5y + 12y^3)
\]

Now, let's simplify the expression step by step.

### Step 1: Distribute the negative sign across the second parenthesis
\[
(5 - 6y - 4y^2) - (-2y^2 + 5y + 12y^3)
\]
becomes:
\[
5 - 6y - 4y^2 + 2y^2 - 5y - 12y^3
\]

### Step 2: Combine like terms
- The constants: \(5\)
- The \(y^1\) terms: \(-6y - 5y = -11y\)
- The \(y^2\) terms: \(-4y^2 + 2y^2 = -2y^2\)
- The \(y^3\) term: \(-12y^3\)

Thus, the simplified expression is:
\[
5 - 11y - 2y^2 - 12y^3
\]

Would you like any additional clarification or details? Here are some related questions:

1. How do you factor cubic expressions?
2. Can this expression be solved for \(y\)?
3. What does each term represent graphically?
4. How does distributing negative signs impact equations?
5. What are other methods to simplify polynomials?

**Tip:** Always remember to handle negative signs carefully when simplifying expressions.

Learn how to simplify the polynomial expression (5 - 6y - 4y^2) - (-2y^2 + 5y + 12y^3) by combining like terms and distributing the negative sign. This detailed solution walks through each step, making it suitable for students in Grades 9-12.

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