To solve the expression \((y - 8)(3y - 4 + 7x)\), we'll distribute \((y - 8)\) across each term inside the parentheses.

The expression is:

\[
(y - 8)(3y - 4 + 7x)
\]

Expanding this using the distributive property:

1. Distribute \(y\) to each term in the second parentheses:
   \[
   y \cdot 3y = 3y^2
   \]
   \[
   y \cdot (-4) = -4y
   \]
   \[
   y \cdot 7x = 7xy
   \]

2. Distribute \(-8\) to each term in the second parentheses:
   \[
   -8 \cdot 3y = -24y
   \]
   \[
   -8 \cdot (-4) = 32
   \]
   \[
   -8 \cdot 7x = -56x
   \]

Now combine all these results:

\[
3y^2 - 4y + 7xy - 24y + 32 - 56x
\]

Combine like terms:

- Combine the \(y\) terms: \(-4y - 24y = -28y\)

Thus, the final expression is:

\[
3y^2 - 28y + 7xy + 32 - 56x
\]

This is the expanded and simplified form of the given expression.

---

Would you like further details or have any questions? 

Here are 5 related questions that might interest you:

1. How do you factor quadratic expressions like \(3y^2 - 28y + 32\)?
2. What are the steps to simplify expressions involving multiple variables?
3. How does the distributive property work in more complex algebraic expressions?
4. Can this expression be set equal to zero to solve for \(y\) or \(x\)?
5. How would this expression change if additional terms were added?

**Tip:** When expanding expressions, always combine like terms to simplify your results. This helps in further steps, such as solving equations or factoring.

Learn how to expand and simplify the expression (y - 8)(3y - 4 + 7x) using the distributive property and combining like terms. This problem involves algebraic manipulation, suitable for students in Grades 7-9.

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