Let's solve the expression step by step:

\[
15[y-4]-2[y-9]+5[y+6]
\]

### Step 1: Distribute the terms inside the brackets.
\[
15[y-4] = 15y - 60
\]
\[
-2[y-9] = -2y + 18
\]
\[
5[y+6] = 5y + 30
\]

### Step 2: Combine all the distributed terms.
\[
15y - 60 - 2y + 18 + 5y + 30
\]

### Step 3: Combine like terms.
- \(15y - 2y + 5y = 18y\)
- \(-60 + 18 + 30 = -12\)

So, the simplified expression is:
\[
18y - 12
\]

Do you want more details or have any questions?

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Here are 5 follow-up questions to deepen your understanding:

1. What happens if the expression is set equal to a value, like \(15[y-4]-2[y-9]+5[y+6] = 0\)?
2. How would the answer change if we multiplied all terms by a constant factor?
3. Can you rewrite the expression in terms of another variable, like \(x\) instead of \(y\)?
4. What if we added an exponent to one of the brackets, such as \(15[y-4]^2\)?
5. How would you solve this if you were given a specific value for \(y\)?

**Tip:** Always distribute first when simplifying expressions involving parentheses!

Learn how to simplify the algebraic expression 15[y-4]-2[y-9]+5[y+6] step-by-step. This solution demonstrates the use of the distributive property and combining like terms to simplify the expression to 18y - 12. Suitable for students in Grades 6-8.

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