https://file.aiquickdraw.com/mathbot/file/1725738973511vigapmcl.jpg

The expression provided is:

\[
-8(3w + 4) - 9(7w + 4)
\]

Let's simplify this step by step:

### Step 1: Distribute the -8 and -9 through the parentheses.
- Distribute \(-8\) to both terms inside \((3w + 4)\):
  \[
  -8 \times 3w = -24w, \quad -8 \times 4 = -32
  \]

- Distribute \(-9\) to both terms inside \((7w + 4)\):
  \[
  -9 \times 7w = -63w, \quad -9 \times 4 = -36
  \]

Now, the expression becomes:
\[
-24w - 32 - 63w - 36
\]

### Step 2: Combine like terms.
- Combine the \(w\)-terms: 
  \[
  -24w - 63w = -87w
  \]
  
- Combine the constant terms:
  \[
  -32 - 36 = -68
  \]

So, the simplified expression is:
\[
-87w - 68
\]

Would you like further details or explanations on any step?

Here are some related questions:
1. What are like terms, and how do you combine them?
2. How can distributing a negative number change the terms inside parentheses?
3. Can you explain what happens if there were positive signs between terms?
4. How would this expression change if one of the parentheses had a different sign?
5. Can you verify the simplification process by expanding other expressions?

**Tip:** Always remember to carefully distribute any negative sign across all terms inside parentheses.

Completely simplify the expression: -8(3w + 4) - 9(7w + 4)

Simplify the algebraic expression -8(3w + 4) - 9(7w + 4) using the distributive property and combining like terms. Step-by-step guide with explanations of key algebraic concepts. Ideal for students in Grades 7-10.

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