Q. Use the Distributive Property to Expand \( 3(x + 8) \)

Problem

Use the Distributive Property to expand \(3(x + 8)\).

Step-by-step explanation

1. State the Distributive Property.

   The Distributive Property says that for any numbers or expressions \(a\), \(b\), and \(c\),
   \[a(b + c) = ab + ac.\]
   This means you multiply the factor outside the parentheses by each term inside the parentheses separately, then add the results.

2. Identify the pieces in this problem.

   Compare \(3(x + 8)\) with \(a(b + c)\). Here \(a = 3\), \(b = x\), and \(c = 8\).

3. Multiply the outside factor by the first term inside the parentheses.

   Compute \(3 \cdot x\). Multiplying a number by a variable gives a coefficient:
   \[3 \cdot x = 3x.\]
   This is the result of distributing 3 to the term \(x\).

4. Multiply the outside factor by the second term inside the parentheses.

   Compute \(3 \cdot 8\):
   \[3 \cdot 8 = 24.\]
   This is the result of distributing 3 to the term \(8\).

5. Add the two results.

   Combine the two products to get the expanded form:
   \[3x + 24.\]

Check (optional verification)

Pick a value for \(x\), for example \(x = 2\). Evaluate both the original and the expanded expressions:

• Original: \(3(2 + 8) = 3 \cdot 10 = 30.\)
• Expanded: \(3 \cdot 2 + 24 = 6 + 24 = 30.\)

Both give the same result, confirming the expansion is correct.

Final answer

\[3(x + 8) = 3x + 24\]