Question

Use the distributive property to write an equivalent expression without parentheses.

9 (a + 8)

Check all that apply.
Distribute 9, by multiplication, to the variable, a, and to the constant, 8.
Write the two multiplications, 9(a) + 9(8)
The expression 9(a) is written as 9a.
The expression 9(8) equals 72.
The equivalent expression is 9a + 8.
The equivalent expression is 9a + 72.

Answer 1

To use the distributive property on the expression \(9(a + 8)\), we'll follow these steps:

1. **Distribute 9**: Multiply 9 by both the variable \(a\) and the constant \(8\):
\[
9(a + 8) = 9(a) + 9(8)
\]

2. **Simplify the expressions**:
- The expression \(9(a)\) simplifies to \(9a\).
- The expression \(9(8)\) equals \(72\).

Combining these results, we get:
\[
9a + 72
\]

Now, checking each statement from the original question:

- **Distribute 9, by multiplication, to the variable, a, and to the constant, 8.** ✅
- **Write the two multiplications, 9(a) + 9(8)** ✅
- **The expression 9(a) is written as 9a.** ✅
- **The expression 9(8) equals 72.** ✅
- **The equivalent expression is 9a + 8.** ❌ (Incorrect, the correct expression is \(9a + 72\))
- **The equivalent expression is 9a + 72.** ✅

Thus, the correct equivalent expression is **9a + 72**.