Question

Apply the Associative and Commutative Properties to generate an expression equivalent to 2(a+5)+4(2a+3)−10
.(1 point)
Responses

12a+10
12 A plus 10

9a +12
9 A plus 12

10a +22
10 A plus 22

10a +12

Answer 1

To simplify the expression \( 2(a+5) + 4(2a+3) - 10 \) using the associative and commutative properties, let's go through the steps:

1. **Distribute the terms**:
\[
2(a + 5) = 2a + 10
\]
\[
4(2a + 3) = 8a + 12
\]

2. **Combine the results**:
\[
2a + 10 + 8a + 12 - 10
\]

Now combine like terms:
- Combine the \( a \) terms:
\[
2a + 8a = 10a
\]
- Combine the constant terms:
\[
10 + 12 - 10 = 12
\]

Thus, the final expression is:
\[
10a + 12
\]

So the equivalent expression is \( 10a + 12 \).

The correct response is **10a + 12**.