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

Question

.(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.