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

10a +22
10 A plus 22

9a +12
9 A plus 12

10a +12

Answer 1

To simplify the expression \( 2(a+5) + 4(2a+3) - 10 \) using the Associative and Commutative Properties, we can proceed with the following steps:

1. Distribute the terms:

   \( 2(a + 5) = 2a + 10 \)

   \( 4(2a + 3) = 8a + 12 \)

   Now substituting these back into the expression:

   \( 2a + 10 + 8a + 12 - 10 \)

2. Combine like terms:

   • Combine the \( a \) terms:

   \( 2a + 8a = 10a \)

   • Combine the constant terms:

   \( 10 + 12 - 10 = 12 \)

   Putting it all together gives:

   \( 10a + 12 \)

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

The correct answer from the options provided is:

10a + 12.