Question

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

Answer 1

To apply the Associative Property, we can group terms that have the same variables.

First, let's start with 2(a + 5) + 4(2a + 3) - 10.

We can distribute the 2 and 4, so it becomes:

2a + 10 + 8a + 12 - 10.

Then, we can simplify it by adding like terms:

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

This simplifies to:

10a + 22.

So, the expression equivalent to 2(a + 5) + 4(2a + 3) - 10 is 10a + 22.