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 rearrange the terms within parentheses. To apply the commutative property, we can rearrange the order of the terms. Let's start:

2(a + 5) + 4(2a + 3) - 10

First, let's simplify the terms within the parentheses:
= 2a + 10 + 8a + 12 - 10

Next, we group the like terms together:
= (2a + 8a) + (10 + 12) - 10

Now, let's simplify further:
= 10a + 22 - 10

Finally, we combine the like terms:
= 10a + 12

Therefore, applying the associative and commutative properties to the expression 2(a+5) + 4(2a + 3) - 10 generates the equivalent expression 10a + 12.