Apply the Associative and Commutative Properties to generate an expression equivalent to 2(a+5)+4(2a+3)−10 .
To apply the Associative and Commutative Properties, we can first rearrange the terms in a way that allows us to group like terms together.
Starting with the given expression:
2(a + 5) + 4(2a + 3) - 10
Using the Commutative Property of Addition, we can rearrange the terms:
2(a) + 2(5) + 4(2a) + 4(3) - 10
Multiplying the coefficients:
2a + 10 + 8a + 12 - 10
Using the Associative Property of Addition, we can group the like terms together:
(2a + 8a) + (10 + 12) - 10
Adding the like terms within each parentheses:
10a + 22 - 10
Simplifying further:
10a + 12
Therefore, the expression equivalent to 2(a+5) + 4(2a+3) - 10 using the Associative and Commutative Properties is 10a + 12.