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 the terms as follows:

2(a + 5) + 4(2a + 3) - 10 = 2a + 10 + 8a + 12 - 10

To apply the commutative property, we can rearrange the order of the terms:

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

Now, we can simplify the expression inside each set of parentheses:

(2a + 8a) + (10 + 12) - 10 = 10a + 22 - 10

Finally, we can combine like terms to obtain the simplified expression:

10a + 22 - 10 = 10a + 12