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