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 group the terms with parentheses together regardless of their coefficients or variables. To apply the commutative property, we can rearrange the order of the terms.

Starting with the expression: 2(a+5) + 4(2a+3) - 10

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

Next, let's combine like terms:
= (2a + 8a) + (10 + 12 - 10) + 10
= 10a + 12 + 10
= 10a + 22

Therefore, the expression 2(a+5) + 4(2a+3) - 10, with the associative and commutative properties applied, is equivalent to 10a + 22.