apply the associative and commutative properties that generate expression equivalent to 2 (a + 5) + 4 (2a + 3) - 10

Answer 1

To apply the associative property, we can group the terms within parentheses together. To apply the commutative property, we can rearrange the terms within each parentheses.

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

Applying the associative property within each parentheses:
= 2a + 10 + 8a + 12 - 10

Rearranging the terms within each parentheses using the commutative property:
= 2a + 8a + 10 + 12 - 10

Combining like terms:
= (2a + 8a) + (10 + 12) - 10

= 10a + 22 - 10

= 10a + 12