The properties used to simplify the expression 4 + 3(9 + 2) are:
- Distributive property of multiplication over addition: This property is used to expand the expression 3(9 + 2) into 3 × 9 + 3 × 2.
- Associative property of addition: This property is used to regroup the terms in the expression 4 + 27 + 6 as (4 + 6) + 27.
- Identity property of addition: This property is used to simplify the expression (4 + 6) to 10.
Therefore, the properties used to simplify the expression are distributive property of multiplication over addition, associative property of addition, and identity property of addition.
The answer choices that apply are:
- Distributive property
- Associative property of addition
- Identity property of addition