Question

34 the expression below was step 1: 5(11x + 6x + 29) step 2: 5(17x + 29) step 3: 85x + 145 which properties were applied in steps 1 and 3, respectively? a commutative property, then distributive property b associative property, then distributive property c commutative property, then identity property d associative property, then commutative property

Explanation:

Step1: Identify property in Step1

Step1 rearranges parentheses: \(5(11z + 6z + 29) = 5[(11z + 6z) + 29]\) (though simplified to \(5(17z + 29)\)), which is associative property of addition (groups terms differently without changing order).

Step2: Identify property in Step3

Step3 multiplies 5 across \(17z + 29\): \(5(17z + 29) = 85z + 145\), which is distributive property (\(a(b + c) = ab + ac\)).

Step3: Match with options

Step1 uses associative property, Step3 uses distributive property—matches option B.

Answer:

B. associative property, then distributive property