Part A: To fill the blank correctly in Statement 3, we need to use the Distributive Property. The Distributive Property states that for any real numbers a, b, and c, the product of a and the sum of b and c can be written as the sum of the product of a and b and the product of a and c.
Therefore, the correct statement to fill the blank in Statement 3 is:
(a+b)(a+b) = a(a+b) + b(a+b)
Part B: The analysis of the proof correctly describing the efficiency of steps is:
B: Using the distributive property first was unnecessary in Step 3 as it was undone in Step 4.
Explanation: In Step 3, the Distributive Property was used to expand the expression (a+b)(a+b) into a(a+b) + b(a+b). However, in Step 4, the like terms ab and ab are combined into 2ab, effectively undoing the Distributive Property. Therefore, using the Distributive Property first in Step 3 was unnecessary and did not contribute to the efficiency of the proof.