Question

This problem has four parts, Part A, Part B, Part C, and Part D. Read the proof, and then answer all four parts.

Given: (a−b)2

Prove: (a−b)2=a2−2ab+b2

Statements Reasons
1. (a−b)2 Given
2. (a−b)(a−b) Rewrite a power as a product of the base
3. _[blank 1]_ Distributive Property
4. a2−ab−ab+b2 Distributive Property
5. a2−2ab+b2 _[blank 2]_










Part A: Which statement correctly fills in blank 1 to complete the proof?

Part B: Which reason correctly fills in blank 2 to complete the proof?

Part C: Why is Statement 3 valid?

Part D: Why is Reason 5 valid?

A: a(a−b)−a(a−b)
D: In order to simplify the expression in the previous step, the Commutative Property of Addition must be applied.
C: In order to multiply the binomials in the previous step, one binomial must be distributed to each term in the other binomial.
A: a(a−b)−b(a−b)
C: In order to multiply the binomials in the previous step, the like terms must be combined.
A: a(a+b)−b(a+b)
D: In order to simplify the expression in the previous step, the Distributive Property must be applied.
D: In order to simplify the expression in the previous step, the like terms must be combined.
B: Combine like terms.
B: Commutative Property of Addition
B: Distributive Property

Answer 1

Much ado about nothing

(a-b)^2
= (a-b)(a-b)
= a^2 - ab - ab + b^2
= a^2 - 2ab + b^2