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?

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

Answer 1

ANSWER:-

Given: (a-b) 2

prove :(a-b) 2= a 2-2 ab +b 2

STATEMENTS REASONS

1 (a-b)2 Given

2 (a-b) (a-b) rewrite a power as a product  of the base

3 ____[blanks 1] __distributive property

4 a 2- ab -ab+ b 2 distributive property

5 a 2 -2 ab +b 2 __ [ 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?

D: In order to simplify the expression in the previous step, the Commutative Property of Addition must be applied.

D: In order to simplify the expression in the previous step, the like terms must be combined.

D: In order to simplify the expression in the previous step, the Distributive Property 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.

C: In order to multiply the binomials in the previous step, the like terms must be combined.

B: Commutative Property of Addition

B: Distributive Property

B: Combine like terms.

A: a(a−b)−b(a−b)

A: a(a+b)−b(a+b)

A: a(a−b)−a(a−b)