Question

Darlene wrote this proof of the identity (x + y)2 - (x - y)2 = 4xy. Which of the following is a justification for Step 4 of her proof?

Step 1: (x + y)2 - (x - y)2 = (x + y)(x + y) - (x - y)(x - y)

Step 2: (x + y)(x + y) - (x - y)(x - y) = (x2 + xy + xy + y2) - (x2 - xy - xy + y2)

Step 3: (x2 + xy + xy + y2) - (x2 - xy - xy + y2) = (x2 + 2xy + y2) - (x2 - 2xy + y2)

Step 4: (x2 + 2xy + y2) - (x2 - 2xy + y2) = x2 + 2xy + y2 - x2 + 2xy - y2

Step 5: x2 + 2xy + y2 - x2 + 2xy - y2 = 4xy

A. Reflexive property
B. Definition of squaring a binomial
C. Combining like terms
D. Distributive property

Answer 1

Distributive property

Explanation:

Make sure your question is about step 4, not step 5

apex

Answer 2

Answer: D. Distributive Property

Explanation:

Step 4: (x² + 2xy + y²) - (x² - 2xy + y²) = x² + 2xy + y² - x² + 2xy - y²

The difference between the left side and the right side is that the sign of the underlined terms changed because -1 was distributed into them.