Darlene wrote this proof of the identity (x + y)2 - (x - y)2 = 4xy. Which of the following is a justification for Step 3 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
Accepted Solution
A:
Solution:we are given thatDarlene wrote this proof of the identity (x + y)2 - (x - y)2 = 4xy.we have been asked to find Which of the following is a justification for Step 3 of her proof? Step 3 of her proof is [tex] Step 3: (x^2 + xy + xy + y^2) - (x^2 - xy - xy + y^2) = (x^2 + 2xy + y2) - (x^2 - 2xy + y^2) [/tex]As we can observe inside each of the paranthesis only like terms have been added. It mean the required justification is C. Combining like terms