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

Solution:

we are given that

Darlene 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

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

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

idk

step-by-step explanation: i just don't