Question

Question 4 of 40Darlene wrote this proof of the identity (x+y)2-(x-y)2 = 4xy Which of thefollowing is a justification for Step 5 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 + y)-(x²-xy- xy + y) = (x² + 2xy + y) - (x²-2xy + y²)Step 4: (x²+2xy + y) - (x²-2xy + y^²) = x² + 2xy + y²-x² + 2xy-j²Step 5: x²+2xy + y²-x² + 2xy-y²= 4xySUBMITA. Definition of squaring a binomialB. Distributive propertyC. Combining like termsOD. Reflexive property

Answer 1

The correct answer is option C. Combining like terms

At the end of step 4, she got:

`x²+2xy+y²-x²+2xy-y²`

We can rearrange this:

`x²-x²+y²-y²+2xy+2xy`

And we can clearly see that there is a pair of squared x of different signs, thus they cancel each other, and the same with the y's squared:

`(x²-x²)+(y²-y²)+2xy+2xy=0+0+4xy=4xy`