AIR MATH

Math Question

Darlene wrote this proof of the identity \( (x+y)^{2}-(x-y)^{2}=4 x y \). 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: \( (x+y)(x+y)-(x-y)(x-y)=\left(x^{2}+x y+x y+y^{2}\right)-\left(x^{2}-x y-x y+y^{2}\right) \) Step 3: \( \left(x^{2}+x y+x y+y^{2}\right)-\left(x^{2}-x y-x y+y^{2}\right)=\left(x^{2}+2 x y+y^{2}\right)-\left(x^{2}-2 x y+y^{2}\right) \) Step 4: \( \left(x^{2}+2 x y+y^{2}\right)-\left(x^{2}-2 x y+y^{2}\right)=x^{2}+2 x y+y^{2}-x^{2}+2 x y-y^{2} \) Step 5: \( x^{2}+2 x y+y^{2}-x^{2}+2 x y-y^{2}=4 x y \) A. Distributive property B. Reflexive property C. Definition of squaring a binomial D. Combining like terms

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