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9 August, 08:49

Darlene wrote this proof of the identity (x + y) 2 - (x - y) 2 = 4xy. Which of the following is a justification for Step 5 of her proof?

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  1. 9 August, 08:53
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    From the given steps:

    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

    The justification for Step 3 of her proof is:

    D. Distributive property
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