Factor this expression completely, and, then, place the factors in the proper location on the grid. Place the binomial factor first. x 3 + y 3

  (x-y)(x^2+xy+y^2) 
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the first parentheses contain the cubed root of both the terms so x and y respectively. second parentheses follows the formula (a^2 + ab + b^2) 
x corresponds to a and y corresponds to b. The signs are what change depending on what the original equation is. Since the original is a subtraction then the signs are -/+/+. you can remember it using the acronym SOAP. (S = same, O = opposite, AP = always positive) So the first sign is x - y (same as subtraction from original), the second and third are x^2 + xy + y^2 (opposite is a plus, and the last sign is always a positive)