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Using the distributive property of multiplication over addition, x*[x - x] = x*[x + (-x)] = x*x + x*(-x)LHS = x*0 = 0
RHS = x^2 + x*(-x)
Therefore x*(-x) = -x^2 and, by commutativity, -x*x = -x^2
Next
-x*[x - x] = -x*[x + (-x)] = -x*x + -x*(-x)
LHS = -x*0 = 0
RHS = -x^2 + -x*(-x)
Therefore (RHS) -x times -x = +x^2 (LHS).
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