SOLUTION: Adapted from Algebra and Trigonometry by P. Forester but I have a textbook by Holt Prove the product of two negatives is a positive (-x)(-y) = (-1*x)(-1*y) Identity

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Question 156521: Adapted from Algebra and Trigonometry by P. Forester but I have a textbook by Holt
Prove the product of two negatives is a positive
(-x)(-y) = (-1*x)(-1*y) Identity
= (-1)[x*(-1)](y) distributive
= (-1)[-1*x](y)
= [-1*(-1)] xy
= 1*xy
= xy
therefore (-x)(-y) = xy
Answer by stanbon(48526) (Show Source):
You can put this solution on YOUR website!
We know -(xy) + xy = 0 by definition of additive inverse
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Now show -(-xy) + xy = 0 where x and y are both positive numbers.
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(-x)(-y) = (-1)(x)(-y) -----associative law
(-1)[(x)(-y)]=(-1)(-xy)--associative law & (positive * negative is negative)
(-1)(-xy) + (-xy) = 0 definition of additive inverse
Therefore (-1)(-xy) = xy ... uniqueness of additive inverse
Therefore (-x)(-y) = xy ... argument above
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Cheers,
Stan H.