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

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) = (-1x)(-1y) Identity

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(75887) (Show Source): You can put this solution on YOUR website!
We know -(xy) + xy = 0 by definition of additive inverse
--------------------------
Now show -(-xy) + xy = 0 where x and y are both positive numbers.
--------------------------
(-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
==================
Cheers,
Stan H.

RELATED QUESTIONS
I am not very good with Algebra. My question is: Add. -3 + (-4) + (+12) I do not... (answered by tutorcecilia)

Just taking algebra again after 21 years. Have a simple question. How do I solve... (answered by ptaylor,sofiyacherni)

text book by holt pre-algebra page 297 please help in finding the radis of a circle with... (answered by solver91311)

A coin bank contains $17.00 in pennies and nickels. If there are 1140 coins in the bank,... (answered by checkley71)

I am working out of the Holt Algebra 1 text book. This problem is from a work- sheet... (answered by stanbon)

This question is from a Holt textbook. I honestly have no idea how to begin. We are... (answered by lynnlo)

I usually do really well with most of these mixture problems, but this one has me stuck: (answered by kev82)

HOW CAN I FIND THE VALUE OF A VARIABLE. THIS PROBLEM IS IN MY GEOMTRY TEXTBOOK .I TAKE... (answered by rapaljer)

Prove that the product of two odd numbers is odd, using an indirect proof and a proof by... (answered by josgarithmetic,ikleyn)