# Why is -x*x=-y?

1. Mar 26, 2005

### Someone502

i tihnk this is a dumb question but why is -x*x=-y? i tried thinking about it like a arrays on a graph but it was kinda confusing.

2. Mar 27, 2005

### honestrosewater

You mean why the product of a negative and positive is negative? This follows from the axioms.
(-x)y + xy =[see note 1] (-x + x)y =[2] 0y =[3] 0. Since (-x)y + xy = 0,[4] (-x)y = -(xy).
1. by the distributive property
3. (0x = 0) is a theorem
4. (If x + y = 0, then x = -y) is a theorem

Last edited: Mar 27, 2005
3. Mar 27, 2005

### HallsofIvy

"-x*x= -y"? Well, that's not always true- it depends on what x and y are!

If you mean "why is a negative number times a positive number negative?" then honestrosewater gave a pretty good answer.
(what would DIShonestrosewater smell like?)

If you are wondering about the distinction between (-x)2 and -x2, it's a matter of the parentheses: (-2)2 means (-2)(-2), a product of two negative numbers, which is positive: 4. -22 means to FIRST square: 22= 4, THEN make it negative: -4.

Last edited by a moderator: Mar 27, 2005
4. Mar 28, 2005