Counter Proof? Negative times a Negative = Positive

[Fran3]

I have reviewed other "proofs" of how a negative number times a negative number equals a positive number ...

But how do I explain this?

Given: (-2 * -4) = X
Then: (-1)* (2 * 4) = X via factoring out negative one
So: (-1)*(8) = X
And so X = -8

Is my simple algebra wrong or what?

Thanks for any help.

 

[Otis]

Given: (-2 * -4)
Then: (-1)* (2 * 4)

Hello Fran. That factorization is not correct. Here's how we evaluate the product (-2 * -4) by factoring:

(-2)(-4) = (-1)(2)(-1)(4) = (-1)(-1)(2)(4) = (1)(8) = 8

I used the Commutative Property of Multiplication, to change the order of the factors.

Perhaps, you were thinking about how we factor sums or differences:

-2 – 4 = (-2 + -4) = (-1)(2 + 4) = (-1)(6) = -6


[imath]\;[/imath]

 

[Steven G]

I have reviewed other "proofs" of how a negative number times a negative number equals a positive number ...

But how do I explain this?

Given: (-2 * -4) = X
Then: (-1)* (2 * 4) = X via factoring out negative one
So: (-1)*(8) = X
And so X = -8

Is my simple algebra wrong or what?

Thanks for any help.

You clearly stated that you factored out -1. Now, if you factor out -1 from -2, you get -2 = (-1)*2. So (-2*-4) = (-2)*(-4)= (-1)*2*(-4)≠(-1)(-2*4). You lost the - sign for the -4.