# Thread: -x^2

1. ## -x^2

I'm sure this has been dealt with before, but I couldn't find an answer.

I remember having a discussion with a math professor a while back on solving -x^2, leaving it in disagreement. I was suddenly reminded that it remained unsolved in my mind, so I ask you all now.

In particular, the portion of the problem was to simplify -3^2. It was obvious in my mind that it should be -9, but I was told that it is in fact 9. Now, we had a fairly long discussion on it, but the point came down to whether it was a minus sign in front, and implicitly 0 - 3^2, or whether it indicated -3.

Perhaps I'm looking at it from more of a CS perspective, but I would have assumed (or liked to believe) that unless it was emphasized with parenthesis, that the minus sign should be separate.

What do you all think?

2. The standard order of operations used in simplifications is, from first to last:
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

Sidenote: multiplication and division have equal precedence, so you can alternate their ranks.

As for your particular question:

$\displaystyle -3^2 = -1 \times 3^2 = -1 \times 9 = -9$

3. I've always been taught that:

$\displaystyle -3^2=-9$ and $\displaystyle (-3)^2=9$

otherwise how would you tell the difference in a problem like: $\displaystyle -3^2-2$

4. Originally Posted by Stroodle
edit* oops. double post...
Just the placement of the negative sign. Its more harder in speech. Look for the pause. But it maths, whenever the equation is just -3^2, the answer is -9. Technically the equation is -1*3^2. If you use your order of operations, the power/exponent comes before the multiplication of -1. Therefore the equation reads -(3^2). If the -3 is in brackets then we do the brackets then the power.