# Negative numbers squared

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• Jun 1st 2008, 02:55 PM
TomSmith
Negative numbers squared
This seems like a a pretty basic problem, but i've been revising maths all day and i can't get my head round it.

When something appears in an equation as '-a²' does that mean '-a*-a' or '-(a²)', and how can you tell the difference. I had thought it meant the former (when using things like the quadratic formula), but thinking about it, in equations such as using the cosine rule, I use the latter form all the time. I have an exam tomorrow and I don't want to make a stupid mistake.

Thanks in advance for any help offered.
• Jun 1st 2008, 03:00 PM
Moo
Hello !

Quote:

Originally Posted by TomSmith
This seems like a a pretty basic problem, but i've been revising maths all day and i can't get my head round it.

When something appears in an equation as '-a²' does that mean '-a*-a' or '-(a²)', and how can you tell the difference. I had thought it meant the former (when using things like the quadratic formula), but thinking about it, in equations such as using the cosine rule, I use the latter form all the time. I have an exam tomorrow and I don't want to make a stupid mistake.

Thanks in advance for any help offered.

This is where parenthesis make all the difference :)

The product and the division have priority to the sum or substraction.

Therefore, you do the multiplication a*a first, and then you "substract" it (multiplying by (-1) is just like substracting to 0).

So yeah, it'd be -(a²).

If it had been (-a)², it would yield (-a)*(-a), which is a² (Wink)

I hope this is clear enough..
• Jun 1st 2008, 03:47 PM
Plato
The notation $- a$ means the additive inverse of $a$.
The rules for operations require that exponentiation is done first.
Thus $- a^2$ is the additive inverse of $a^2$: so $- 4^2 = -16$.
• Jun 1st 2008, 05:01 PM
Mathstud28
Quote:

Originally Posted by TomSmith
This seems like a a pretty basic problem, but i've been revising maths all day and i can't get my head round it.

When something appears in an equation as '-a²' does that mean '-a*-a' or '-(a²)', and how can you tell the difference. I had thought it meant the former (when using things like the quadratic formula), but thinking about it, in equations such as using the cosine rule, I use the latter form all the time. I have an exam tomorrow and I don't want to make a stupid mistake.

Thanks in advance for any help offered.

Also, I don't know if you are a physics student, but when you are presented with an equation it is almost illogical to have $-x^2=(-x)^2$ because this implies that whenever you see -x² it is the same as x², which seems illogical
• Jun 1st 2008, 05:05 PM
sean.1986
BIDMAS!

Brackets, Indices, Division, Multiplication, Addition and Subtraction.

And of course, rooting counts as indices.