# Thread: Negative numbers squared

1. ## 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.

2. Hello !

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

I hope this is clear enough..

3. 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 $- 4^2 = -16$.

4. 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

5. BIDMAS!

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

And of course, rooting counts as indices.