# Proof of attribute in fields

1. Nov 2, 2012

### fastidious1

1. The problem statement, all variables and given/known data

I need to prove that in any field :

(a+b)^2=a^2+2ab+b^2

2. Relevant equations

3. The attempt at a solution
i dont know how to start the proof ... I know all the attributes of fields but i got stuck

2. Nov 2, 2012

### tiny-tim

welcome to pf!

hi fastidious1! welcome to pf!
commutative, associative, … ?

3. Nov 2, 2012

### fastidious1

ok, and what about a*a=a^2 ?
do I need to supply a proof for this product?
and a*b+a*b=2ab
can i say that it is axioms?
tnx!

4. Nov 2, 2012

### tiny-tim

no, that's just the definition of (or another name for) a2 !
imo, the question is a bit weird …

"2" isn't in any of the axioms

"2" needs to be defined, and the question hasn't defined it

i think you'll have to define it! (how? )​

5. Nov 2, 2012

### fastidious1

what is 2 ?
2=1+1
in any field the number 1 is exist and in any field addition is already defined so we have 1+1 we call it 2. we can also can to call to all the following numbers 3'4
it is doesn't mean that any field include all the natural number. it is possible that in some condition that 2=0(like in field F2) does it correct ? tnx

6. Nov 2, 2012

### tiny-tim

hi fastidious1!
yup, that's perfect

there's a 1, and 1 + 1 must be something, so we call it 2 …

of course, you still need to prove that a + a = 2a !
yes …

but it doesn't matter, because the original equation would still be true! :tongue2: