# Math problem

1. Dec 28, 2012

### Wardlaw

Math problem!!!

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

Is (a+b)^2 ALWAYS equal to a^2+2ab+b^2?

2. Relevant equations

3. The attempt at a solution

2. Dec 28, 2012

### Dick

Re: Math problem!!!

Yes, if a and b represent objects in a commutative ring like the real numbers. If multiplication is not commutative, (for example a and b are matrices) then (a+b)^2=a^2+ab+ba+b^2 which is not generally the same. Why do you ask?

Last edited: Dec 28, 2012
3. Dec 28, 2012

### Mentallic

Re: Math problem!!!

If a and b are numbers as they should be if you're in high school, then yes, they're always equal. Why?

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

And I'm sure you can expand out the rest.

4. Dec 28, 2012

### SteamKing

Staff Emeritus
Re: Math problem!!!

Math formulas generally don't have expiration or 'black out' dates.

5. Dec 29, 2012

### MrWarlock616

Re: Math problem!!!

Well this was weird.. xD

6. Dec 29, 2012

### Wardlaw

Re: Math problem!!!

Is p+q+r=p+q+s never valid?

7. Dec 29, 2012

### MrWarlock616

Re: Math problem!!!

Only if r=s. Why do you want to know?