Is (a+b)^2 Always Equal to a^2+2ab+b^2?

[Wardlaw]

Math problem!

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[Dick]

Homework Statement

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

Homework Equations

The Attempt at a Solution

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?

 

[Mentallic]

Homework Statement

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

Homework Equations

The Attempt at a Solution

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.

 

[SteamKing]

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

 

[MrWarlock616]

Well this was weird.. xD

 

[Wardlaw]

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

 

[MrWarlock616]

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

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