Many times in this class we will use identities, i.e., statements of equality that are true for all values of the variables involved.
For example, $$x+y = y + x$$ for all real (or complex) numbers $x$ and $y$. (This particular identity is called the commutative law of addition . It does not matter in what sequence we add two numbers.) In the next few problems, enter the string "=" if the identity holds and the string "N" (or "n") if it does not. In all cases, omit the quotation marks.
To get the hang of this we start with the above identity:

$x+y$ $y+x$.

(Enter an equality sign.)

Here is an example of a non-identity (enter an upper case N):

$x+y$ $x-y$.

Many algebraic mistakes are caused by equating algebraic expressions that are not identical.
The next few problems illustrate widely used identities and frequently believed non-identities. You could conceivably get credit for these problems by rushing through the various possibilities, but you should pause each time that the answer is not what you expect and figure out why you were wrong and what is really going on. The benefits from those moments of thoughtfulness will be significant and long lasting!

Unless stated otherwise, identities need to hold for all real numbers. This includes positive and negative real numbers. We don't consider complex numbers.