Self-expression can take a lot of forms. We can wear crazy clothes, create sculptures dedicated to Shmoop, and gab on and on about our innermost thoughts.
In math, an expression is pretty much any stand-alone mathematical formula. They're made up of constants and variables. They can't have dragons and fairies in them, though; those are just plain made-up.
We can simplify expressions by performing operations—like addition or applying exponents, not brain surgery—and gathering like terms together. Just be sure to follow the order of operations, PEMDAS. Notice again that brain surgery is not on the list. Put the saw away.
Equations are expressions linked together by an equal sign. They declare that their two sides, no matter how complicated or different-looking they may seem, are actually equal. It doesn't matter if we're dealing with constants on each side, one variable, two, or a hundred.
It also doesn't matter what those variables look like. They can be raised to a power, like x2, rising as a power, like 2x, or mangled up in some other crazy contraption.
Although the two parts of an equation are separated by an equal sign, this isn't like the Berlin Wall. Parts of the equation can pass over from one side to the other. Whether it's through addition, subtraction, multiplication, or division, we have to do it to both sides, though.