Brackets show multiplication. In $3(x+2)$, the 3 multiplies both $x$ and $2$, so expanding means removing brackets by multiplying.

Factorising is the reverse process. You look for something every term shares, called a common factor, and put it outside a bracket.

An expression has no equals sign, while an equation does. Like terms have the same variable part, so $5x$ and $2x$ combine but $5x$ and $2x^2$ do not.