Lesson 2 in Udacity's College Algebra course is about expressions. It starts by going back over the commutative property of both addition and multiplication. As a reminder the commutative property just means that the order of terms or factors doesn't matter. So a+b+c is the same thing as b+a+c and a*b*c is the same as c*a*b and so on. When combining like terms it is important to remember that they need to have the same variable and power (x cannot be added to x squared). So 2x+3x+4-2y can be simplified to 5x-2y+4 but no further.
A polynomial is an expression with constants and/or variables that are combined using addition, subtraction and multiplication, where all exponents are non-negative integers. The degree of a term is the sum of exponents on the variables in that term. So x squared times y cubed would have a degree of 5 because the exponents 2 and 3 add up to 5. The degree of a polynomial is equal to the highest degree of any of its terms. the standard form of a polynomial is to put the terms in order from highest degree to lowest degree.