Algebraic Expressions and Their Uses

This course is about algebraic expressions, which are terms joined by plus and minus signs. It is for students who already know terms, co-efficients and like terms from the earlier course Introduction to Algebra.

The lessons build up in order. You begin with what an algebraic expression is, and the five types: monomial, binomial, trinomial, polynomial and multinomial. Next comes the degree, one number that measures the size of a term. Then you put numbers back in place of the letters and work the expression out. The last two lessons handle whole expressions: adding and subtracting them, then multiplying them.

By the end you will be able to:

• name an expression as a monomial, binomial, trinomial, polynomial or multinomial, and say why $\displaystyle \frac{5}{x} + 2$ is not a polynomial
• find the degree of a term by adding the powers of its letters, and the degree of a polynomial by taking the greatest of those
• explain why the degree of $5$ is $0$, and why the degree of $0$ is undefined
• substitute a value for every letter, putting brackets round a negative one, and tell $x^{2}$ apart from $2x$
• add and subtract expressions along a line or in columns, changing every sign inside a bracket you take away
• multiply term by term, adding the powers of a repeated letter, and use a grid so that no pair is missed