Algebra I

Sometimes algebra problems will ask you to combine polynomials with multiplication.  These problems can look intimidating, but they are very similar to multiplying binomials (remember FOIL?).  The secret to these problems is being methodical and making sure that every term in each polynomial is multiplied by every term in each of the other polynomials. 

Remember that:

In algebra problems, you will often have to combine polynomials with addition or subtraction. These problems can look confusing, but they are fairly simple. You just have to do them carefully, paying particular attention to negative signs.

There is an associative property of addition, so you can remove the parentheses and just combine the like terms from each polynomial.  Pay chose attention to:

We all know how to multiply, but sometimes multiplying expressions that contain variables can get confusing.  The main point you want to remember is that multiplication works the same, no matter what you are multiplying:

Fractions can be undefined. An undefined fraction is a fraction that doesn't make sense.  Simply: an undefined fraction is a fraction with a zero denominator. 

Let's think about it:

If a have a pizza and cut it into 6 pieces, I can give you 1 piece ($\dfrac{1}{6}$) or 4 pieces ($\dfrac{4}{6}$).

Because rational expressions are just fractions with variables, the process of simplifying rational expressions is conceptually the same as the process of dividing numeric fractions. You can divide the top and the bottom of the rational expression by the same number. Because dividing the numerator and denominator by the same number is the same as dividing by 1, it leaves you with an equivalent fraction.

Expressions are different from equations in that they don't have equal signs. The contain variables, but because they are not equal to anything, you can't solve for the variable.

However, sometimes you will be asked to evaluate expressions when you are given the value of the variable (or several variables).

Every linear equation can be represented by a line (thus, the name linear equation!).  The equations take the form of $y=mx+b$.  (There are other ways to write linear equations, but $y=mx+b$ is the easiest form for graphing and finding the graphs of a line.   

$y=mx+b$ has several components: