# Factoring Simple Expressions

Need some basic practice recognizing products and sums? Recognizing Products and Sums; Identifying Factors and Terms

Need some basic practice identifying common factors? Identifying Common Factors

*factor an expression*means to take the expression and rename it as a product.

That is, to *factor an expression* means to write the expression as a product.

## Examples

The expression
$\,ab + ac\,$ is a *sum*,
since the last operation is addition.
The expression $\,a(b + c)\,$ is a *product*,
since the last operation is multiplication.
The process of factoring took us from the sum $\,ab + ac\,$ to the product $\,a(b + c)\,.$

Notice that $\,\,ab + ac = a(b + c)\,\,$ is just the distributive law, backwards!

In going from the name $\,ab + ac\,$ to the name $\, a(b + c) \,,$ the common factor ($\,a\,$) is first identified, and written down. Next, an opening parenthesis ‘ ( ’ is inserted. Then, the remaining parts of each term are written down. Finally, the closing parenthesis ‘ ) ’ is inserted.

Note: In the exercises below, exponents are typed in using the ‘^’ key. For example, $\, x^2(5 - y^2) \,$ is typed in as: x^2(5 - y^2)

Note: The product $\,(2x+1)(x-3)\,$ can also be written as $\,(x-3)(2x+1)\,.$ There is no convention here about which name is ‘best’. The exercise below recognizes both answers.