# Recognizing Products and Sums; Identifying Factors and Terms

*product*is an expression where the last operation is multiplication. In a product, the things being multiplied are called the

*factors*.

A

*sum*is an expression where the last operation is addition. In a sum, the things being added are called the

*terms*.

As an example, consider the expression $\,a(b+c)\,.$ If numbers are chosen for $\,a\,,$ $\,b\,,$ and $\,c\,,$ then here is the order that computations would be done:

- Add $\,b\,$ and $\,c\,$
- (Pre)-multiply this sum by $\,a\,$

Notice that the *last*
operation done is multiplication.
Thus, the expression $\,a(b+c)\,$ is a product.
The factors are $\,a\,$ and $\,(b+c)\,.$

As a second example, consider the expression $\,ab + c\,.$ Given numbers $\,a\,,$ $\,b\,,$ and $\,c\,,$ here is the order that computations would be done:

- Multiply $\,a\,$ and $\,b\,$
- Add this result to $\,c\,$

Notice that the *last*
operation done is addition.
Thus, the expression $\,ab+c\,$ is a sum.
The terms are $\,ab\,$ and $\,c\,.$

## Examples

User input is in bold.

The expression $\,3xy\,$ is a product.

The factors are: 3, x, y

Note: The factors must be listed in order from left to right, and must be separated by commas.

The expression $\,-4x(x+2)\,$ is a product.

The factors are: -4, x, x+2

Note: Do not use parentheses when listing factors. (That is, don't put the x+2 inside parentheses.)

The expression $\,5x - y + 1\,$ is a sum.

The terms are: 5x, -y, 1

Note: The terms must be listed in order from left to right, and must be separated by commas. Remember that a term includes its sign.

The expression $\,x^2 + 2y^3 - 7\,$ is a sum.

The **terms** are:
x^2, 2y^3, -7

Note: Exponents are input using the ‘ ^ ’ key.