# Recognizing Products and Sums; Identifying Factors and Terms

DEFINITIONS product, factors, sum, terms
A 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.

The expression
is a:
PRODUCT
SUM
The
FACTORS
TERMS
are: