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.

Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Identifying Common Factors

(an even number, please)