Problem 63 - Elementary and Intermediate Algebra

Question

List the terms in each expression. $$ x+x y z+19 $$

Step-by-Step Solution

Answer

The terms are \( x \), \( xyz \), and \( 19 \).

Step 1: Identify the Expression

The given expression is \( x + xyz + 19 \).

Step 2: Understand What Terms Are

Terms in an algebraic expression are the parts of the expression that are added or subtracted. Each term can contain variables, constants, or both.

Step 3: Break Down the Expression

In the expression \( x + xyz + 19 \), identify each part separated by the plus (+) sign.

Step 4: List the Terms

The terms in the expression \( x + xyz + 19 \) are: \( x \), \( xyz \), and \( 19 \).

Key Concepts

Terms in Algebra

In algebra, it's important to understand what terms are.
Terms are individual parts of an algebraic expression.
They are usually separated by plus (+) or minus (-) signs.
Each term can include:

• Variables (letters that represent numbers)
• Constants (fixed numbers)
• Coefficients (numbers multiplying the variables)

For example, in the expression \(3x + 4y - 5\), the terms are \(3x\), \(4y\), and \(-5\).
Each part is distinct and contributes to the algebraic expression in its own way.

Variables and Constants

An algebraic expression often includes both variables and constants.
Variables are symbols (usually letters) that represent unknown numbers.
Common variables include \(x\), \(y\), and \(z\).
They can take on different values depending on the situation.
Constants, on the other hand, are fixed numbers that do not change.
In the expression \(x + xyz + 19\), the variables are \(x\) and \(xyz\), while the constant is \(19\).
Variables and constants together form terms in algebra and help us create meaningful mathematical relationships.

Identifying Terms

Identifying terms in an algebraic expression is a vital skill.
To do this, look for the plus (+) or minus (-) signs that separate the terms.
For example, in the given expression \(x + xyz + 19\), the terms are separated by plus signs.
So, we identify the terms:

• First term: \(x\)
• Second term: \(xyz\)
• Third term: \(19\)

In this way, we can clearly see the parts that make up the entire expression.
Recognizing individual terms helps in performing algebraic operations and solving equations effectively.