Problem 41 - Beginning and Intermediate Algebra

Question

Identify each group of terms as like or unlike. \(x, y\)

Step-by-Step Solution

Answer

Unlike terms

Step 1: Understand the Problem

The task is to identify whether the given terms are 'like' or 'unlike'. Like terms have the same variable parts, while unlike terms have different variable parts.

Step 2: Analyze the Given Terms

Examine the given terms: The terms provided are 'x' and 'y'.

Step 3: Compare the Variables

Compare the variables in the given terms. 'x' and 'y' are different variables.

Step 4: Conclude

Since 'x' and 'y' have different variable parts, they are unlike terms.

Key Concepts

Variables

In algebra, variables are symbols that represent numbers or values we don't yet know. Most commonly, these symbols are letters, like 'x', 'y', or 'z'. For example, in the equation \(x + 2 = 5\), 'x' is a variable that we need to solve for.

Variables can hold different values depending on the context of the problem. If we change the value of a variable, it affects the entire equation or expression it is a part of.

Knowing what variables are and how they function is key to understanding algebraic expressions and equations. They help us generalize mathematical problems and find solutions by substituting values.

Algebraic Terms

In algebra, terms are the building blocks of expressions and equations. A term can be a single number (constant), a variable, or the product of numbers and variables. For instance, in the expression \(3x + 4y - 5\), there are three terms: \(3x\), \(4y\), and \(-5\).

Each term is separated by a plus (+) or minus (-) sign. When dealing with algebraic terms, it's essential to recognize 'coefficients' and 'variables':

• The coefficient is the number multiplying the variable (e.g., in \(3x\), 3 is the coefficient).
• The variable is the letter representing an unknown value (e.g., 'x' in \(3x\)).

By understanding these parts, you can simplify and solve algebraic expressions more effectively.

Comparison of Terms

When comparing terms in algebra, we look at their variable parts to determine if they are 'like' or 'unlike' terms.

Like Terms: These are terms with the same variable parts raised to the same power. For example, \(3x\) and \(5x\) are like terms because both terms have the variable 'x' raised to the same power. Like terms can be combined through addition or subtraction.

Unlike Terms: These are terms with different variable parts or the same variable raised to different powers. For example, \(x\) and \(y\) are unlike terms, as they contain different variables. Likewise, \(x^2\) and 'x' are also unlike terms because the variables are raised to different powers.

In the exercise, we have 'x' and 'y'. Since these terms have different variable parts, we classify them as unlike terms. Understanding the distinction helps in simplifying and solving algebraic expressions.