Problem 14 - Algebra 1

Question

Find the terms of the expression. $$ 23-5 w-8 y $$

Step-by-Step Solution

Answer

The terms of the expression \( 23-5 w-8 y \) are 23, -5w, -8y.

Step 1: Identify First Term

The first term in the expression \( 23-5 w-8 y \) is 23. It is a constant term because it does not have a variable.

Step 2: Identify Second Term

The second term in the expression \( 23-5 w-8 y \) is \(-5 w\). This term consists of a coefficient, -5, and a variable, w.

Step 3: Identify Third Term

The third term in the expression \( 23-5 w-8 y \) is \(-8 y\). This term consists of a coefficient, -8, and a variable, y.

Key Concepts

Understanding the Terms of an Expression

In algebra, an expression can be seen as a combination of different components. These components are known as terms. When we look at an expression like \(23 - 5w - 8y\), we break it down into its individual terms. Each term represents a distinct part of the expression and is generally separated by addition or subtraction signs.

In our example, the terms are:

• 23
• -5w
• -8y

Terms can come in two forms: constant terms and variable terms. A constant term, like 23, doesn’t change its value because it has no attached variables. On the other hand, both \(-5w\) and \(-8y\) are variable terms because they contain variables alongside coefficients that modify these variables.

Exploring Coefficients

Coefficients are the numerical parts of the terms in an expression. They tell us how many times to multiply the variable by its value. Recognizing coefficients is crucial as they directly influence the magnitude and direction (positive or negative) of a term.

In the expression \(23 - 5w - 8y\), let's examine the coefficients more closely:

• In the term \(-5w\), the coefficient is \(-5\). This means 'subtract 5 times the value of \(w\)'.
• In the term \(-8y\), the coefficient is \(-8\). Similarly, this indicates 'subtract 8 times the value of \(y\)'.

Coefficients can be either positive or negative, influencing whether the term contributes positively or negatively to the total value of the expression. This addition or subtraction effect is key to accurately understanding and calculating expressions containing multiple terms.

The Role of Variables

Variables are symbols that represent unknown values. In algebra, they function as placeholders for numbers we might not know yet or that can change. Variables give an expression its dynamic, flexible quality, allowing us to form and solve equations.

In the expression \(23 - 5w - 8y\), the variables are:

• \(w\)
• \(y\)

These variables might stand for specific numbers depending on the context of the problem. For instance, \(w\) could represent the width of a rectangle, while \(y\) might denote a year's worth of time. The exact meaning of a variable usually depends on the problem you're trying to solve.

Using variables allows expressions to remain general, enabling them to model real-world scenarios where exact numbers are not known upfront. This makes variables a powerful tool in algebra and mathematics in general.