Question

Find the terms of the expression. $$ x-y-7$$

Short answer

The terms of the expression \(x-y-7\) are 'x', '-y' and '-7'

Step-by-step solution

Identify the terms

In an algebraic expression, terms are separated by addition or subtraction operations. In the expression \(x-y-7\), based on this rule we can identify three terms: 'x', '-y', '-7'

Key concepts

Identifying Terms in Algebra

Understanding the fundamental building blocks of algebra starts with a crucial skill: identifying terms in an algebraic expression. In essence, a term is an individual part of an expression or equation, usually consisting of constants and/or variables, and can include numbers, variables (letters that represent numbers), or the product of numbers and variables. These terms are typically separated by plus (+) or minus (-) signs.

Let's take a closer look at an example. Consider the algebraic expression \( x-y-7 \). Here, we identify its three terms by searching for the components that are separated by the subtraction signs. The first term is \( x \), simply representing a variable that can take any number value. The second term is \( -y \), indicating the negative of a variable. It's essential to note that the negative sign is part of this term. The third term is \( -7 \), a constant that stands alone without a variable. Recognizing each term independently is a stepping stone to mastering algebraic manipulations and operations.

Subtraction in Algebraic Expressions

Subtraction in algebraic expressions isn't vastly different from subtraction in basic arithmetic; however, it introduces the need for keen attention to signs and the placement of terms. Algebra elevates the importance of understanding both the numerical value and the sign associated with a term. When dealing with the expression \( x-y-7 \), we handle subtraction by considering each term's sign.

The subtraction operation can transform a positive term into a negative one, as seen with the term \( -y \) and \( -7 \) in our example. This process is essentially adding the inverse of the term that comes after the subtraction sign. For practical purposes, one can think of \( x-y-7 \) as \( x + (-y) + (-7) \), which exhibits the operation with more clarity. This explanation can help us visualize why the terms 'y' and '7' carry their negative signs, providing a framework that will prove invaluable as algebraic problems increase in complexity.

Algebraic Terms Separation

Identifying and separating terms in an algebraic expression is a skill that provides the groundwork for further calculations, such as simplifying, adding, or multiplying expressions. An expression like \( x-y-7 \) is composed of individual terms that can often be manipulated independently of one another. Separating terms means recognizing and potentially isolating each term to work with them one by one.

To separate terms effectively, one has to understand the concept of 'like terms' and 'unlike terms.' Like terms are terms that have the same variable parts raised to the same power, for instance, \( 2x \) and \( -3x \). Unlike terms, such as \( x \) and \( -7 \) in our expression, do not share this commonality and cannot be combined through addition or subtraction. By parsing out 'like terms' and 'unlike terms,' we can simplify expressions, solve equations, and understand how different components of an algebraic expression can affect the overall value. For beginners, practicing term separation is invaluable, as it builds the analytical approach needed for tackling more elaborate algebraic problems.