Problem 58 - Algebra 1

Question

Find the terms of the expression. $$-3 x+5-8 y$$

Step-by-Step Solution

Answer

The terms of the expression \(-3x+5-8y\) are \(-3x\), \(5\), and \(-8y\).

Step 1: Identify the terms

Rewrite \(-3x + 5 - 8y\) as \((-3x) + (5) + (-8y)\). Each part separated by \(+\) or \(-\) signs is a term.

Step 2: List the terms

The three terms of the expression are \(\boxed{-3x,\ 5,\ -8y}\).

Key Concepts

Terms of an expression

Terms in an algebraic expression are the building blocks that come together to create the full expression. They are separated by plus (+) or minus (−) signs.
Each term consists of a number, a variable, or a combination of both. For example, in the expression

• \(-3x\) is a term that includes both a coefficient (-3) and a variable (x).
• \(+5\) is a term that is purely numerical.
• \(-8y\) is a term that includes both a coefficient (-8) and a variable (y).

Identifying these separate terms is crucial for simplifying and solving algebraic expressions since we deal with each independently during calculations. Understanding how terms work will help you manipulate expressions more easily.

Identifying terms

To identify the terms in an expression, one of the easiest methods is to look at the expression and find the addition or subtraction operations. These operate as natural breaks between the terms. In our example,

• The addition sign before \(+5\)
• The subtraction sign before \(-8y\)

These signs help us to segment the expression into different terms. Notably, terms are said to be 'like' when they have the same variables raised to the same powers. For example,

• In a different expression like \(4x-2x\), these are 'like terms'.

For learners, ensuring accuracy in spotting these terms is key for setting up maneuvers in algebraic calculations such as factorization and simplification.

Addition and subtraction in expressions

Addition and subtraction are crucial when working with and manipulating algebraic expressions. They dictate how terms are grouped together and modified. When adding or subtracting expressions, it's important to focus on the terms involved. Often, you will be asked to simplify an expression by combining like terms, which are terms that have the exact same variables. For example:

• When given \(3x + 6x\), these can be combined to give \(9x\).

On a broader level, understanding these operations allows you to simplify, expand, and solve equations and expressions efficiently. Always be mindful of keeping like terms together for efficient calculations.