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Chapter 3: Problem 31

Simplify expression. \(r-3 r\)

Short Answer

Expert verified
The simplified expression is \(-2r\).

Step by step solution

01

Identify Like Terms

The expression given is \(r - 3r\). Both terms are 'like terms' since they contain the variable \(r\). Like terms in algebra are terms that contain the same variables raised to the same power.
02

Apply Subtraction to Like Terms

Since the terms are like terms, we can combine them by performing the subtraction: \(1r - 3r\). This is a simple arithmetic operation involving the coefficients of the terms.
03

Simplify the Result

Perform the subtraction: \(1r - 3r = -2r\). This is done by subtracting the coefficients \(1 - 3\) which equals \(-2\), resulting in \(-2r\). The variable \(r\) remains unchanged.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Like Terms
In algebra, it's important to know what "like terms" are because they allow you to easily simplify expressions. Like terms are terms that have the same variables raised to the same powers. The coefficients, which are the numbers in front of the variables, can be different.

In the expression given, both terms are like terms: the first is just 'r' and the second is '-3r'. They both contain the same variable, 'r', raised to the same power of 1.

Recognizing like terms gives you the gateway to combining them into a simpler form. You can only directly do arithmetic operations like addition or subtraction on like terms.
Simplification of Expressions
Simplifying algebraic expressions makes them easier to work with. When you simplify, you're essentially combining or translating the expression into a more compact form, so you avoid unnecessary complexity.

For example, in the expression \(r - 3r\), we simplify by combining like terms. Here, since both terms include the same variable, we can directly combine them by focusing on their coefficients.

When simplifying, always pay close attention to maintaining the integrity of each variable and its power. This ensures the expression remains equivalent to the original.
Coefficients in Algebra
The term 'coefficient' refers to the numerical factor that multiplies a variable in an algebraic term. In the expression \(r - 3r\), the coefficients are 1 and -3.

The coefficient helps in performing arithmetic operations like addition and subtraction on the terms. It's crucial for combining like terms effectively. In this case, subtract the coefficients: 1 and -3, which results in the new expression \(-2r\).

Remember, the variable itself remains unaffected during operations involving coefficients. The coefficient determines the scale or quantity of the variable, but not its inherent properties.

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Most popular questions from this chapter

Use the Distributive Property to write each expression as an equivalent algebraic expression. $$3(a+b)$$

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