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Chapter 15: Problem 75

Combine like terms. $$ 3 p-2 p $$

Short Answer

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p

Step by step solution

01

Identify the Terms

In the expression, identify the like terms. Here, both terms contain the variable 'p'. The terms are: - First Term: \(3p\) - Second Term: \(-2p\)
02

Combine the Coefficients

Since the terms are like terms, combine them by adding their coefficients (numerical values in front of the variable). For the terms \(3p\) and \(-2p\), combine the coefficients:\(3 + (-2) = 1\)
03

Write the Simplified Expression

Attach the coefficient from step 2 to the variable 'p'. This gives the simplified expression:\(1p\), which is commonly written as simply \(p\)

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Key Concepts

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

algebraic expressions
Algebraic expressions are mathematical phrases that can contain numbers, variables, and operators (such as +, -, *, and /). These expressions do not have an equals sign and can be simplified but not solved for a specific value. In the expression from our exercise, we see two terms: \(3p\) and \(-2p\). Each term consists of a coefficient (the numerical part) and a variable (in this case, 'p'). Understanding algebraic expressions is crucial because they help us represent and solve real-world problems in a mathematical way. By learning how to manipulate these expressions, you can simplify complex problems and make them easier to understand and work with.
simplifying expressions
Simplifying expressions involves combining like terms and reducing the expression to its simplest form. Like terms are terms that have the same variable raised to the same power. In the example given (\(3p - 2p\)), both terms have the variable 'p'. To simplify, you combine these like terms by adding or subtracting their coefficients.
In our case, the coefficients are 3 and -2. When combined, they yield:
  • Step 1: Identify the coefficients (3 and -2).
  • Step 2: Perform the arithmetic operation: \(3 + (-2) = 1\).
Attach the resulting coefficient to the variable 'p', giving us \(1p\). Typically, we drop the 1 and simply write \(p\).
Simplifying expressions is a fundamental skill in algebra that makes working with equations and inequalities more manageable.
coefficients
Coefficients play a key role in algebraic expressions. They are the numerical components that multiply the variable in a term. For example, in \(3p\), the number 3 is the coefficient of 'p'. In the expression \(-2p\), -2 is the coefficient.
When combining like terms, focus on the coefficients:
  • Add coefficients of like terms to simplify the expression.
  • In the exercise above, we see \(3p\) and \(-2p\). By combining them, we handle the coefficients 3 and -2: \(3 + (-2) = 1\).
The loop-back coefficient '1' might be omitted, leaving us with just 'p'.
Understanding coefficients helps you correctly combine and simplify algebraic expressions, making further operations, such as solving equations, much easier.

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