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Chapter 5: Problem 45

Simplify. $$ (x n)-2 $$

Short Answer

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

Step by step solution

01

Understand the Expression

The given expression is \((xn) - 2\). It suggests that \(xn\) is an expression which we subtract 2 from. Our goal is to simplify this expression if possible.
02

Simplify the Expression

The expression \((xn) - 2\) is already in its simplest form. 'Simplifying' typically involves combining like terms or factoring, but in this expression, there are no like terms or further simplifications that can be done. Therefore, \((xn) - 2\) remains as it is.

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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 combinations of numbers, variables, and operations. They might include addition, subtraction, multiplication, or division. For example, in the expression \((xn) - 2\), "\(xn\)" is a term. This term combines a variable "\(x\)" and another placeholder or coefficient "\(n\)" via multiplication.

We use these expressions in algebra to represent real-world scenarios and solve problems. The key is to remember that algebraic expressions can be transformed in several ways, including simplifying them or solving for a variable.
  • **Numbers and Variables**: They are the building blocks of expressions. "\(x\)" and "\(n\)" are variables, often representing unknown values.
  • **Operations**: Addition, subtraction, multiplication, and division are the operations used to form expressions.
Understanding algebraic expressions helps us in simplifying equations and solving mathematical problems effectively.
Like Terms
Like terms are terms in an algebraic expression that have the same variable raised to the same power. Identifying like terms is essential in simplifying expressions as it allows combining terms to make the expression simpler. For instance, in the expression \((xn) - 2\), there are no like terms present since it contains a single term with variables and a constant.

Here are a few key points about like terms:
  • **Identifying Like Terms**: They must have identical variable parts. For example, \(3x\) and \(5x\) are like terms, but \(3x\) and \(3x^2\) are not.
  • **Combining Like Terms**: You can add or subtract like terms by combining their coefficients. For example, \(3x + 4x = 7x\).
  • **Simplifying Expressions**: Always look for like terms as a first step in simplifying any algebraic expression.
While the original expression doesn't combine like terms, recognizing them in other contexts can streamline the problem-solving process.
Factoring
Factoring is the process of breaking down an expression into a product of simpler expressions. This step is crucial in solving equations, especially quadratics and polynomials. While factoring won鈥檛 apply to \((xn) - 2\) due to its simplicity, understanding how it works is beneficial.

Factoring involves:
  • **Finding Common Factors**: Look for numbers or variables common in all terms. For example, in \(3x + 6\), the common factor is 3.
  • **Using Different Methods**: There are various methods like factoring by grouping, using the difference of squares, and more.
  • **Simplifying Problem Solving**: It can transform complex expressions into manageable pieces.
Knowing when and how to factor is instrumental in solving more complex problems, even if it's not needed for the original exercise provided.

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