In Exercises 117–130, simplify each algebraic expression. 6x²-x²

Verified step by step guidance

1. Identify the like terms in the expression: \(6x^2\) and \(-x^2\).
2. Combine the like terms by subtracting the coefficients: \(6 - 1\).
3. Write the simplified expression using the result from the subtraction: \((6 - 1)x^2\).
4. Simplify the expression to get the final form: \(5x^2\).
5. The expression is now simplified to \(5x^2\).

Key Concepts

Algebraic Expressions

Algebraic expressions are mathematical phrases that can include numbers, variables, and operation symbols. They do not contain an equality sign and can represent a wide range of values. Understanding how to manipulate these expressions is fundamental in algebra, as it allows for simplification and solving equations.

Like Terms

Like terms are terms in an algebraic expression that have the same variable raised to the same power. For example, in the expression 6x² and -x², both terms are like terms because they contain the variable x raised to the second power. Combining like terms is a key step in simplifying algebraic expressions.

Simplification

Simplification is the process of reducing an algebraic expression to its simplest form. This involves combining like terms, factoring, and eliminating any unnecessary components. In the given expression 6x² - x², simplification results in 5x², demonstrating how to efficiently condense expressions for clarity and ease of use.