Like Terms

Definition

Like terms are algebraic expressions that have the same variable(s) raised to the same power. They can be combined by adding or subtracting their coefficients, allowing for the simplification of algebraic expressions.

5 Must Know Facts For Your Next Test

1. Like terms can be combined by adding or subtracting their coefficients, while maintaining the same variable(s) and exponent(s).
2. Combining like terms is an essential step in simplifying algebraic expressions, as it reduces the number of terms and makes the expression more manageable.
3. Identifying like terms is crucial when solving equations, as it allows for the proper application of the addition, subtraction, and other properties of equality.
4. The Distributive Property is often used in conjunction with combining like terms to further simplify algebraic expressions.
5. Recognizing and combining like terms is a fundamental skill that underpins many topics in pre-algebra, including polynomial operations and equation solving.

Review Questions

• Explain how the concept of like terms is applied when evaluating, simplifying, and translating algebraic expressions.
  • The concept of like terms is essential when evaluating, simplifying, and translating algebraic expressions. To evaluate an expression, you must first identify the like terms and combine them by adding or subtracting their coefficients. Simplifying an expression often involves combining like terms to reduce the number of terms and make the expression more manageable. When translating verbal phrases into algebraic expressions, recognizing like terms allows you to correctly represent the relationships between the quantities using appropriate variables and coefficients.
• Describe how the understanding of like terms is applied when solving equations using integers, decimals, and the properties of equality.
  • The understanding of like terms is crucial when solving equations using integers, decimals, and the properties of equality. When solving equations, you must isolate the variable by performing inverse operations, which often involves combining like terms on each side of the equation. This allows you to simplify the equation and apply the addition, subtraction, multiplication, and division properties of equality to solve for the unknown. Properly identifying and combining like terms ensures that the equation remains balanced and the solution is accurate.
• Analyze how the concept of like terms is applied in the context of polynomial operations, such as addition, subtraction, and multiplication.
  • The concept of like terms is fundamental to performing operations with polynomials. When adding or subtracting polynomials, you must first identify the like terms and combine them by adding or subtracting their coefficients. This simplifies the polynomial expression and makes it easier to work with. Similarly, when multiplying polynomials, recognizing and combining like terms is an essential step in the process, as it allows you to efficiently apply the distributive property and arrive at the final product. Understanding the role of like terms in polynomial operations is crucial for mastering these algebraic skills.

Related terms

Coefficient: The numerical factor that multiplies a variable in an algebraic expression.

Variable: A symbol, usually a letter, that represents an unknown or changing quantity in an algebraic expression.

Exponent: The power to which a variable is raised in an algebraic expression.