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, as they represent the same type of quantity.

5 Must Know Facts For Your Next Test

1. Like terms can be combined by adding or subtracting their coefficients, as they represent the same type of quantity.
2. Identifying like terms is crucial for simplifying polynomial expressions and solving linear equations.
3. The variables in like terms must be raised to the same power, such as $x^2$, $3x^2$, and $-5x^2$ being like terms.
4. Coefficients of like terms are added or subtracted, but the variables remain the same, such as $2x + 3x = 5x$.
5. Combining like terms is an essential skill for working with polynomials and solving linear equations in one variable.

Review Questions

• Explain how identifying like terms is important in the context of polynomials.
  • Recognizing like terms is crucial when working with polynomials, as it allows you to combine and simplify the expression by adding or subtracting the coefficients of the terms with the same variables and exponents. This simplification process is essential for tasks such as evaluating, factoring, and graphing polynomial functions.
• Describe the role of like terms in the context of solving linear equations in one variable.
  • Like terms play a vital role in solving linear equations in one variable. When solving these equations, you must isolate the variable on one side of the equation by performing operations that maintain the equality. This often involves combining like terms on each side of the equation, allowing you to simplify the expression and solve for the unknown variable.
• Analyze how the concept of like terms is connected to the understanding of real numbers in algebra.
  • The concept of like terms is deeply rooted in the understanding of real numbers in algebra. Real numbers, which include both rational and irrational numbers, can be represented in algebraic expressions using variables. Like terms, which have the same variables raised to the same power, are a fundamental aspect of working with real numbers in algebraic contexts. Recognizing and manipulating like terms is essential for performing operations, simplifying expressions, and solving equations involving real numbers.

Related terms

Coefficient:

The numerical factor multiplying a variable in an algebraic expression.

Variable:

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

Algebraic Expression: A mathematical phrase that combines variables, coefficients, and operations such as addition, subtraction, multiplication, and division.