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, which are the numerical factors in front of the variables.
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Like terms can be combined by adding or subtracting their coefficients, but they must have the same variable(s) raised to the same power.
Identifying and combining like terms is a fundamental skill in simplifying algebraic expressions and solving equations.
The concept of like terms is essential for performing operations such as addition, subtraction, and multiplication of polynomials.
Recognizing and manipulating like terms is crucial when solving equations with variables on both sides or when solving formulas for a specific variable.
Understanding like terms is also important in the context of factoring, where common factors are identified and extracted from polynomial expressions.
Review Questions
Explain how the concept of like terms is used in solving linear equations with variables and constants on both sides.
When solving linear equations with variables and constants on both sides, the concept of like terms is used to simplify the equation by combining terms with the same variable(s). By identifying and combining like terms on each side of the equation, the equation can be reduced to a simpler form, making it easier to isolate the variable and solve for the unknown. This process of combining like terms is a fundamental step in the process of solving these types of linear equations.
Describe how the understanding of like terms is applied when adding and subtracting polynomials.
The concept of like terms is essential when adding and subtracting polynomials. To perform these operations, you must first identify the like terms within the polynomials, which are the terms that have the same variable(s) raised to the same power. Once the like terms are identified, you can combine them by adding or subtracting their coefficients. This simplification of the polynomial expression by combining like terms is a crucial step in performing polynomial arithmetic operations.
Analyze how the recognition of like terms is important when using a problem-solving strategy to solve real-world applications involving algebraic expressions.
When applying a problem-solving strategy to real-world applications involving algebraic expressions, the understanding of like terms is crucial. Often, these applications require you to translate the problem statement into an algebraic expression, which may contain a mixture of terms with different variables and coefficients. Identifying and combining the like terms within this expression is a vital step in simplifying the expression and making it easier to manipulate and solve. By recognizing and properly handling like terms, you can effectively apply problem-solving strategies to find the solution to these types of real-world problems involving algebraic concepts.