key term - Combining Like Terms

Definition

Combining like terms is the process of simplifying an algebraic expression by adding the coefficients of terms that have the same variable(s). This technique is essential in solving linear equations, as it helps to reduce the complexity of the expression and make it easier to manipulate and solve.

5 Must Know Facts For Your Next Test

1. Combining like terms is a crucial step in the general strategy for solving linear equations, as it helps to isolate the variable(s) on one side of the equation.
2. The process of combining like terms involves identifying terms that have the same variable(s) and then adding or subtracting their coefficients.
3. Combining like terms can simplify an expression by reducing the number of terms, making it easier to manipulate and solve.
4. When combining like terms, the variables must be exactly the same, including the exponent, for the terms to be considered like terms.
5. Combining like terms is a foundational skill that is necessary for understanding and solving more complex algebraic equations and expressions.

Review Questions

• Explain how combining like terms is used in the general strategy for solving linear equations.
  • Combining like terms is a crucial step in the general strategy for solving linear equations. By identifying and combining terms with the same variable(s), the expression can be simplified, making it easier to isolate the variable on one side of the equation. This step helps to reduce the complexity of the equation, allowing for more straightforward steps in the solving process, such as using the addition or multiplication property of equality to solve for the unknown.
• Describe the criteria for determining whether two terms are considered like terms.
  • For two terms to be considered like terms, they must have the same variable(s), including the same exponent. For example, $3x$ and $5x$ are like terms because they both have the variable $x$ with an exponent of 1. However, $2x$ and $3x^2$ are not like terms because they have different exponents. Similarly, $4y$ and $4z$ are not like terms because they have different variables, even though they have the same coefficient.
• Analyze the benefits of combining like terms when solving linear equations.
  • Combining like terms provides several benefits when solving linear equations. First, it simplifies the expression by reducing the number of terms, making the equation easier to manipulate and solve. Second, it helps to isolate the variable(s) on one side of the equation, a crucial step in the solving process. Third, combining like terms can reveal patterns or relationships within the equation, allowing for more efficient and effective strategies for finding the solution. By mastering the skill of combining like terms, students can develop a stronger understanding of algebraic concepts and improve their problem-solving abilities.

Related terms

Coefficient:

The numerical factor in front of 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 expression that contains one or more variables, constants, and operations.