key term - Combining Like Terms

Definition

Combining like terms is the process of adding or subtracting the coefficients of algebraic terms that have the same variable(s) and exponent(s). This technique is essential for simplifying and solving linear equations, as it allows for the reduction of the number of terms in an expression.

5 Must Know Facts For Your Next Test

1. Combining like terms is a fundamental skill in solving linear equations, as it allows for the simplification of complex expressions.
2. The key to combining like terms is to identify terms that have the same variable(s) and exponent(s), and then add or subtract their coefficients.
3. Combining like terms can reduce the number of terms in an expression, making it easier to solve for the unknown variable.
4. Proper use of combining like terms is essential for correctly solving linear equations and simplifying algebraic expressions.
5. Combining like terms is a crucial step in applying a general strategy to solve linear equations, as it helps to isolate the variable on one side of the equation.

Review Questions

• Explain the process of combining like terms and how it simplifies algebraic expressions.
  • The process of combining like terms involves identifying terms that have the same variable(s) and exponent(s), and then adding or subtracting their coefficients. For example, if an expression has the terms 3x and 5x, these are considered like terms because they both have the variable x. By combining them, the expression can be simplified to 8x, which is easier to work with when solving linear equations. Combining like terms reduces the number of terms in an expression, making it more manageable and allowing for more efficient problem-solving.
• Describe how combining like terms is an essential step in the general strategy for solving linear equations.
  • Combining like terms is a crucial step in the general strategy for solving linear equations. After isolating the variable on one side of the equation, the next step is to combine any like terms on both sides of the equation. This simplifies the expression and makes it easier to perform the next steps, such as dividing or multiplying both sides to solve for the unknown variable. By combining like terms, the number of terms in the equation is reduced, and the equation becomes more manageable to solve. Proper use of combining like terms is essential for correctly solving linear equations and simplifying algebraic expressions.
• Analyze the importance of combining like terms in the context of solving linear equations and simplifying algebraic expressions.
  • Combining like terms is a fundamental skill that is essential for solving linear equations and simplifying algebraic expressions. It allows for the reduction of the number of terms in an expression, making it easier to isolate the variable and perform the necessary operations to find the solution. Without the ability to combine like terms, solving linear equations would be significantly more complex and time-consuming. Additionally, the simplification of algebraic expressions through combining like terms is crucial for understanding the underlying relationships and patterns in mathematical problems. By mastering the skill of combining like terms, students can develop a deeper understanding of algebraic concepts and apply them more effectively in solving a wide range of mathematical problems.

Related terms

Coefficient:

The numerical factor that multiplies a variable in an algebraic term.

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 term.