Combining Like Terms - Quick Example

🔑 Key Concepts

  • Like terms have the same variable part.
  • Only like terms can be combined.
  • Add or subtract the coefficients while keeping the variable part unchanged.
  • Terms with different variables must remain separate.
  • A simplified expression has no remaining like terms that can be combined.

✏️ Worked Examples — Combining Like Terms

🧠 Math Vocabulary

  • Term: A number, variable, or product of numbers and variables separated by addition or subtraction.
  • Coefficient: The number multiplying a variable, such as the \(5\) in \(5x\).
  • Like terms: Terms that have identical variable parts.
  • Variable: A symbol used to represent an unknown or changing value.
  • Constant: A number without a variable.
  • Simplify: To rewrite an expression in an equivalent form with no remaining operations that can be completed.
  • Equivalent expressions: Expressions that have the same value for every possible value of their variables.

💡 Main Idea

Simplifying an expression by combining like terms means adding or subtracting the coefficients of terms that have identical variable parts. In \(3x+5x+y+y+y\), the \(x\)-terms combine to make \(8x\), and the \(y\)-terms combine to make \(3y\). Because \(x\) and \(y\) are different variables, the final simplified expression is \(8x+3y\).

📚 What You Should Already Know

Before this lesson, students should understand addition and subtraction, recognize variables and constants, and identify individual terms in an algebraic expression. Students should also know that a variable written without a visible coefficient has an understood coefficient of \(1\).

🚀 What Comes Next

Next, students can simplify expressions that include negative coefficients, decimals, fractions, parentheses, and the distributive property. These skills support evaluating expressions, identifying equivalent expressions, and solving multi-step equations.

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