Combining Like Terms To Simplify An Expression

🔑 Key Concepts

  • Like terms must have identical variable parts.
  • Terms containing \(a\) can combine with other \(a\)-terms but not with \(b\)-terms.
  • Constants combine with other constants.
  • A subtraction sign belongs to the term immediately following it.
  • Add or subtract the coefficients while keeping the variable part unchanged.
  • 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 \(8\) in \(8a\).
  • Constant: A number without a variable, such as \(7\) or \(-3\).
  • Like terms: Terms that have identical variable parts, such as \(8a\) and \(-5a\).
  • Unlike terms: Terms with different variable parts that cannot be combined.
  • Simplify: To rewrite an expression in an equivalent form with no remaining like terms to combine.
  • Equivalent expressions: Expressions that have the same value for every possible value of their variables.

💡 Main Idea

To simplify an expression, identify terms with identical variable parts and combine their coefficients. In \(8a+2b+7-3-5a\), the \(a\)-terms combine to make \(3a\), the \(b\)-term remains \(2b\), and the constants combine to make \(4\). The simplified expression is \(3a+2b+4\). The new expression is equivalent to the original because both expressions have the same value for every value of \(a\) and \(b\).

📚 What You Should Already Know

Before this lesson, students should know how to identify terms, coefficients, constants, and variables. Students should also be comfortable adding and subtracting integers and recognize that different variables represent different quantities.

🚀 What Comes Next

Next, students can simplify expressions containing negative coefficients, fractions, decimals, and parentheses. Combining like terms will also be used with the distributive property, perimeter and area expressions, equivalent expressions, and multi-step equations.

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