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Algebra Foundations

Combining Like Terms

In Algebra 1, one of the fundamental skills you'll need to master is combining like terms. Think of it as organizing a messy room where items need to be grouped based on their similarities.

When working with algebraic expressions, "like terms" are terms that have the same variables with the same exponents. Combining like terms means adding or subtracting the coefficients of these terms while keeping the variables and exponents the same.

Here's a step-by-step breakdown of how to combine like terms:

  1. Identify like terms: Look for terms in the expression that have the same variables and exponents. For example, in the expression 3x + 5y - 2x + 7y, the like terms are 3x and -2x, as well as 5y and 7y.

  2. Add or subtract coefficients: Combine the coefficients of the like terms. In our example, we add the coefficients of the x terms: 3 + (-2) = 1. Then, we add the coefficients of the y terms: 5 + 7 = 12.

  3. Rewrite the expression: Write the simplified expression with the combined like terms. In our example, the simplified expression is 1x + 12y, or simply x + 12y.

To help you remember the process of combining like terms, think of this mnemonic: I Am Rewriting (Identify, Add, Rewrite). It reminds you of the steps you need to take to simplify expressions by combining like terms.

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