How to Combine Like Terms

Combining like terms is one of the most important skills to master in Algebra. Without knowing how to combine like terms, it is impossible to learn algebra or any higher level Math. Luckily, combining like terms is easy once you understand what's going on. Here's a quick guide on what to do and how to do it.

Steps

  1. Image titled Combine Like Terms Step 1
    1
    Define all the constants and the variables.
    • Constants are numbers that stand on their own. They will not have an "x", "y", "z", or any other variable attached to them. They can be small numbers, like "7", or big numbers, like "23,849".
    • Variables are symbols that stand for numbers that vary. A variable is usually written as a letter, such as "x", "y", or "z".
    • The difference between constants and variables is that the value of a variable can change, while the value of a constant stays the same.
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    2
    Add or subtract all constants. Remember, constants are numbers that stand all alone and never change.
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    3
    Add or subtract the coefficients of all like variables.
    • Variables need to be exactly the same for you to add up their coefficients:
      Image titled Combine Like Terms Step 3Bullet1
      • "x3 + 3x2" have different exponents, so you cannot add them up.
      • "x3 + 3x3" both have "x3" as a variable, so you can add them up.
    • Only add or subtract the value of the coefficient; don't try to add or subtract the variable.
      Image titled Combine Like Terms Step 3Bullet2
      • 2y2 + 5y2 = 7y2 — not 7y4.
      • 6xy3 - 4 xy3 = 2xy3 — not 2xy.

Tips

  • Even though it's not needed, in algebra you write expressions in order of alphabetical order, e.g. 2x + y and not y + 2x, even though they mean the same thing.

Warnings

  • You cannot add terms with different exponents. e.g. x + x^2 cannot be combined
  • You cannot add terms with different variables e.g. 2x + 3yx does NOT equal 5yx.

Article Info

Categories: Algebra