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Understanding and Combining Like Terms in Algebra

This guide provides a comprehensive overview of combining like terms in algebra. It explains the concept of coefficients and how to identify like terms, which are terms that have the same variable raised to the same power. Through clear examples, such as combining apples and oranges, the guide demonstrates how to correctly simplify expressions by adding or subtracting coefficients. Additionally, it includes practice problems to reinforce understanding and application of the topic. Perfect for students looking to enhance their algebra skills.

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Understanding and Combining Like Terms in Algebra

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  1. Bell Work Answers 18 -9 -4 60 • 1. 4 + x = 22 • 2. 3 – y = 12 • 3. 5x = -20 • 4.

  2. Combining Like Terms

  3. Coefficient • A coefficient is the number part of a term that includes a variable. • Example: 2x • 2 is the coefficient • x is the variable

  4. Constant term Coefficients are 4 and 8 4x + 8x +1 4x and 8x are like terms

  5. Combine like terms + – + By combining apples with apples and oranges with oranges, you get... + like terms: terms with the same variable or variables, raised to the same power. Like terms can be combined by adding their coefficients. Example: What do you get when you add the fruit shown? 3 apples+ 2 oranges– 2 apples+ 2 oranges coefficients 1 apple +4 oranges

  6. Only combine terms that are exactly the same!! • What’s the “same” mean? • If numbers have a variable, then you can combine only ones that have the same variable • You can also combine numbers that have no variables

  7. Example: Simplify 2x + 3y + 5x + 6y + 12 Find the like terms, combine their coefficients... 2x+ 3y+ 5x + 6y+ 12 7x + 9y + 12 Example: Simplify 3x – 3y – 8x – y This is the same as 3x – 3y – 8x – 1y = – 5x – 4y

  8. Examples • Which numbers are the “same”? 5x, 8y, 9z, 10, 12x, 14z, 7 Same: 5x and 12x Same: 10 and 7 Same: 9z and 14z

  9. Let’s try it! 4x + 9x 13x -7y + 9y 2y -8y + (-4y) -12y 4x + 8y + 10x 14x + 8 y 5 + 8x + 7y + 10 8x + 7y + 15

  10. Final Problems: • 4x + 5y – 2x + 3y 2. 5(x + y) + 2(x + y) 3. 3 + 5x – 4y + 2y – 8x

  11. Answers: 2x + 8y 7x + 7y 3 – 3x – 2y

  12. Practice: worksheet

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