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Understanding Variable Expressions: Terms, Coefficients, and Like Terms

This guide clarifies the components of variable expressions, focusing on key vocabulary such as terms, constants, like terms, and coefficients. You will learn how to identify and categorize parts of an expression, and subsequently combine like terms by adding their coefficients while preserving the variable. Through examples, such as simplifying expressions like (3y + y) and (7p - 3q + 2p - 8), you’ll gain hands-on experience in this fundamental algebra concept. Practice combining like terms to master your skills in algebra.

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Understanding Variable Expressions: Terms, Coefficients, and Like Terms

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  1. Simplifying Variable Expressions

  2. Vocabulary: • Term- a number or the product of a number and variables • Constant- a term that has no variables • Like terms- have identical variable (has the same variable with the same exponent) • Coefficient- a number that multiplies a variable

  3. Identifying the parts of an Expression4m-3n+7m-9 • Coefficients: • Like terms: • Constants: 4, -3, 7 4m and 7m -9

  4. Identifying the parts of an Expression7x+3y-x+4y • Coefficients: • Like terms: • Constants: 7, 3, -1, 4 7x, -x and 3y, 4y none

  5. Identifying the parts of an Expression4v • Coefficients: • Like terms: • Constants: 4 none none

  6. Identifying the parts of an Expression9a + 4b + c - 3a + b • Coefficients: • Like terms: • Constants: 9, 4, 1, -3, 1 9a, -3a and 4b,b none

  7. Combining Like Terms • When combining like terms add the coefficients and keep the variable the same.

  8. Simplify 3y + y 1. What are the like terms? 3y and y 2. What are the coefficients of the like terms? 3 and 1 3. Add the coefficients and keep the variable the same. 3y + 1y = 4y 4. Your answer: 3y + y = 4y

  9. Simplify 3b – 4b + b 1. What are the like terms? 3b, -4b, b 2. What are the coefficients of the like terms? 3, -4, 1 3. Add the coefficients and keep the variable the same. 3b + -4b + 1b =0 4. Your answer: 3b – 4b + b = 0

  10. Simplify 7p - 3q + 2p - 8 1. What are the like terms? 7p and 2p 2. What are the coefficients of the like terms? 7, 2 3. Add the coefficients and keep the variable the same. 7p + 2p = 9p 4. Your answer: 7p – 3q + 2p -8 = 9p – 3q - 8

  11. Try on your own 1. 9 + 4f + 3 + 2f = 6f + 12 2. 2b + b – 4 = 3b - 4 3. 5(7 – 3x) + 20x = 35 + 5x Assignment: Page 78 Problems 12-32 even

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