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The Distributive Property and Terms

Learn about terms, coefficients, and like terms, and how to simplify expressions using the distributive property. Practice with examples and test your knowledge.

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The Distributive Property and Terms

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  1. The Distributive Property and Terms

  2. A term is a 1) number, 2) variable, or 3) a product / quotient of numbers and variables. Example 5 m 2x2

  3. 3) The coefficient is the numerical part of the term. Examples 1) 4a 4 2) y2 1

  4. Like Termsare terms with the same variable AND exponent. To simplify expressions with like terms, simply combine the like terms.

  5. Are these like terms? 1) 13k, 22k Yes, the variables are the same. 2) 5ab, 4ba Yes, the order of the variables doesn’t matter. 3) x3y, xy3 No, the exponents are on different variables.

  6. Answer Now Which of the following is the simplified form of -4x + 7x ? • -4 • 3x • -3x • 4

  7. are like terms and 5a and a are like terms The above expression simplifies to:

  8. Simplify1) 5a + 7a 12a 2) 6.1y - 3.2y 2.9y 3) 4x2y + x2y 5x2y 4) 3m2n + 10mn2 + 7m2n - 4mn2 10m2n + 6mn2

  9. 7) y 5) 13a + 8a + 6b 21a + 6b 6) 4d + 6a2 - d + 12a2 18a2 + 3d

  10. Answer Now Which of the following is the simplified form of 5x - 4 - 7x + 14 ? • -12x + 10 • -2x + 10 • 2x - 18 • 12x – 18

  11. Answer Now If a triangle has sides 3x - 2, 5 - x and 2x - 5, what is the perimeter of the triangle? • 4x - 2 • 4x + 2 • 5x - 2 • 5x - 7

  12. Answer Now Which figure below models the simplification of - 4x - 5 + 7x + 7 using these tiles?

  13. The Distributive Property The process of distributing the number on the outside of the parentheses to each term on the inside. a(b + c) = ab + ac and (b + c) a = ba + ca a(b - c) = ab - ac and (b - c) a = ba - ca Example #1 5(x + 7) 5 • x + 5 • 7 5x + 35

  14. Example #2 3(m - 4) 3 • m - 3 • 4 3m - 12 Example #3 -2(y + 3) -2 • y + (-2) • 3 -2y + (-6) -2y - 6

  15. Answer Now Which statement demonstrates the distributive property incorrectly? • 3(x + y + z) = 3x + 3y + 3z • (a + b) c = ac + bc • 5(2 + 3x) = 10 + 3x • 6(3k - 4) = 18k - 24

  16. Answer Now Bonus! Which of the following is the simplified form of a + 3a - 4(9 - a) ? • -36 • 3a - 36 • 8a - 36 • 8a + 36

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