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Simplifying Expressions Using the Distributive Property

This lesson helps students master the distributive property to simplify expressions effectively. The distributive property allows for distributing a number outside parentheses to each term inside, transforming expressions like (a(b + c) = ab + ac). Through engaging examples and practice problems, students will learn how to apply this fundamental algebraic principle. The lesson also covers like terms and how to combine them for simplification. Students will complete various exercises to reinforce their understanding of concepts illustrated in real-life applications.

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Simplifying Expressions Using the Distributive Property

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  1. ObjectiveThe student will be able to: use the distributive property to simplify expressions. Designed by Skip Tyler and Nicole Kessinger, Edited by Mr. Nealey

  2. 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

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

  4. 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

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

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

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

  8. 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.

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

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

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

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

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

  14. 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

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

  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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