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The Distributive Property

Dive into the Distributive Property of Algebra, essential for understanding how to simplify expressions effectively. Learn about key terms such as terms, coefficients, and constants, and see how the distributive property works through examples like a(b + c) = ab + ac. This guide includes various practice problems to reinforce your skills, especially in distributing and combining like terms. Be cautious with negative signs! Join us in honing your algebraic skills with engaging examples and hands-on practice using whiteboards.

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The Distributive Property

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  1. The Distributive Property Words you may remember… Terms, Like Terms, Coefficients, Constant Term

  2. The Distributive Property ALGEBRA: a (b + c) = ab + ac a (b – c) = ab - ac NUMBER EXAMPLE: 6 (4 + 3) = 6(4) + 6(3) 7 (8 – 5) = 7(8) – 7(5)

  3. Let’s go over this and add this to our Notebooks! Find the definitions for our vocabulary on Page 89!

  4. Now let’s look at an example… 5 (2x) + 5 (3) = 10x + 15 So what exactly is a term again? How about a coefficient?

  5. Let’s look at some interesting situations... = -2 (3x) + -2 (5) = -6x + -10 NEGATIVE SIGNS – BE CAREFUL!

  6. Now we need to combine like terms. What is an example of a like term in this problem?

  7. LET’s TRY The Distributive Property! Use Whiteboards and markers

  8. Distribute using whiteboards! 8 ( y + 4 ) 3 (p -11) 2 ( c – 7) 9 (3a – 5) 7 (y + 8) 4 (z + 12) -5 (a + 4b) -5 (2m – 3n)

  9. A little harder! Distribute and don’t forget to combine like terms! 3 (4y + 1) + 5(3y +2) 5 (4y + 2) - 5(3y +1) 2 (3y + 2) + 6(4y +2) 2 (3y + 2) + 6(4y -2) 4(7m + 6) – 3(4m + 8) 4(5m + 2) – 3(3m - 4) -7(2s +1) + 6(4s – 1) 3 (6y + 1) - 5(3y -2)

  10. Practice Problems Let’s go over some of these together. Today we will work on Problems 1 and 2

  11. EXPAND Problem 1 The direction for the most basic problem using the distributive property. Same as the direction “DISTRIBUTE.”

  12. EXPAND and SIMPLIFY by collecting LIKE TERMSProblem 2 Your answer should only have one of each variable!

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