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The Distributive Property

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

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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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