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On the distributive property

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- 1. #108 Distributing: You Can Do it!
- 2. properties... The process of “distributing” which you have been learning and practicing is one of the series of properties that you will eventually learn and master. (What were the two we talked about yesterday?) Properties are facts about mathematical processes. They are learned by memorizing rules.
- 3. the distributive properties So, what are the rules? For real numbers x, y, and z, x ( y + z ) = xy + xz and x ( y - z ) = xy - xz
- 4. You already know this • You have already been using these rules. Now, you know why you are supposed to do what you have been doing.
- 5. Let’s try some out, just for memory’s sake.
- 6. 3(4 + 7) = 3*4 + 3*7
- 7. 3(4 + 7) = 3*4 + 3*7 = 12 + 21 = 33 Your answer
- 8. Think about the old way. Does it work? 3(4 + 7) = 3(11) = 3*11 = 33 It works!
- 9. 3(x + 7) = 3*x + 3*7
- 10. 3(x + 7) = 3*x + 3*7 = 3x + 21 Your answer
- 11. Don’t freak out! -5(6 - x) What should you do FIRST???
- 12. ADD THE OPPOSITE! -5(6 - x) = -5(6 + -x) = -5*6 + -5*-x = -30 + 5x
- 13. The important thing to remember is to keep up with your positive and negative signs. AND ADD THE OPPOSITE!
- 14. What if I gave you a problem like this? x(x + 9)
- 15. You should be able to get this far... x(x + 9) x*x + 9*x Note: Why did I put the x after the 9? Numbers always come before variables. Think of it as always sitting in the front seat.
- 16. So... now what? x*x + 9x What if I told you the answer was... x + 9x 2
- 17. Why? Let’s see if you can ﬁgure out the rule... x*x=x2 x*x*x=x3 So, when you multiply variables together, count how many times you multiplied and that is your new exponent.
- 18. One last one on your own... x(10 + x) x(10 + x) = x*10 + x*x = 10x + x 2

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