Distributive Property(2)

					               2(x + 3)
Distributive property - used to multiply a
 single term and two or more terms inside a
 set of parentheses.
        Distributive Property
   Recall the distributive property of
     multiplication over addition . . .
symbolically:



        a × (b + c) = a × b + a × c
     Distributive Property
      For any numbers a, b & c,
   it is true that a(b + c) = ab + ac

                Example:
If we do the parenthesis first (PEMDAS)
           2(2 + 5) = 2(7) = 14
                    or
       2(2 + 5) = 2(2) + 2(5) = 14
Example

2 (3x + 4)
             Rainbow
             Arrows!


2 (3x + 4)
  6x +8
                   Practice
6(2 quarters + 3 nickels) =
12 quarters + 18 nickels = $3.90

5(3a + 2b)
15a + 10b

2(3n – 4)
6n - 8
     Variables Multiplied by
            Variables
Remember w * w = w2 - Not 2w!
           Distribute

X(x + 3)           x(y – 6)

X2 + 3x            xy – 6x
Distributing a Negative

       -2(3x – 4)

       -2(3x – 4)   What is a negative
                    times a positive?
        -6x + 8     Negative times a
                    negative?
    Stop for today

     Coming up!



Combining Like Terms!
        Yea!
             Like Terms
Terms that have the EXACT same variables
  or no variables.

Example:
2x x -3x            Like terms.

2x   4x2 3xy 2     NOT like terms. Why?
       Combining Like Terms
If there are Like Terms, you can (and should)
   combine them to make a simpler
   expression.
Example: 3x – x + 6x = 8x

Try one 7b – 2b + 3b        = 8b
                Practice
    2           2                 2
 2x + 3x – 4x + 4x = -2x + 7x


                    2   2
3xy + 2x + 3xy – 6x – 2x =
                              2
                            -8x + 6xy + 2x
Distributive Property and Combining
             Like Terms
4(x-4) + 2x – 6
4x -16 + 2x – 6 àFirst, distribute
                the 4
6x – 16 – 6     à then, combine the x
6x - 22         à then combine the
                     constants
          Another Example
12x – 6(x + 3) -5x + 2 à what to
                            distribute?
12x – 6x -18 -5x + 2 à combine like
                        terms
12x – 6x -18 -5x + 2
1x -18 + 2          à combine constants

1x -16   or x -16 ß final answer
               Practice!
4x -2(x + 6)
4x – 2x – 12
2x -12 ß Final answer

22x + 3(x – 9)
22x + 3x – 27
25x -27 ß Final answer
           Challenge
4y + 4(y-7) + 2(x+3)
4y + 4y – 28 + 2x + 6
8y – 28 + 2x + 6
8y - 22 + 2x ß final answer

				
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posted:7/27/2013
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Jun Wang Jun Wang Dr
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