Distributive Property, Collecting Similar Terms, and Factoring by hcj

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									Distributive Property, Collecting
 Similar Terms, and Factoring


                Use of Equivalent
                Expressions to simplify
                similar (like) terms
Equivalent Expressions

 Equivalent Expressions are expressions which
 always result in the same number when we
 substitute values for the variables.
 2(x+3) and 2x + 6 are equivalent expressions
 Check: Let x = 4
 2(4+3) = 2(4)+6
 2(7) = 8+6
 14 = 14
Distributive Property

Forms of the distributive property:
  a(b + c) = ab + ac Note: You can distribute a
                         number from either side!
 (b + c)a = ba + ca
Examples: 3(x + 5) = 3x + 15
            7(x + 3 – y) = 7x + 21 – 7y
            (r + s)x = rx + sx
Similar (Like) Terms

l   Similar or like terms are terms that have
    exactly the same bases and exponents.
l       3x2       and    5x2 are similar terms
    Coefficient      Exponent   Coefficient          Exponent
              Base                            Base


      7x and 16x2 are NOT similar terms
    because the exponents are not exactly the
    same.
Collecting Similar Terms

l   To collect like terms we use the distributive
    property in reverse.




    The rule for collecting like terms is to:
    1) Copy the bases and exponents, and
    2) Add or subtract the coefficients
Collecting Like Terms (More Examples)

       42x + 6 + 4x + 2 = 42x + 4x + 6 + 2
                        = (42 + 4)x + (6 + 2)
                        = 46x +8     Answer




                          Answer
Factoring (Greatest Common Factor)

l Factoring using the Greatest Common Factor is
  the distributive property in reverse.
l Example: Factor 6x + 24
 The GCF between 6 and 24 is 6, so




                      Answer
Factoring Using the GCF

l   Another Example.
    Factor: 7 + 14b+ 56w
     Notice that 7 is the Greatest Common Factor, so…




                                               Answer

								
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