Distributive Property by HC121104002213

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									                         Objective
     The student will be able to:
use the distributive property to
simplify expressions.

                                    PFA 8
Designed by Skip Tyler, Varina High School and Nicole Kessinger, Deep Run High School
Edited by Dave Wesley Crestwood Middle School
     The Distributive Property
The process of distributing the number
 on the outside of the parentheses to
 each term on the inside.
 a(b + c) = ab + ac and (b + c) a = ba + ca
 a(b - c) = ab - ac and (b - c) a = ba - ca
                   Example #1
                    5(x + 7)
                   5•x+5•7
                     5x + 35
 Example #2
  3(m - 4)
 3•m-3•4
  3m - 12
 Example #3
    -2(y + 3)
-2 • y + (-2) • 3
   -2y + (-6)
     -2y - 6
     Which statement demonstrates the
     distributive property incorrectly?
1.   3(x + y + z) = 3x + 3y + 3z
2.   (a + b) c = ac + bc
3.   5(2 + 3x) = 10 + 3x
4.   6(3k - 4) = 18k - 24

       Answer Now
            A term is a
1) number,
2) variable, or
3) a product / quotient of numbers
  and variables.
              Example
                 5
                 m
                2x2
        The coefficient is
   the numerical part of the term.
             Examples
1) 4a
                 4
2) y2
                 1
3) 5x 2
    7             5
                  7
Like Terms are terms with the same
     variable AND exponent.


To simplify expressions with like
terms, simply combine the like
terms.
       Are these like terms?
1) 13k, 22k
 Yes, the variables are the same.
2) 5ab, 4ba
  Yes, the order of the variables
  doesn’t matter.
3) x3y, xy3
  No, the exponents are on different
  variables.
Which of the following is the simplified
                form of
              -4x + 7x ?
1.   -4
2.   3x
3.   -3x
4.   4

      Answer Now
         2            2
       8x  2x  5a  a
   2          2
 8x and 2x        are like terms
 5a and a         are like terms

The above expression simplifies to:
                  2
             10x  6a
                 Simplify
1) 5a + 7a
                  12a
2) 6.1y - 3.2y
                  2.9y
3) 4x2y + x2y
             5x2y
4) 3m2n + 10mn2 + 7m2n - 4mn2
         10m2n + 6mn2
5) 13a + 8a + 6b
              21a + 6b
6) 4d + 6a2 - d + 12a2
              18a2 + 3d
7) 3y y
      
    4 4          y
           3y 1y   4y
                     1y
           4   4   4
Which of the following is the simplified
                form of
           5x - 4 - 7x + 14 ?
1.   -12x + 10
2.   -2x + 10
3.   2x - 18
4.   12x – 18

      Answer Now
If a triangle has sides 3x - 2, 5 - x and 2x - 5,
        what is the perimeter of the triangle?

1.   4x - 2
2.   4x + 2
3.   5x - 2
4.   5x - 7

      Answer Now
Which figure below models the simplification
   of - 4x - 5 + 7x + 7 using these tiles?


 1.
 2.
 3.
 4.

      Answer Now
 Bonus! Which of the following is the
   simplified form of a + 3a - 4(9 - a) ?
1.   -36
2.   3a - 36
3.   8a - 36
4.   8a + 36

      Answer Now
          Homework


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