Distributive Property by dffhrtcv3

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									The Distributive Property &
  Combining Like Terms
   USING THE DISTRIBUTIVE PROPERTY

 THE DISTRIBUTIVE PROPERTY

The product of a and (b + c):


a(b + c) = ab + ac        2(x + 5) = 2(x) + 2(5) = 2x + 10

(b + c)a = ba + ca        (x + 5)2 = (x)2 + (5)2 = 2x + 10


                           y(1 + x) = y(1) +y(x) = y + xy

                         (1 + 5x)2 =(1)2 + (5x)2= 2 + 10x
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 USING THE DISTRIBUTIVE PROPERTY

 Remember that a factor must multiply each term of an expression.


(–3)(1 + x)= (–3)(1) + (–3)(x)              Distribute the –3.
                                            Simplify.
          = –3 – 3x
–(y – 5)     = (y)(–1) + (–5)(–1)           Distribute the –1.
             = –y + 5                       Simplify.


–(7 – 3x) = (–1)(7) + (–1)(–3x) –a = –1 • a
                                            Simplify.
            = –7 + 3x
   Forgetting to distribute the negative sign when
   multiplying by a negative factor is a common error.
                                                                 BACK
          SIMPLIFYING BY COMBINING LIKE TERMS


      Like Terms are expressions that contain the same
      variable raised to the same power like 4mn and 7mn.


  8x + 3x + y = 11x +y      The 8x and 3x are like terms and can
                            be combined.




4x2 + 2 + x2 - 6 = 4x2 +1 x2 + 2 - 6    Group like terms.

                 = 5x2 - 4             Combine like terms.

                                                                   BACK
BACK
Combine like terms with parenthesis…




                                BACK
                Objectives
• Use the Distributive Property to solve
  equations.
• Solve real-world problems by using
  multistep equations.
                  Key Skills
Solve 3(x - 4) = 48   Use the distributive property.
3 * x + 3 * -4 = 48    Multiply
                      Add both sides of the =
 3x - 12 = 48
                      sign.
   +12 +12
                       Divide both sides of
 3x    = 60
                       the = sign by 3.
 3       3
  x     = 20
                   Key Skills
                       TRY THIS

Solve 5(x +2) = 35   Use the distributive property.
5 * x + 5 * 2 = 35    Multiply
                     Subtract 10 from both
 5x + 10 = 35
                     sides of the = sign.
      -10    -10
                      Divide both sides of
 5x         = 25
                      the = sign by 3.
 5            5
  x         = 5
                  Key Skills
                      Combine like terms that are
Solve 3y – 8 –y = 6   on the same side of the = sign.

2y – 8 = 6        Add 8 to both sides of the = sign.
     +8 +8
2y    = 14 Divide both sides of the equal sign by 2
2        2

 y=7
                     Key Skills
                         TRY THIS

                         Combine like terms that are
Solve 6y +2 –3y = 8      on the same side of the = sign.

 3y +2 = 8             Subtract 2 from both
     -2     -2         sides of the = sign.
3y        = 6    Divide both sides of the equal sign by 3
 3          3

  y=2
                    Key Skills
 Solve
 4x -8(x + 1) = 8          Distribute -8
4x -8 * x + -8 * 1 = 8     Multiply
4x -8x -8 = 8             Combine like terms.
-4x -8 = 8          Add 8 to both sides of the = sign.
    +8 +8
 -4x = 16 Divide both sides of the equal sign by -4
 -4    -4
 x    = -4
                   Key Skills
Use the Distributive Property to solve multistep
equations.
 Solve 8x – 2(3x 4) = 5x – 7.
 Solve 8x – 2(3x –– 4) = 5x – 7. Distributive -2

8x + (–2)(3x) + (–2)(–4) = 5x – 7   Multiply.


                        Combine like terms
8x – 6x + 8 = 5x – 7
8x – 6x + 8 = 5x – 7    that are on the same
 2x + 8 = 5x – 7        side of the = sign.
2x + 8 = 5x – 7       Subtract 2x from both
                      sides of the = sign.
-2x           -2x
          8 = 3x -7   Add 7 to both sides
                      of the = sign.
      +7         +7
      15 = 3x          Divide both sides of
                       the = sign by 3
      3      3

      5=x
                    Key Skills
                        TRY THIS
Use the Distributive Property to solve multistep
equations.
 Solve 4y – 7(y +6) = 5y – 2.      Distributive -7
4y + (–7)(y) + (–7)(+6) = 5y – 2     Multiply.


                         Combine like terms
4y – 7y -42 = 5y – 2
4y – 7y -42 = 5y – 2     that are on the same
 -3y -42 = 5y – 2        side of the = sign.
-3y -42 = 5y – 2   Add 3y to both sides of
                   the = sign.
+3y         +3y
   -42 = 8y -2     Add 2 to both sides
                   of the = sign.
  +2          +2
   -40 = 8y         Divide both sides of
                    the = sign by 8
  8     8

   -5 = y
The Distributive Property &
  Combining Like Terms




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