gcf present distributive property in reverse

Download GCF present Distributive Property in Reverse

Post on 06-Jan-2018

213 views

Category:

Documents

0 download

Embed Size (px)

TRANSCRIPT

  • GCF present

  • Distributive Property in Reverse

  • Distributive Property in Reverse

  • Distributive Property in ReverseExample 1

  • Distributive Property in ReverseExample 1

  • Difference of 2 SQUARES

  • Example 1

  • Example 1

  • Example 2

  • Example 3

  • Example 4

  • Is this a perfect Square?

  • Difference of 2 CUBES

  • The Difference of Two Cubes:The difference of cubes can be modeled using volume. The volume of a cube is:

  • Imagine taking a cube with a volume of x3

    xxx

  • Imagine taking a cube with a volume of x3

    The volume of the resulting figure must be x3 - y3. xxxyyyand cutting out and removing a smaller cube with a volume of y3 .

  • Imagine taking a cube with a volume of x3

    We call this the difference of two cubes.xxxyyyand cutting out and removing a smaller cube with a volume of y3 . The volume of the resulting figure must be x3 - y3.

  • We are going to discover how to factor the difference of two cubes by breaking the diagram into rectangular prisms and finding the sum of the volumes of the rectangular prisms.

  • xxx - yxxxyyy

  • xxx - yxxxyyy

  • xxx - yxxxyyy

    yx-yx

  • xxx - yxxxyyy

    yx-yx

  • xxx - yxxxyyy

    yx-yxyx-yy

  • xxx - yxxxyyy

    yx-yxyx-yy

  • 4x26x92x 3

  • 4x26x92x 3

  • 9x23x13x 1

  • 9x23x13x 1

  • Sum of 2 CUBES

  • x22x4x 2

  • x22x4x 2

  • GCF presentDifference of 2 SQUARESDifference of 2 CUBESSum of 2 CUBES

  • 2

    36

    x

    -

    xx

    66

    ( )( )

    (

    )

    (

    )

    abab

    -+

    x

    6

    2

    25

    x

    +

    33

    ab

    -

    -

    22

    ab

    -

    33

    ab

    -

    acbc

    +

    33

    ab

    +

    (

    )

    cab

    +

    (

    )

    (

    )

    abab

    +-

    (

    )

    (

    )

    22

    abaabb

    +-+

    2

    2)16

    y

    -

    a

    cc

    b

    +

    (

    )

    c

    ab

    +

    22

    xx

    2

    41

    x

    -

    11

    2

    x

    1

    33

    ab

    +

    (

    )

    (

    )

    -=-++

    3322

    xyxyxxyy

    6

    36

    x

    -

    33

    xx

    3

    x

    3

    Vxxx

    or

    Vx

    =

    =

    (

    )

    (

    )

    22

    b

    a

    b

    aa

    b

    +-+

    (

    )

    3

    3

    2

    3

    x

    -

    3

    8

    x

    +

    (

    )

    (

    )

    2

    224

    xxx

    +-+

    (

    )

    (

    )

    22

    222

    xxx

    +-+

    33

    a

    b

    +=

    2

    b

    =

    ax

    =

    3

    827

    x

    -

    33

    a

    b

    -=

    (

    )

    (

    )

    22

    b

    a

    b

    aa

    b

    -++

    36

    -

    2

    ax

    =

    3

    b

    =

    (

    )

    (

    )

    (

    )

    2

    2

    22

    2

    333

    xx

    x

    -

    ++

    (

    )

    (

    )

    2

    23

    469

    x

    xx

    -

    ++

    3

    27

    x

    +

    (

    )

    (

    )

    2

    339

    xxx

    +-+

    3

    271

    x

    -

    (

    )

    (

    )

    2

    31931

    xxx

    -++

    6

    x

    -

    2

    x

    18

    x

    -

    m

    (

    )

    (

    )

    2

    23

    469

    x

    xx

    -

    =++

    6

    x

    +

    6

    x

    2

    11

    mm

    -

    (

    )

    11

    m

    m

    -

    2

    x

    27

    -

    2

    12

    x

    18

    x

    2

    12

    x

    -

    3

    8

    x

    18

    x

    -

    2

    9

    x

    -

    2

    12

    x

    2

    12

    x

    -

    18

    x

    1

    -

    3

    x

    -

    2

    9

    x

    3

    x

    2

    9

    x

    -

    3

    27

    x

    3

    x

    2

    9

    x

    3

    x

    -

    (

    )

    (

    )

    2

    224

    xxx

    =+-+

    3

    x

    6

    x

    33

    2

    x

    +

    (

    )

    3

    3

    2

    3

    x

    -

    (

    )

    3

    3

    2

    3

    x

    -

    (

    )

    3

    3

    2

    3

    x

    -

    (

    )

    3

    3

    2

    3

    x

    -

    (

    )

    3

    3

    2

    3

    x

    -

    (

    )

    3

    3

    2

    3

    x

    -

    (

    )

    3

    3

    2

    3

    x

    -

    (

    )

    3

    3

    2

    3

    x

    -

    (

    )

    3

    3

    2

    3

    x

    -

    33

    2

    x

    +

    33

    2

    x

    +

    33

    2

    x

    +

    33

    2

    x

    +

    33

    2

    x

    +

    33

    2

    x

    +

    33

    2

    x

    +

    33

    2

    x

    +

    33

    2

    x

    +

    33

    2

    x

    +

    33

    2

    x

    +

    2

    2

    x

    -

    4

    x

    2

    2

    x

    33

    ab

    -

    33

    ab

    -

    33

    ab

    +

    (

    )

    (

    )

    22

    abaabb

    -++

    (

    )

    (

    )

    22

    abaabb

    +-+

    4

    x

    -

    2

    036

    xx

    +

    -

    2

    6

    6

    6

    3

    x

    x

    x

    -+

    -

    (

    )

    (

    )

    66

    xx

    -+

    33

    ab

    +

    -

    +

    =

    Vlengthwidthheight

    +

    -

    +

    =

    Vlwh

    8

    2

    2

    x

    4

    x

    (

    )

    (

    )

    =-

    =-

    2

    Vxxxy

    xxy

    (

    )

    (

    )

    =-

    =-

    Vxyxy

    xyxy

    (

    )

    (

    )

    =-

    =-

    2

    Vyyxy

    yxy

    x

    3

    -

    y

    3

    =

    x

    2

    x

    -

    y

    (

    )

    +

    x

    y

    x

    -

    y

    (

    )

    +

    y

    2

    x

    -

    y

    (

    )

    -

    33

    xy

    (

    )

    -

    2

    xxy

    (

    )

    -

    xyxy

    (

    )

    -

    2

    yxy

    =

    x

    -

    y

    (

    )

    x

    2

    +

    x

    y

    +

    y

    2

    (

    )

    \

    x

    3

    -

    y

    3

    =

    x

    -

    y

    (

    )

    x

    2

    +

    x

    y

    +

    y

    2

    (

    )

    2

    4)9

    x

    +

    2

    3)49

    x

    -

    (

    )

    (

    )

    33

    xx

    -+

    (

    )

    (

    )

    44

    yy

    -+

    (

    )

    (

    )

    2323

    xx

    -+

    -

    33

    xy

    2

    1)9

    x

    -

    22

    ab

    -

    (

    )

    (

    )

    abab

    -+

    2

    2

    x

    -

    4

    x

    -