Opakování z 8.roč. - mnohočleny

Vypočítejte:

 

a)      3 . ( a + b ) - 2 . ( a - b ) =                                   a + 5b

b)      2 + 5 . ( z - 1 ) - 3z =                                          2z - 3

c)      ( -5a ) . ( -a + b ) - a . ( 3 + 4a - b ) =                a2 – 4ab – 3a

d)      7 . ( x + y ) - 5 . ( y - x ) =                                 12x + 2y

e)      5 + 4 . ( x - 9 ) - 3x =                                        x - 31

f)        ( -9a ) . ( b - a ) - b . ( 4 + b - 3a ) =                9a2 – 6ab – 4b – b2

g)      ( x + 2 ) . ( x + 5 ) - ( x - 1 ) . ( x - 4 ) =           12x + 6

h)      ( a + 5 ) . ( a + 5 ) - ( a + 7 ) . ( a + 3 ) =         4

i)        ( 6 - a ) . ( a + 6 ) =                                         36 – a2

j)        ( 2a + 3b ) . ( 2a - 5b ) =                                 4a2 – 4ab – 15b2

k)      ( 5p - 3q ) . ( 4p - q ) =                                   20p2 – 17pq + 3q2

l)        ( 3m - 2 ) . ( 2m - 1 ) =                                    6m2 – 7m + 2

m)    ( b - 3c ) . ( 8b + 5c ) =                                   81b2 – 19bc – 15c2

n)      ( 4a + 2 ) . ( 4a - 2 ) =                                    16a2 – 4

o)      ( -3 + 9x ) . ( 3 + 9x ) =                                  81x2 – 9

p)      ( 2a + 5b ) . ( 2a - 3b ) =                                4a2 + 4ab – 15b2

 

 

Vypočítej podle vzorců

 

1.      ( 8x + 4 )2 =

2.      ( 9a + 5 )2 =

3.      ( 3x + y )2 =

4.      ( 6c + 4a )2 =

5.      ( 2x + 12 )2 =

6.      ( 5x + 2y )2 =  

7.      25x2 + 20xy + 4y2  =

8.      ( x + 2y )2 =

9.      ( 9b + 13 )2 =

10.  ( x + 6 )2 =

11.  ( 4n3v + 10 )2 =

Rozlož na součin činitelů (vytýkání):

 

a)    m5 - m2 =                                          [ m2 ( m3 – 1 ) ]                                  

b)   8tu – 10uv =                                      [ 2u ( 4t  - 5v ) ]                                 

c)    15a3 +16a4 =                                                  [ a3 ( 15 + 16a ) ]

d)   x3y2 + 8x3y3 =                                                 [ x3y2 ( 1 + 8y ) ]

e)    2n3 – 2n =                                                       [ 2n ( n + 1 ) ( n – 1 ) ]

f)     75c – 45c3 =                                                   [ 15c ( 5 – 3c2 ) ]

g)    18ab2 + 21a2b2 =                                            [ 3ab2 ( 6 + 7a ) ]

h)    3x2y - 9xy2 =                                                   [ 3xy ( x – 3y )]

i)      p2q4 + q3r2 =                                                   [ q3 ( p2q + r2 ) ]

j)     35u3 + 56u =                                                   [ 7u ( 5u2 + 8 ) ]

k)   20ax - 42by =                                                 [ 2 ( 10ax – 21by ) ]

l)      105r3 + 63r5 =                                                [ 21r3 ( 5 + 3r2 ) ]

m)  30n2 – 9n =                                                    [ 3n ( 10n – 3 ) ]

n)      10m – 25n =                                                   [ 5 ( 2m – 5n ) ]

o)     15xy – 10xz =                                                 [ 5x ( 3y – 2z )]

p)     ab + ab2 =                                                       [ ab ( 1 + b )]

q)     6a2 – 3a =                                                       [ 3a ( 2a – 1 )]

r)       15x - 12y =                                                    3 ( 5x – 4y )

s)       12x - 8y =                                                      4 ( 3x – 2y )

t)        7ab + 21a2b – 14ab2 =                                   [ 7ab ( 1 + 3a – 2b ) ]

u)      5ax + 5bx – 5cx =                                          [ 5x ( a + b – c ) ]

v)      xy3z2 – x2yz3 – x3y2z =                         [ xyz ( y2z – xz2 – x2y ) ]

w)    3mn2 – 6mn + 3m =                                        [ 3m ( n – 1 ) ( n - 1 ) ]

x)      20u4 + 32u3 – 4u2 =                                        [ 4u2 ( 5u2 + 8u – 1 ) ]

 

Rozlož na součin činitelů (vytýkání):

 

a)         (x + y) + b (x + y) =                                     [ ( x + y ) ( 1 + b ) ]

b)        p (r + 2s) – q (r + 2s) =                                [ ( r + 2s ) ( p – q ) ]

c)         x (3y + 7) – (3y + 7) =                                 [ ( 3y + z ) ( x – 1 ) ]

d)        x ( m – n) + 5 (m – n) =                                [ ( m – n ) ( x + 5 ) ]

e)         (4 – p) – 2q (4 – p) =                                   [ (4 – p ) ( 1 – 2q ) ]

f)          3d (c + ab) – 8 (ab + c) =                            [ ( c + ab ) ( 3d – 8 ) ]

 

 Rozlož na součin činitelů (podle vzorců):

 

a)    x2 – y2 =                                                                     [ ( x + y ) ( x – y ) ]

b)   4 – a2 =                                                                      [ ( 2 + a ) ( 2 – a ) ]

c)    b2 – 1 =                                                                      [ ( b + 1 ) ( b – 1 )]

d)   25a2 – b2 =                                                                 [ ( 5a + b ) ( 5a – b ) ]

e)    9m2 – 64n2 =                                                      [ ( 3m + 8n ) ( 3m – 8n ) ]

f)     1 – x2 =                                                                      [ ( 1 + x ) ( 1 – x ) ]

g)    z2 – 9 =                                                                      [ ( z + 3 ) ( z – 3 ) ]

h)    p2 – 49 =                                                                    [ ( p + 7 ) ( p – 7 ) ]

i)      100 – v2 =                                                                  [ ( 10 + v ) ( 10 – v ) ]

j)     c2d2 – 16 =                                                                 [ ( cd + 4 ) ( cd – 4 )]

k)   81p2 – r2q2 =                                                        [ ( 9p + rq ) ( 9p – rq ) ]

l)      –x2 + 16 =                                                                  [ ( 4 + x ) ( 4 – x ) ]

 

 

Rozlož na součin činitelů (podle vzorců):

 

a)           x2 + 2xy + y2 =                                                                    ( x + y )2

b)          16s2 – 8s + 1 =                                                                    ( 4s – 1 )2

c)           9 + 6a + a2 =                                                                       ( 3 + a )2

d)          p2 – 14p + 49 =                                                                   ( p – 7 )2

e)           9a2 – 24ab + 16b2 =                                                            ( 3a – 4b )2

f)            49a2 + 126ab + 81b2 =                                                        ( 7a + 9b )2

g)           y2 + 1 – 2y =                                                                       ( y – 1 )2

h)           z2 + 9 + 6z =                                                                        ( z + 3 )2

i)             1 + 4t2 – 4t =                                                                       ( 1 – 2t )2

j)              –2mn + m2 + n2 =                                                                ( m – n )2

k)            4a2 + 4ab + b2 =                                                                 ( 2a + b )2

l)              9p2 + 6pq + q2 =                                                                 ( 3p + q )2

m)          4m2 + 28m + 49 =                                                              ( 2m + 7 )2

n)            9a2 + 30a + 25 =                                                                ( 3a + 5 )2

o)            1 + 6x + 9x2 =                                                                    ( 1 + 3x )2

p)            49 - 70x + 25x2 =                                                               ( 7 – 5x )2

q)            16n2 – 40n + 25 =                                                               ( 4n – 5 )2

r)             64y4 – 16y2x3 + x6 =                                                ( 8y2 – x3 )2

s)             m8 - 6m4n3 + 9n6 =                                                              ( m4 – 3n3 )2

 

 

Rozlož na součin činitelů (postupné vytýkání):

 

a)                            r3 – r =                                                [ r ( r + 1 ) ( r – 1 ) ]

b)                            z3 – z5 =                                              [ z3 ( 1 + z ) ( 1 – z ) ]

c)                            2a2 – 8 =                                            [ 2 ( a + 2 ) ( a – 2 ) ]

d)                            5a2 – 20b2 =                                       [ 5 ( a + 2b ) ( a – 2b ) ]

e)                            rs + ry + st + ty =                                ( s + y ) ( r + t )

f)                              qr + r + q + 1 =                                  ( q + 1 ) ( r + 1 )

g)                            3a + 3b + ac + bc =                           ( a + b ) ( c + 3 )

h)                            5u + 5 + uv + v =                                ( u + 1 ) ( v + 5 )

 

 

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Kontakty
Základní škola Čáslav
Sadová 1756
28601 Čáslav

Telefon:
ředitel školy:     327 315 741
zástupkyně:        327 315 743
ekonomka:     327 315 700
školní jídelna:     327 315 742

mail:  reditel@sadovazs.cz

Kontakty

Základní škola Čáslav
Sadová 1756
28601 Čáslav

Telefon:
ředitel školy: 327 315 741
zástupkyně: 327 315 743
ekonomka: 327 315 700
školní jídelna: 327 315 742

e-mail: reditel@sadovazs.cz
seja@sadovazs.cz

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16. 12. Albína

Zítra: Daniel
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