wz

Mnohočleny

Součet a rozdíl

 

1.      Vypočítej:

 


a)      2a2 + 3a2 =                                                                                   5a2

b)      7x2 – 28x + 13x2 + 12x =                                                          20x2 – 16x

c)      7a5 + 4a3 – 9a3 + 4a5 =                                                                  11a5 – 5a3

d)      4a2 – 8a + 9a2 – 24a =                                                                   13a2 – 32a

e)      –3x2 – 2x3 + 6x3 – 5x2 =                                                                 -8x2 + 4x3

f)        4a2 – 3a + 7a2 – 14a =                                                                   11a2 – 17a

g)      5m – 9n + 15 – 3m + 12n – 6 =                                                     2m + 3n + 9

h)      12x – 16y + 15 – 9y + 12x – 36 =                                                  24x – 25y - 21

i)        14x – 15y + 13 – 4y + 18x – 36 =                                                  32x – 19y - 23

j)        14x – 35y + 16 – 14y + 38 + 13x =                                               27x – 49y + 54

k)      3x2 – 5x + 6x2 – 12x =                                                               9x2 – 17x                  

l)        8x – 2x – 7x =                                                                                -x

m)    15a2 – 9a – 14a + 23a2 =                                                               38a2 – 23a

n)      8a – 3a + ( -5a ) =                                                                          0                                   

    

2.      Vypočítej a proveď zkoušku dosazením a  = 5, b = 4

( 5a – 3b ) – ( 7b + 8a ) – ( -9a + 13b ) =                                            6a – 23b;    -62 = -62

             6a – 23b, -62

3.      Vypočítej a proveď zkoušku dosazením x = 12, y = 9

4x – ( -12y ) + ( +9y ) – ( +7x ) =                                                        -3x + 21y;   153 = 153

 

4.      Vypočítej:

 

o)            ( 5m2 - 5m + 3 ) + ( -4m2 - 5m - 3 ) =                                         m2 – 10m

p)            ( 6a2 - 6a + 10 ) + ( -2a2 - 10a + 8 ) =                                        4a2 – 16a + 18

q)            5x – ( 6x – y ) + 9x – ( x + 13 ) =                                               

r)             ( 8a2 – 6a + 12 ) + ( 39 + 14a – 25a2 ) =                                    

 

5.      Vypočítej:

 

a)      ( -8p - 16q + 24 ) - ( 20 + 12p ) =                                                 -20p – 16q + 4

b)      -10xy + 6x - ( 3y + xy - 9x ) + 5y =                                               -11xy + 15x + 2y

c)      ( -9z - 16y + 4 ) - ( 8 + 12z ) =                                                      -21z – 16y - 4

d)      ( 5a – 3b ) – ( 4a + 6b ) – ( -7b – 3a ) =                                       

e)      ( 6a2 – 9a + 12 ) – ( 6a – 7a2 + 15 ) =                                            13a2 – 15a - 313a2 – 15a - 3

f)        ( 9a – 13b ) – ( 15a + 11b ) – ( -6b – 8a ) =                                  2a – 18b

g)      ( 5a2 – 3a + 16 ) – ( 8a – 3a2 + 14 ) =                                            8a2 – 11a + 2

h)      ( 7a – 3b ) – ( 2a + 5b ) – ( -9b – 6a ) =                                        11a + b

i)        ( 6m2 – 7m + 30 ) – ( 4m – 3m2 + 18 ) =                                   9m2 – 11m + 12

j)        ( 6a2 – 9a + 12 ) – ( 6a – 7a2 + 15 ) =

k)      2p – ( -5p ) + 4p =

l)        ( 4a + b ) – ( 3a – 5b ) =

 

6.      Vypočítej a proveď zkoušku dosazením x = 2, y = 3

( 3x – 4y ) – ( 5y + 7x ) – ( -6x + 2y ) =

 

7.      Vypočítej a proveď zkoušku dosazením  a  = 5, b = 4

( 5a – 3b ) – ( 7b + 8a ) – ( 9a – 13b ) =

 

8.      Vypočítej:

 

a)      4x - ( 2x + y ) + 7y - ( x + y ) =                                                 x + 5y

b)      ( 3a - 7b ) - ( a - 5b ) + ( -4a + b ) =                                              -2a - b

c)      ( 4a2 + 2ab - b2 ) - ( -a2 +b2 ) + 3a2 - 2ab + b2 =                            8a2 - b

d)      7a - ( 4a + 2b ) + 6b - ( 3a - b ) =                                                  5b

e)      ( 2x - 4y ) - ( x - 6y ) + ( -2x + 3y ) =                                        -x + 5y

f)        -5ab + 10a - ( 4b + 9ab - 12a ) + 40b =                                        22a – 14ab + 36b

g)      ( 3x2 + 6xy - y2 ) - ( -x2 + 2y2 ) + 9x2 - 4xy + y2 =                     13x2 + 2xy – 2y2

h)      ( a2 + 2a - 7 ) + ( 2a2 + 4 ) - ( 2a2 - 9 ) =                                      

i)        ( 3m2 - 5 ) + ( m2 - 6m + 9 ) - ( 4m2 - m ) =                              

j)        5x – ( 6x + y ) + 9x – ( x + 13 ) =                                                  7x – y - 13

7x – y - 13

9.      Vypočítej a proveď zkoušku dosazením x = 4, y = 6

5x – ( +6y ) – ( -9x ) + ( +12y ) =

 

Násobení číslem

 

10.  Vypočítej:

 


a)      0,3 . ( 5x2 + 3x – 2x2 – 14x ) =                                                       0,9x2 – 3,3x

b)      0,4 . ( 3a + 12a2 –14a2 + 6a ) =                                                     -0,8a2 + 3,6a

c)      0,3 . ( 3x + 12x2 – 15x2 + 4x ) =                                                    -0,9x2 + 2,1x

d)      0,5 . ( 3r + 14r2 – 12r2 – 23r3 ) =                                                   1,5r + r2 – 11,5r3

e)      –1 ( 4z – 6 ) =                                                                                -4z + 6

f)        0,5 . ( 4x2 – 3x – 9x + 12 ) =                                                     2x2 – 6x + 6    

g)      0,5 . ( 3r + 14r2 – 12r2 – 23r3 ) =                                                   1,5r + r2 – 11,5r3

 

Násobení jednočlenem

 

11.  Vypočítej:

 


a)      5a . ( 2a3 + 5a2 - a - 6 ) =                                                               10a4 + 25a3 -5a2 – 30a

b)      3x2y3 . ( 4x2y5 – 2xy ) =   

c)      3a3b4 . ( 4a2b – 3ab2 ) =  

d)      4xy . ( 2x + 3y ) =                                                                          8x2y + 12xy2

e)      3xy . ( 8x - 9y ) =                                                                           24x2y – 27xy2

f)        2x . ( 3x4 + 2x2 - x + 8 ) =                                                              6x5 + 4x3 -2x2 + 16x

g)      -3a . ( 4a2 - 8 ) =                                                                            -12a3 + 24a

h)      -7k . ( 4h - 3k ) =

i)        -4x2 . ( 2x3 + 3x - 1 ) =

j)        -5a2 . ( 2a2 - 3a + 1 ) =

k)      ( 3y - 12x2 – 6 ) .  =

l)        5m ( 3b – 2a ) =

m)    2n . ( n – 6v ) . ( -3v ) =

n)      3z – 2 . ( 4z – 5 ) – 10 =

 

Násobení dvojčlenem

 


12.  Vypočítej:

 


a)      ( m + 2 ) . ( m + 5 ) =

b)      ( 6m + 5 ) . ( 4m - 3 ) =

c)      ( 4 - a ) . ( 1 + a ) =

d)      ( 9m - 8 ) . ( 4 - 3m ) =

e)      ( 4x + 2 ) . ( 4x - 2 ) =

f)        ( x - 7 ) . ( x - 3 ) =

g)      ( 4 - m ) . ( 3 + m ) =

h)      ( a + b ) . ( a + 2 ) =

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

q)      ( 6x - 4y ) . ( 5x - y ) =                                                                   30x2 – 26xy + 4y2

r)       ( 2a - 4 ) . ( 5a + 6 ) =                                                                    10a2 – 8a - 24

s)       ( x - 4y ) . ( 3y + 4x ) =                                                                  4x2 – 13xy – 12y2

t)        ( 2a + 5 ) . ( 2a - 5 ) =                                                                    4a2 - 25

u)      ( 6 - 3b ) . ( 3b + 6 ) =                                                                   36 – 9b2

v)      ( 7x – 8 ) . ( 9x + 6 ) =                                                              63x2 – 30x - 48

 

x)      ( 3x + 5 ) ( 2x – 4 ) =

y)      ( 4x – 6y ) . ( 2x + 3y ) =


 

Pořadí početních operací

 


13.  Vypočítej:

 

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)        ( x + 1 ) . ( x + 2 ) + ( x + 1 ) ( x + 4 ) =                                         2x2 + 8x + 6

j)        ( a + 3 ) . ( a - 2 ) - ( a - 3 ) . ( a - 5 ) =                                          9a - 21

k)      ( x + 2 ) . ( x + 2 ) - ( x + 3 ) . ( x + 3 ) =                                   -2x - 5

l)        ( a + 8 ) . ( a - 10 ) + ( a + 8 ) . ( a + 9 ) =                                     2a2 + 15a - 8

m)    –8 ( 12 – 7x ) + 13 ( 2x – 9 ) =                                                     

n)      6 ( 5m – 4n + 9 ) – 7 ( 9m + 13n – 12 ) =

o)      4 ( 13a – 18 ) – 6 ( 3a + 14 ) =

p)      7 ( 12a – 16 ) – 4 ( 9a + 12 ) =

q)      –8 ( 12 – 7x ) + 13 ( 2x – 9 ) =

r)       3 ( 27 – 14a ) – 9 ( 5a + 7 ) =   

s)       –18 ( 3 – 9b ) + 12 ( 3b + 5 ) =

t)        8 ( 2a – 3b + 12 ) – 6 ( 5b – 2a – 27 ) =

u)      7 ( 14a – 15 ) – 3 ( 5a + 18 ) =

v)      3 ( 2x – y ) – 2 ( 3x – y ) =

w)    ( 7a – 3b + 2 ) . 3 – ( -9b + 5 ) =

x)      a ( b – 3 ) – b ( a – 3 ) + 3 ( a – b ) =

y)      ( 3a – 9 ) .

Dělení jednočlenem

 

14.  Vypočítej:

 


a)      ( 12a – 36b + 8 ) : 4 =

b)      ( 35a2 – 28a + 14 ) : 7 =

c)      ( -54x – 36y ) : ( -9 ) =

d)      ( 2y + 14 ) : 2 + ( 72y – 27 ) : 9 =

e)      ( 16a2b2 – 48ab2 ) : 8ab =

f)        ( -8x2 – 12x ) : ( -4x ) =

g)      ( 56a – 24b + 96 ) : 8 =

h)      ( 105a2 – 63a + 91 ) : 7 =

i)        ( -96b – 56a ) : ( -8 ) =

j)        ( 9a + 15 ) : 3 + ( 108a – 27 ) : 9 =

k)      ( 32a2b – 24ab2 ) : ( -8ab ) =

l)        ( -27a2 + 42a ) : ( -3a ) =


 

Dělení dvojčlenem

 

15.  Vypočítej:

 


a)      ( r2 + 2r - 24 ) : ( r + 6 ) =

b)      ( y2 + y - 20 ) : ( y + 5 ) =


 

 

Vzorce

 

16.   Vypočítej pomocí vzorců:

 


a)            ( 8x + 4 )2 =

b)            ( 9a + 5 )2 =

c)            ( 3x + y )2 =

d)            ( 6c + 4a )2 =

e)            ( 2x + 12 )2 =

f)              ( 5x + 2y )2 =                                                                              25x2 + 20xy + 4y2

g)            ( x + 2y )2 =

h)            ( 9b + 13 )2 =

i)              ( x + 6 )2 =

j)              ( 4n3v + 10 )2 =



17.  Vypočítej pomocí vzorců:

 


a)            ( 9 – 2a )2 =

b)            ( 6 – 2b )2 =

c)            ( 5a - 9 )2 =                            

d)            ( 6a - 2 )2 =

e)            ( u - 7 )2 =


 

18.  Vypočítej pomocí vzorců:

 

a)            ( -8 – 3y )2 =

b)            ( -9 -3x )2 =

c)            ( x – 1 )2  ( x + 1 )2 =

d)            ( -9b + 2a )2 =

 

Rozklad výrazů na součin

 

A

19.   Rozlož na součin činitelů:

 

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 )

 

 

B

20.        Rozlož na součin činitelů:

 

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 ) ]

g)            7 . ( x – 2 ) + p . ( x – 2 ) =              ( x – 2 ) ( 7 + p )

h)          

 

C

21.              Rozlož na součin činitelů:

 

a)         x (a – 1) + 2 (1 – a) =              [ ( a – 1 ) ( x – 2 ) ]

b)        3s (5 – r) + t (r – 5) =              [ ( 5 – r ) ( 3s – t ) ]

c)         4 (x – y) + 7z (y – x) =             [ ( x – y ) ( 4 – 7z ) ]

d)        q (p – 4) – r (4 – p) =              [ ( p – 4 ) ( q + r ) ]

e)         a (c – d) – b (d – c) =              [ ( c – d ) ( a + b ) ]

f)          y (2 – x) – (x – 2) =                 [ ( 2 – x ) ( y + 1 ) ]

 

D

22.              Rozlož na součin činitelů:

 

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

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

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

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

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

f)          2r5s2 – 14r4s3 + 10r3s4=           [ 2r3s2 ( r2 – 7rs + 5s2 ) ]

g)            6u3 - 2u + 4uv =                 2u ( 3u2 -1 + 2v )

h)            4a2b + 10ab2 + 6ab =             2ab ( 2a + 5b + 3 )

i)              6r3 - 3r2 + 3r =                   3r ( 2r2 –r + 1 )

j)              12p3q + 8p2q2 + 4p2q =          4p2q ( 3p + 2q + 1 )

k)            ku2 + 12kuv + 9kv2 =              k ( u2 + 12uv + 9v2 )

 

 

E

23.              Rozlož na součin činitelů:

 

a)         y (3 + z) + 3 + z =                        [ ( 3 + z ) ( y + 1 ) ]

b)        u ( 2 – v) – 2 + v =                       [ ( 2 – v ) ( u – 1 ) ]

c)         ab (2c + d) + 2c + d =                  [ ( 2c + d ) ( ab + 1 ) ]

d)        5x (a – 7) – a + 7 =                      [ ( a – 7 ) ( 5x – 1 ) ]

e)         2a2 (m  + n2) – m – n2 =                [ ( m + n2 ) ( 2a2 – 1 ) ]

f)          m2 (p – 1) + p – 1 =                     [ ( p – 1 ) ( m2 + 1 ) ]

g)         3x (4 + y) – 4 – y =                      [ ( 4 + y ) ( 3x – 1 ) ]

h)         rs3 (t – 12) + t – 12 =                   [ ( t – 12 ) ( rs3 + 1 ) ]   

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

j)          3a ( x2 – 3y ) – 8b ( 3y – x2 ) =              [ (x2 – 3y ) ( 3a + 8b ) ]

k)        2u ( v + z ) + 3 ( v + z ) =                  [ ( v + z ) ( 2u + 3 ) ]

l)              a2 ( 2a – 3 ) + ( 3 – 2a ) =               [ ( 2a – 3 ) ( a + 1 ) ( a – 1 ) ]

m)          x . ( a – 1 ) – 1 + a =                   ( a – 1 ) ( x + 1 )

n)            3x . ( 4 + y ) – y – 4 =                 ( y + 4 ) ( 3x - 1 )

o)            2r . ( 3a – 5 ) – 6 .( 5 – 3a ) =          ( 3a – 5 ) ( 2r + 6 )

p)            4x2 ( a - b ) + 9y2 ( b - a ) =                  ( a – b ) ( 2x + 3y ) ( 2x – 3y )

q)            –16a2 . ( x + y ) + x + y =                 ( x + y ) ( 1 + 4a ) ( 1 – 4a )

 

F

24.   Rozlož na součin činitelů:

 

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 ) ]

m)       1 – 36u2 =                           [ ( 1 + 6u ) ( 1 – 6u )]

n)         4g2h2 – 100x2y2 =                    [ 4 ( gh + 5xy ) ( gh – 5xy ) ]

o)      -9 + 4c2 =                             [ ( 2c + 3 ) ( 2c – 3 )]

p)      49 – m2n2 =                           [ ( 7 + mn ) ( 7 – mn ) ]

q)      25 – a2b2 =                            [ ( 5 + ab ) ( 5 – ab ) ]

r)       49a2 - 36 =                                ( 7a + 6 ) ( 7a – 6 )

s)       16z2 - 9 =                                  ( 4z + 3 ) ( 4z – 3 )   

t)        25 - x2y2 =                                 ( 5 + xy ) ( 5 – xy )

u)      z4 - 49 =                                    ( z2 + 7 ) ( z2 – 7 )

v)      a4 – 36b2 =                                ( a2 + 6b ) ( a2 – 6b )

w)    49a2 – b4 =                                ( 7a + b2 ) ( 7a – b2 )

x)      9x2 – 0,01 =                               ( 3x + 0,1 ) ( 3x – 0,1 )

 

 

G

25.   Rozlož na součin činitelů:

 

a)         x4 – 1 =                          [ ( x2 + 1 ) ( x + 1 ) ( x – 1 ) ]

b)        p4 – 25q4 =                         [ ( p2 + 5q2 ) ( p2 – 5q 2 ) ]

c)         144m2 – n4 =                           [ ( 12m + n2 ) ( 12m – n2 ) ]

d)        a4 – b4 =                         [ ( a2 + b2 ) ( a + b ) ( a – b ) ]

e)      x2y4 – a4b2 =                          [ ( xy2 + a2b ) ( xy2 – a2b ) ]

 

H

26.   Rozlož na součin činitelů:

 

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

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

c)         m5 – m =                             [ m ( m2 + 1 ) ( m + 1 ( m – 1 ) ]

d)        4x – x3 =                             [ x ( 2 + x ) ( 2 – x ) ]

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

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

g)         49s2 – 36t2 =                           [ ( 7s + 6t ) ( 7s – 6t ) ]

h)         45 – 5m2 =                          [ 5 ( 3 + m ) ( 3 – m )]

i) 8x2 – 18y2 =                            [ 2 ( 2x + 3y ) ( 2x – 3y ) ]

j) 2ay2 – 2a3 =                             [ 2a ( y + a ) ( y – a )]

k)        7x7 – 28x3 =                            [ 7x3 ( x2 + 2 ) ( x2 – 2 )]

l) 5a2 – 125b2 =                          [ 5 ( a + 5b ) ( a – 5b ) ]

m)         12a6b – 75a2b5 =                     3a2b ( 2a2 + 5b2 ) ( 2a2 – 5b2 )

n)         135x3y2 - 240xy4 =                       15xy2 ( 3x + 4y ) ( 3x – 4y )

o)        10a2b2 - 40a2b4 =                    10a2b2 ( 1 + 2b ) ( 1 – 2b )

p)      25x2 - 25y2 =                             25 ( x + y) ( x - y )

q)      2p2 – 2q2 =                                2 ( p + q ) ( p - q )

r)       16a2 – 16b2 =                            16 ( a + b ) ( a - b )

s)       ab2 – 2abc + ac2 =                     a ( b – c )2

t)        3p2 – 6pq + 3q2 =                      3 ( p – q )2

u)      4z2 + 32z + 64 =                        4 ( z + 4 )2

v)      9a2 - 36b2 =                               9 ( a + 2b ) ( a – 2b )

w)    a2 ( x – 1 ) – b2 ( x – 1 ) =                   ( x – 1 ) ( a + b ) ( a - b )

 

 

I

27.   Rozlož na součin činitelů:

 

a)         (a + b)2 – r2 =                               ( a + b + r ) ( a + b – r )

b)        (x – y)2 – 1 =                                ( x – y – 1 ) ( x – y + 1 )

c)         25 – (a + 1)2 =                             ( 6 + a ) ( 4 – a )

d)        x2 – (u + 3)2 =                              ( x + u + 3 ) ( x – u – 3 )

e)         (s – 7)2 – p2q2 =                            ( s – 7 + pq ) ( s – 7 – pq )

f)          (2x + y)2 – x2 =                        ( 3x + y ) ( x + y )

g)         (m + 2)2 – (2m – 1)2 =                       ( 3m + 1 ) ( 3 – m )

h)         (a – b)2 – (3a + 4b)2 =                       ( 4a + 3b ) ( -2a – 5b )

i)           (a + 5)2 – (3 + a)2 =                          4 ( a + 4 )

j)          (3x – y)2 – (x – 5y)2 =                       4 ( 2x – 3y ) ( x + 2y )

k)            ( 2x + 3 )2 - 16 =                              ( 2x + 7 ) ( 2x – 1 )

l)              ( 3x + 2 )2 - a2 =                          ( 3x + 2 + a ) ( 3x + 2 - a )

m)          ( 2a + b )2 - 9 =                           ( 2a + b + 3 ) ( 2a + b – 3 )

n)            16 - ( a + 3 )2 =                           ( a + 7 ) ( 1 - a )

o)            ( x + y )2 – z2 =                            ( x + y + z ) ( x + y - z )

p)            a2 – ( 6 + b )2 =                           ( a + 6 + b ) ( a – 6 – b )

 

 

J

28.   Rozlož na součin činitelů:

 

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

 

 

K

29.   Rozlož na součin činitelů:

 

a)            32 + 16x + 2x2 =                         2 ( 4 + x )2

b)            4x2 – 48x + 144 =                            4 ( x – 6 )2

c)            45x2 + 60xy + 20y2 =                       5 ( 3x + 2y )2

d)            -20a – 100 – a2 =                             - ( a + 10 )2

e)            5a2 + 10ab + 5b2 =                           5 ( a + b )2

f)              2a2 + 12a + 18 =                         2 ( a + 3 )2

g)            -b2 – 2by – y2 =                           - ( b + y )2

h)            27x2 + 90x + 75 =                            3 ( 3x + 5 )2

i)              36x2 – 120x + 100 =                        4 ( 3x – 5 )2

j)              –2m2n – 12mn – 18n =                     -2n ( m + 3 )2

k)            –50pr2 + 120prs – 72ps2 =                    -2p ( 5r – 6s )2

l)              3a2 + 30a + 75 =                         3 ( a + 5 )2 ( x – 2 ) . ( 7 + p )

 

L

30.   Rozlož na součin činitelů:

 

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

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

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

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

e)            a3 – a2 + a – 1 =                          ( a + 1 ) ( a - 1 )2

f)              mn - 5m - 5 + n =                             ( n – 5 ) ( m + 1 )

g)            u + 4 - uv - 4v =                          ( u + 4 ) ( 1 – v )

h)            pm – pq + 7m – 7q =                       ( m – q ) ( p + 7 )

i)              qr + r + q + 1 =                           ( q + 1 ) ( q – 1 )

j)              m3 – 8m2 – m + 8 =                     ( m – 8 ) ( m2 + 1 )

k)            5a + 5b + ax + bx =                         ( a + b ) ( 5 + x )

l)              3m – 3 + mn – n =                            ( m – 1 ) ( 3 + n )

m)          2a + 6ab + 3x + 9bx =                     ( 1 + 3b ) ( 2a + 3x )

n)            6m – 18 + mn – 3n =                        ( m – 3 ) ( 6 + n )

o)            ax + bx + ay + by =                          ( a + b ) ( x + y )

p)            4m + 6mx + 10n + 15nx =                     ( 2 + 3x ) ( 2m + 5n )

q)            x3 + x2 + x + 1 =                          ( x + 1 ) ( x2 + 1 )

r)             y4 + y3 – y – 1 =                          ( y + 1 )2 ( y – 1 )