Vytýkání

1)        Rozložte na součin:

\displaystyle a)\quad 6x+9y=

\displaystyle b)\quad 16a-12b=

\displaystyle c)\quad 3m+6{{m}^{2}}=

\displaystyle d)\quad 10{{n}^{3}}-8{{n}^{2}}=

\displaystyle e)\quad 2{{y}^{2}}z-yz=

\displaystyle f)\quad 17a{{b}^{2}}-21{{a}^{2}}b=

\displaystyle g)\quad -21{{c}^{4}}{{d}^{3}}+14{{c}^{2}}{{d}^{4}}=

\displaystyle h)\quad -81{{r}^{2}}s-27{{s}^{3}}=

 

2)        Rozložte na součin:

\displaystyle a)\quad 42a+30b=

\displaystyle b)\quad 5k-5=

\displaystyle c)\quad 3{{s}^{2}}-3s=

\displaystyle d)\quad 6a+24b=

\displaystyle e)\quad c-{{c}^{2}}d=

\displaystyle f)\quad 4x-8y=

\displaystyle g)\quad 10ax+15ay=

\displaystyle h)\quad -10r+5s=

\displaystyle i)\quad -3p-q=

\displaystyle j)\quad 2{{r}^{2}}+4r+4=

\displaystyle k)\quad 25{{u}^{2}}-25u-15=

\displaystyle l)\quad 24{{x}^{2}}y-18x{{y}^{2}}+33xy=

\displaystyle m)\quad -5ax-5bx-5cx=

\displaystyle n)\quad -21x+28y-14z+49=

 

3)        Rozložte na součin vytknutím před závorku:

\displaystyle a)\quad 5x+5y=

\displaystyle b)\quad -3k+6=

\displaystyle c)\quad 8a{{b}^{2}}+4b=

\displaystyle d)\quad -9{{x}^{2}}+12x=

\displaystyle e)\quad -16xy{{z}^{2}}-8xz=

\displaystyle f)\quad -3ab-6{{b}^{2}}=

\displaystyle g)\quad 2x-2y-2z=

\displaystyle h)\quad 12m-8n+16=

\displaystyle i)\quad 10ab+15a+20a{{b}^{2}}=

\displaystyle j)\quad {{u}^{2}}v+{{u}^{3}}{{v}^{2}}-2u{{v}^{4}}=

\displaystyle k)\quad {{k}^{2}}l+8klm+3{{k}^{3}}=

\displaystyle l)\quad 5{{x}^{3}}{{y}^{2}}+25x{{y}^{2}}=

 

4)        Rozložte na součin vytknutím před závorku:

\displaystyle a)\quad 12{{a}^{3}}-6{{a}^{2}}+3a=

\displaystyle b)\quad 4{{a}^{4}}-8{{a}^{3}}+6{{a}^{2}}=

\displaystyle c)\quad {{x}^{4}}{{y}^{2}}+2x{{y}^{3}}-3{{y}^{2}}=

\displaystyle d)\quad {{x}^{5}}-3{{x}^{3}}-{{x}^{2}}y=

\displaystyle e)\quad -12{{u}^{3}}v-9{{u}^{2}}{{v}^{2}}+6{{u}^{3}}{{v}^{3}}=

\displaystyle f)\quad -16u{{v}^{2}}-12u{{v}^{3}}-36{{u}^{3}}v=

 

5)        Rozložte na součin:

\displaystyle a)\quad x\left( y+1 \right)+2\left( y+1 \right)=

\displaystyle b)\quad 3x\left( 5+2y \right)+4\left( 5+2y \right)=

\displaystyle c)\quad 6a\left( b-7 \right)-3a\left( b-7 \right)=

\displaystyle d)\quad 9a\left( b+5 \right)+\left( 5+b \right)=

\displaystyle e)\quad {{m}^{2}}\left( 2x-y \right)-3n\left( 2x-y \right)=

\displaystyle f)\quad m\left( 4-3x \right)-\left( -3x+4 \right)=

\displaystyle g)\quad 2\left( a+b \right)-c\left( a+b \right)=

\displaystyle h)\quad 6\left( m-n \right)-3a\left( m-n \right)=

\displaystyle i)\quad \left( a+5 \right)-3b\left( a+5 \right)=

\displaystyle j)\quad \left( x-2y \right)+6z\left( x-2y \right)=

 

6)        Rozložte na součin:

\displaystyle a)\quad m\left( k+1 \right)+k+1=

\displaystyle b)\quad {{x}^{2}}\left( 2a-3b \right)+2a-3b=

\displaystyle c)\quad r-6+3\left( r-6 \right)=

\displaystyle d)\quad 2z-3-x{{y}^{2}}\left( 2z-3 \right)=

 

7)        Rozložte na součin:

\displaystyle a)\quad 2c\left( 4a+7b \right)+7b+4a=

\displaystyle b)\quad 8m+3n-2\left( 3n+8m \right)=

\displaystyle c)\quad 7{{x}^{2}}\left( 3y-5z \right)-5z+3y=

\displaystyle d)\quad -y+9z-3x\left( 9z-y \right)=

\displaystyle e)\quad v+5u\left( v-3 \right)-3=

\displaystyle f)\quad 3v+7\left( 3v-4u \right)-4u=

 

8)        Rozložte na součin:

\displaystyle a)\quad 2ax-bx+2a-b=

\displaystyle b)\quad cd-ce-3e+3d=

\displaystyle c)\quad 20a+5ab+4b+{{b}^{2}}=

\displaystyle d)\quad 3x+3xy+2y+2{{y}^{2}}=

\displaystyle e)\quad 24{{a}^{2}}+12ab+18a+9b=

\displaystyle f)\quad 12uv+6{{v}^{2}}+2u+v=

\displaystyle g)\quad 6{{a}^{2}}-4ab+3a-2b=

\displaystyle h)\quad 12xy+6{{y}^{2}}-30x-15y=

 

9)        Rozložte na součin:

\displaystyle a)\quad 2\left( a-3 \right)+b\left( 3-a \right)=

\displaystyle b)\quad 3a\left( 7-2c \right)+4b\left( 2c-7 \right)=

\displaystyle c)\quad m\left( 2n-5 \right)-3\left( 5-2n \right)=

\displaystyle d)\quad 4\left( 6n-1 \right)-\left( 1-6n \right)=

\displaystyle e)\quad 8x\left( y+3z \right)-3z-y=

\displaystyle f)\quad 6\left( 4y-3z \right)-4y+3z=

 

10)        Rozložte na součin:

\displaystyle a)\quad 5a+5b+ax+bx=

\displaystyle b)\quad ax+bx+ay+by=

\displaystyle c)\quad 3m-3+mn-n=

\displaystyle d)\quad 6m-18+mn-3n=

\displaystyle e)\quad 2a+6ab+3x+9bx=

\displaystyle f)\quad 4m+6mx+10n+15nx=

 

11)        Doplňte místo teček správné hodnoty:

\displaystyle a)\quad 2ab+\ \ldots \ =2a\left( \ \ldots \ +3 \right)

\displaystyle b)\quad 10a+\ \ldots \ =\ \ldots \ \left( 2a+3b \right)

\displaystyle c)\quad 18m-12n=6\left( \ \ldots \ -\ \ldots \  \right)

\displaystyle d)\quad \ldots \ -2{{x}^{2}}=2x\left( 1-\ \ldots \  \right)

\displaystyle e)\quad \ldots \ +6x=\ \ldots \ \left( 2x+1 \right)

\displaystyle f)\quad \ldots \ +\ \ldots \ -\ \ldots \ =3\left( 3{{y}^{2}}+4y-2 \right)

\displaystyle g)\quad c{{d}^{2}}-\ \ldots \ =\ \ldots \ \left( d-c \right)

\displaystyle h)\quad \ldots \ -12{{a}^{2}}+a=a\left( 3{{a}^{2}}-12a+\ \ldots \  \right)

\displaystyle i)\quad {{x}^{4}}+\ \ldots \ +{{x}^{2}}y=\ \ldots \ \left( {{x}^{3}}+2+\ \ldots \  \right)

\displaystyle j)\quad \ldots \ -{{m}^{2}}{{n}^{4}}={{m}^{2}}{{n}^{2}}\left( {{m}^{2}}-\ \ldots \  \right)

 

12)        Doplňte místo teček správné hodnoty:

\displaystyle a)\quad 5x+15y-\,\ldots \,=5\left( x+3y-2z \right)

\displaystyle b)\quad \,\ldots \,-8mn-16mt=8m\left( 2m-n-2t \right)

\displaystyle c)\quad 81v-\,\ldots \,-45{{v}^{2}}=9v\left( 9-7z+5v \right)

\displaystyle d)\quad \,\ldots \,+24{{a}^{2}}b-\,\ldots \,=6ab\left( -3c+4a-7ab \right)

\displaystyle e)\quad \,\ldots \,-\,\ldots \,+88rs=-8rs\left( -9r+7s-11 \right)

\displaystyle f)-40{{t}^{2}}+\,\ldots \,-\,\ldots \,+\,\ldots \,=-4t\left( 10t-9u+8v-7z \right)