Násobení a dělení výrazů

1)        Vypočítejte:

\displaystyle a)\quad a\cdot {{a}^{3}}=

\displaystyle b)\quad {{x}^{2}}\cdot {{x}^{4}}=

\displaystyle c)\quad {{z}^{3}}\cdot {{z}^{4}}=

\displaystyle d)\quad {{y}^{5}}\cdot {{y}^{8}}=

\displaystyle e)\quad {{b}^{8}}\cdot {{b}^{4}}=

\displaystyle f)\quad {{c}^{3}}\cdot {{c}^{10}}=

\displaystyle g)\quad {{u}^{5}}\cdot {{u}^{5}}=

\displaystyle h)\quad {{n}^{7}}\cdot {{n}^{8}}=

\displaystyle i)\quad 2x\cdot {{x}^{3}}=

\displaystyle j)\quad 4{{x}^{2}}\cdot 3{{x}^{2}}=

\displaystyle k)\quad 5{{z}^{2}}\cdot 2{{z}^{3}}=

\displaystyle l)\quad 4{{y}^{3}}\cdot 4{{y}^{5}}=

\displaystyle m)\quad 4{{b}^{2}}\cdot 5{{b}^{5}}=

\displaystyle n)\quad 8{{z}^{4}}\cdot 5{{z}^{3}}=

\displaystyle o)\quad 6{{c}^{8}}\cdot 7{{c}^{2}}=

\displaystyle p)\quad 2{{y}^{2}}\cdot 2{{y}^{7}}=

 

2)        Vypočítejte:

\displaystyle a)\quad 3b\cdot {{b}^{3}}=

\displaystyle b)\quad 2x\cdot 4x=

\displaystyle c)\quad \left( -{{x}^{2}} \right)\cdot 3xy=

\displaystyle d)\quad -3xy\cdot {{y}^{2}}=

\displaystyle e)\quad \left( -{{n}^{2}} \right)\cdot \left( -2n \right)=

\displaystyle f)\quad \frac{1}{2}a\cdot ax=

\displaystyle g)\quad {{b}^{2}}\cdot a{{b}^{2}}=

\displaystyle h)\quad ab\cdot {{a}^{2}}{{b}^{2}}=

\displaystyle i)\quad b\cdot 2b\cdot c=

\displaystyle j)\quad \left( -{{p}^{2}} \right)\cdot \left( -{{p}^{3}} \right)=

\displaystyle k)\quad {{a}^{5}}\cdot 4{{a}^{2}}=

\displaystyle l)\quad \frac{1}{3}{{x}^{3}}\cdot 6xy=

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

\displaystyle n)\quad 3u\cdot 6{{u}^{4}}=

\displaystyle o)\quad 5xy\cdot \left( -2xy \right)=

\displaystyle p)\quad uv\cdot \left( -{{u}^{2}} \right)=

\displaystyle q)\quad \left( -{{n}^{2}} \right)\cdot 3n=

\displaystyle r)\quad \left( -3u \right)\cdot \frac{1}{3}{{u}^{3}}=

 

3)        Vypočítejte:

\displaystyle a)\quad {{k}^{2}}\cdot 3k\cdot {{k}^{3}}=

\displaystyle b)\quad 2{{a}^{3}}\cdot ab\cdot {{b}^{4}}=

\displaystyle c)\quad 2{{m}^{3}}\cdot {{m}^{2}}\cdot 7=

\displaystyle d)\quad \left( -{{a}^{2}} \right)\cdot {{a}^{3}}\cdot 2a=

\displaystyle e)\quad {{t}^{2}}\cdot {{t}^{3}}\cdot \left( -3t \right)=

\displaystyle f)\quad x\cdot {{x}^{2}}\cdot {{x}^{7}}=

\displaystyle g)\quad 2{{k}^{4}}\cdot {{k}^{3}}\cdot \left( -k \right)=

\displaystyle h)\quad \left( -{{x}^{3}} \right)\cdot \left( -{{x}^{5}} \right)\cdot 2x=

\displaystyle i)\quad {{p}^{2}}\cdot \left( -2p \right)\cdot 3{{p}^{5}}=

\displaystyle j)\quad {{l}^{3}}\cdot \left( -{{l}^{3}} \right)\cdot 3l=

\displaystyle k)\quad \left( -{{t}^{3}} \right)\cdot {{t}^{2}}\cdot \left( -t \right)=

\displaystyle l)\quad {{b}^{2}}\cdot \left( -6b \right)\cdot \left( -b \right)=

\displaystyle m)\quad \left( -2a \right)\cdot \left( -2a \right)\cdot {{a}^{3}}=

\displaystyle n)\quad 4{{c}^{2}}\cdot \left( -{{c}^{2}} \right)\cdot 5c=

\displaystyle o)\quad 2x\cdot \left( -2{{x}^{3}} \right)\cdot \left( -3{{x}^{2}} \right)=

 

4)        Doplňte tak, aby platila rovnost:

\displaystyle a)\quad 2x\cdot \,\ldots =2{{x}^{3}}

\displaystyle b)\quad \left( -t \right)\cdot \ldots =-4{{t}^{2}}

\displaystyle c)\quad a\cdot \ldots \cdot b=2a{{b}^{2}}

\displaystyle d)\quad \ldots \cdot 3u=-6{{u}^{2}}

\displaystyle e)\quad 2xy\cdot \ldots =-4{{x}^{2}}y

\displaystyle f)\quad 3p\cdot \ldots =3p{{q}^{2}}

\displaystyle g)\quad 0,5{{t}^{2}}\cdot \ldots =-{{t}^{2}}

\displaystyle h)\quad \ldots \cdot 2u=-4{{u}^{2}}v

\displaystyle i)\quad \ldots \cdot {{b}^{4}}=3{{b}^{5}}

\displaystyle j)\quad -7x\cdot \ldots =49{{x}^{2}}

\displaystyle k)\quad 2a\cdot \ldots =6a{{b}^{2}}

\displaystyle l)\quad x{{y}^{2}}\cdot \ldots =2{{x}^{2}}{{y}^{3}}

 

5)        Vydělte pro proměnné různé od nuly:

\displaystyle a)\quad {{x}^{5}}:{{x}^{2}}=

\displaystyle b)\quad {{m}^{4}}:m=

\displaystyle c)\quad {{a}^{3}}:{{a}^{3}}=

\displaystyle d)\quad {{c}^{6}}:{{c}^{5}}=

\displaystyle e)\quad {{y}^{2}}:y=

\displaystyle f)\quad {{z}^{8}}:{{z}^{3}}=

\displaystyle g)\quad {{u}^{5}}:{{u}^{5}}=

\displaystyle h)\quad {{m}^{6}}:{{m}^{2}}=

\displaystyle i)\quad {{p}^{7}}:{{p}^{6}}=

\displaystyle j)\quad {{s}^{5}}:{{s}^{2}}=

\displaystyle k)\quad {{y}^{4}}:{{y}^{4}}=

\displaystyle l)\quad {{h}^{3}}:{{h}^{2}}=

\displaystyle m)\quad {{r}^{3}}:r=

\displaystyle n)\quad {{t}^{10}}:{{t}^{7}}=

\displaystyle o)\quad {{a}^{6}}:{{a}^{2}}=

\displaystyle p)\quad 2{{q}^{2}}:q=

\displaystyle q)\quad 12{{x}^{6}}:6{{x}^{2}}=

\displaystyle r)\quad 5{{x}^{3}}:5{{x}^{2}}=

\displaystyle s)\quad 3{{m}^{2}}:3{{m}^{2}}=

\displaystyle t)\quad 9{{z}^{2}}:3z=

 

6)        Vydělte pro proměnné různé od nuly:

\displaystyle a)\quad 8ab:\left( -4b \right)=

\displaystyle b)\quad 7rs:\left( -7s \right)=

\displaystyle c)\quad 9{{a}^{2}}x:3ax=

\displaystyle d)\quad 15u{{v}^{2}}:3uv=

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

\displaystyle f)\quad 2r{{s}^{3}}:rs=

\displaystyle g)\quad \left( -6{{p}^{3}} \right):\left( -2p \right)=

\displaystyle h)\quad 5{{z}^{2}}:z=

\displaystyle i)\quad \left( -4{{a}^{2}} \right):2a=

\displaystyle j)\quad 10{{x}^{2}}{{y}^{3}}:5{{x}^{2}}=

\displaystyle k)\quad 32{{x}^{2}}y:\left( -8xy \right)=

\displaystyle l)\quad {{l}^{3}}{{k}^{2}}:lk=

 

7)        Vydělte pro proměnné různé od nuly:

\displaystyle a)\quad 2x:2=

\displaystyle b)\quad 17{{x}^{2}}:x=

\displaystyle c)\quad {{a}^{3}}:a=

\displaystyle d)\quad 2ab:b=

\displaystyle e)\quad 4{{t}^{2}}:2t=

\displaystyle f)\quad \left( -4{{b}^{2}} \right):2b=

\displaystyle g)\quad 56{{x}^{2}}y:7xy=

\displaystyle h)\quad 2abc:bc=

\displaystyle i)\quad 12{{p}^{2}}{{q}^{2}}:6pq=

\displaystyle j)\quad 3{{a}^{2}}bc:{{a}^{2}}bc=

\displaystyle k)\quad \left( -20{{b}^{2}} \right):\left( -10b \right)=

\displaystyle l)\quad 20x:\left( -5x \right)=

\displaystyle m)\quad \left( -10{{t}^{2}} \right):{{t}^{2}}=

\displaystyle n)\quad {{u}^{2}}v:uv=

\displaystyle o)\quad 16{{x}^{2}}{{y}^{2}}:\left( -4y \right)=

 

8)        Vydělte pro proměnné různé od nuly:

\displaystyle a)\quad 3{{m}^{7}}:{{m}^{3}}=

\displaystyle b)\quad {{a}^{5}}:\left( -{{a}^{2}} \right)=

\displaystyle c)\quad \left( -5x \right):5x=

\displaystyle d)\quad \left( -4{{p}^{3}} \right):\left( -p \right)=

\displaystyle e)\quad \left( -2{{v}^{6}} \right):\left( -2{{v}^{3}} \right)=

\displaystyle f)\quad 12{{c}^{7}}:\left( -3{{c}^{4}} \right)=

\displaystyle g)\quad {{a}^{11}}:\left( -{{a}^{7}} \right)=

\displaystyle h)\quad \left( -3{{r}^{2}} \right):\left( -{{r}^{2}} \right)=

\displaystyle i)\quad 9{{u}^{2}}:9u=

\displaystyle j)\quad \left( -6{{x}^{5}} \right):\left( -6x \right)=

\displaystyle k)\quad 10{{z}^{4}}:\left( -5{{z}^{3}} \right)=

\displaystyle l)\quad 8{{q}^{9}}:\left( -2q \right)=

 

9)        Doplňte tak, aby platila rovnost:

\displaystyle a)\quad 24{{a}^{2}}{{b}^{3}}:\ldots =6ab

\displaystyle b)\quad {{x}^{7}}{{y}^{2}}{{z}^{3}}:\ldots =xy

\displaystyle c)\quad -5{{a}^{3}}{{b}^{3}}:\ldots =-ab

\displaystyle d)\quad \ldots :2xy=6x

\displaystyle e)\quad \ldots :\left( -2a \right)={{a}^{3}}{{b}^{2}}

\displaystyle f)\quad \ldots :\left( -rs \right)=3{{r}^{2}}{{s}^{3}}

\displaystyle g)\quad -6{{x}^{3}}y:\ldots =2y

\displaystyle h)\quad -a{{b}^{4}}:\ldots =b

\displaystyle i)\quad 12{{s}^{5}}{{r}^{3}}:\ldots =-2sr

\displaystyle j)\quad \ldots :pq=pq

\displaystyle k)\quad \ldots :{{a}^{3}}b=1

\displaystyle l)\quad \ldots :\left( -2l \right)=l{{k}^{2}}

 

10)       Vynásobte:

\displaystyle a)\quad 3\cdot \left( 2a+3b-4+5k-6m \right)=

\displaystyle b)\quad 2\cdot \left( 5k+9 \right)=

\displaystyle c)\quad 6\cdot \left( 7m+n-8-4o-5p \right)=

\displaystyle d)\quad \left( -5p-6u-7r-3v+3 \right)\cdot 4=

\displaystyle e)\quad \left( s+h-2q+6g-1 \right)\cdot \left( -2 \right)=

\displaystyle f)\quad \left( 6t-5w+5j-11g+9 \right)\cdot \left( -11 \right)=

\displaystyle g)\quad \left( -4 \right)\left( 7o-9p-7r+6t+11 \right)=

\displaystyle h)\quad \left( 4y-9k+h-9 \right)\cdot 20=

\displaystyle i)\quad \left( 6q-2a+7z-3h+9 \right)\cdot \left( -8 \right)=

\displaystyle j)\quad \left( 9p+5m+3 \right)\cdot 4=

 

11)       Vynásobte:

\displaystyle a)\quad \left( 11o+18p-9k \right)\cdot 17=

\displaystyle b)\quad \left( 3u+9j-5f+6 \right)\cdot 24=

\displaystyle c)\quad 21\left( 9p+3v-6d+3 \right)=

\displaystyle d)\quad \left( 8r-6z+6w+4 \right)11=

\displaystyle e)\quad 5\left( 8o-9p+k+\text{ }7z-h-6 \right)=

\displaystyle f)\quad 12\left( -6u+9v-8d-5c-6k+8 \right)=

\displaystyle g)\quad \left( 11t-2s+2u-8r+5w+6x-2 \right)\cdot 8=

\displaystyle h)\quad \left( 14a-5b+3d-5o-9p+3t+6 \right)\cdot 7=

 

12)        Vypočítejte:

\displaystyle a)\quad m\left( m+5 \right)=

\displaystyle b)\quad \left( -6x \right)\left( x+y \right)=

\displaystyle c)\quad 4n\left( 3n-7 \right)=

\displaystyle d)\quad 7x\left( x-2y+3 \right)=

\displaystyle e)\quad \left( 3m-8n+2 \right)4n=

\displaystyle f)\quad \left( 0,6x+\frac{1}{2}y-3 \right)\left( -2x \right)=

\displaystyle g)\quad 2s\left( 3s-5{{s}^{2}} \right)=

\displaystyle h)\quad 5r\left( 2r-0,2 \right)=

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

\displaystyle j)\quad \left( -6a \right)\left( 4a-3b-7 \right)=

\displaystyle k)\quad \left( -8r+s-5 \right)\left( -2 \right)=

\displaystyle l)\quad \left( -3,2a+0,25b-1 \right)\left( -4b \right)=

 

13)        Vypočítejte:

\displaystyle a)\quad 5x+3\left( x-7 \right)=

\displaystyle b)\quad 9a-6\left( 2a-1 \right)=

\displaystyle c)\quad 12ab+4a\left( a-3b \right)=

\displaystyle d)\quad 3xy-2x\left( 4x-y \right)=

\displaystyle e)\quad \left( m-2n \right)3m+6mn=

\displaystyle f)\quad \left( 4x-5y \right)3-2x=

 

14)        Vypočítejte:

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

\displaystyle b)\quad 6\left( 3x+4y \right)-8\left( 5x-y \right)+x-y=

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

\displaystyle d)\quad \left( a+b \right)4-\left( a-b \right)3=

\displaystyle e)\quad 4+3\left( u-1 \right)-3u=

\displaystyle f)\quad 2d\left( {{d}^{2}}+3,5d-1 \right)-7{{d}^{2}}=

 

15)        Vypočítejte:

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

\displaystyle b)\quad 6ab-3b\left( 2a-4b \right)-12{{b}^{2}}=

\displaystyle c)\quad 8\left( x-2y \right)+3\left( 2x-y \right)=

\displaystyle d)\quad 4\left( 3a-5b \right)-6\left( 2a+3b \right)=

\displaystyle e)\quad \left( 2m-n \right)\left( -3 \right)+6\left( m-2n \right)=

\displaystyle f)\quad \left( -8 \right)\left( -r+s \right)-3\left( 4r-7s \right)=

 

16)        Vypočítejte:

\displaystyle a)\quad -5-2\left( x+3 \right)+2\left( 5-4x \right)-3\left( 2x-7 \right)=

\displaystyle b)\quad 4\left( 3-5a \right)-a-2\left( 4a+1 \right)-3+4\left( 6a-1 \right)=

\displaystyle c)\quad 0,5\left( 6-2b \right)-0,2\left( b-3 \right)+1,5\left( 3-5b \right)=

\displaystyle d)\quad 0,3\left( 3y-5 \right)-4\left( 1,5-2y \right)-1,1\left( -3-4y \right)=

\displaystyle e)\quad -5k-\left( k-3 \right)-5\left( 3-3k \right)+\left( -2k-1 \right)-2=

\displaystyle f)\quad 0,4x-\left( -0,6x \right)-1-4\left( 0,5x-2,5 \right)+2\left( 1,5-3,5x \right)=

\displaystyle g)\quad 2,2\left( 3s-2 \right)-\left( -2,5s-1 \right)+1,2\left( 6-7s \right)-\left( -5s \right)=

\displaystyle h)\quad 4\left( p+2 \right)-7\left( 3-2p \right)-\left( 8p+7 \right)-2p=

\displaystyle i)\quad 2,5\left( 6-2x \right)-\left( 8x+3 \right)-1,2\left( 5-10x \right)-2\left( 3,5x+7 \right)=

\displaystyle j)\quad 10+\left( 1-2v \right)-0,5\left( 2v-6 \right)+8\left( 1-0,5v \right)-4v=

\displaystyle k)\quad -7a-\left( a-3 \right)+2,1\left( 10a-3 \right)-3,7-\left( -2a \right)=

\displaystyle l)\quad 6\left( 3x-8 \right)-5\left( 2x+1 \right)-4\left( 3-2x \right)-3\left( 7x-1 \right)=

\displaystyle m)\quad -0,5b-\left( -0,5 \right)-0,5\left( 2b-1 \right)-1,5\left( 3-2b \right)=

\displaystyle n)\quad 1-1,4\left( 5y-10 \right)+\left( -2y \right)+4\left( 3-1,5y \right)-8y=

 

17)        Vynásobte a zjednodušte:

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

\displaystyle b)\quad \left( 2a-5 \right)\left( 7-3a \right)=

\displaystyle c)\quad \left( 4a-9 \right)\left( -5a+3 \right)=

\displaystyle d)\quad \left( -6a+11 \right)\left( -7a-4 \right)=

\displaystyle e)\quad \left( x-1 \right)\left( 2x+3 \right)=

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

\displaystyle g)\quad \left( 2y-3 \right)\left( 3y-2 \right)=

\displaystyle h)\quad \left( 0,5x-3y \right)\left( 2x+4y \right)=

\displaystyle i)\quad \left( 3m+6 \right)\left( 5n-3m \right)=

\displaystyle j)\quad \left( 8a-12b \right)\left( \frac{1}{4}b-\frac{3}{4}a \right)=

 

18)        Vynásobte a zjednodušte:

\displaystyle a)\quad \left( m+3 \right)\left( m+5 \right)=

\displaystyle b)\quad \left( m+4 \right)\left( m-7 \right)=

\displaystyle c)\quad \left( 2n+3 \right)\left( 4-n \right)=

\displaystyle d)\quad \left( 5n-6 \right)\left( 7-3n \right)=

\displaystyle e)\quad \left( 6a+b \right)\left( a-5b \right)=

\displaystyle f)\quad \left( 3a-7b \right)\left( 2b-5a \right)=

\displaystyle g)\quad \left( -9x+2y \right)\left( 2y-9x \right)=

\displaystyle h)\quad \left( 4x+5y \right)\left( -4x-5y \right)=

 

19)        Zjednodušte:

\displaystyle a)\quad 7x-3x\left( 8y-7 \right)+4y\left( 6x-2 \right)=

\displaystyle b)\quad \left( 2y-3 \right)3x-\left( 5x+7 \right)4y+6y=

\displaystyle c)\quad y-2\left( 9x-5 \right)+4-6x\left( y-3 \right)=

\displaystyle d)\quad \left( 7x-3x \right)\left( 8y-7 \right)+4y\left( 6x-2 \right)=

\displaystyle e)\quad \left( 2y-3 \right)3x-\left( 5x-7 \right)\left( 4y+6y \right)=

\displaystyle f)\quad \left( y-2 \right)\left( 9x-5 \right)+\left( 4-6x \right)\left( y-3 \right)=

 

20)        Zjednodušte:

\displaystyle a)\quad \left( 2a+3 \right)\left( 8b-6 \right)+\left( 7a-3 \right)\left( 4b-1 \right)=

\displaystyle b)\quad \left( 4a+2 \right)\left( 6b-9 \right)-\left( 3a+6 \right)\left( 3-8b \right)=

\displaystyle c)\quad \left( 9a-8 \right)\left( 4b+5 \right)-\left( 6a+10 \right)\left( 6b-4 \right)=

\displaystyle d)\quad \left( 18a-24 \right)\left( b-3 \right)-\left( 3a-4 \right)\left( 6b-18 \right)=