Vzorce

1)        Umocněte podle vzorce:

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

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

\displaystyle c)\quad {{\left( c+10 \right)}^{2}}=

\displaystyle d)\quad {{\left( 7-g \right)}^{2}}=

\displaystyle e)\quad {{\left( d-5 \right)}^{2}}=

\displaystyle f)\quad {{\left( e-6 \right)}^{2}}=

\displaystyle g)\quad {{\left( f-100 \right)}^{2}}=

\displaystyle h)\quad {{\left( 8-h \right)}^{2}}=

 

2)        Umocněte podle vzorce:

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

\displaystyle b)\quad {{\left( 3y-5 \right)}^{2}}=

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

\displaystyle d)\quad {{\left( 5a+2 \right)}^{2}}=

\displaystyle e)\quad {{\left( 7b-6 \right)}^{2}}=

\displaystyle f)\quad {{\left( 7+3c \right)}^{2}}=

\displaystyle g)\quad {{\left( 10-5d \right)}^{2}}=

\displaystyle h)\quad {{\left( 11f+3 \right)}^{2}}=

 

3)        Umocněte podle vzorce:

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

\displaystyle b)\quad {{\left( c-5d \right)}^{2}}=

\displaystyle c)\quad {{\left( e+3f \right)}^{2}}=

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

\displaystyle e)\quad {{\left( 5u+6v \right)}^{2}}=

\displaystyle f)\quad {{\left( 2x-y \right)}^{2}}=

\displaystyle g)\quad {{\left( 3u-v \right)}^{2}}=

\displaystyle h)\quad {{\left( m+10n \right)}^{2}}=

\displaystyle i)\quad {{\left( 5x-4y \right)}^{2}}=

\displaystyle j)\quad {{\left( 4x+10y \right)}^{2}}=

 

4)        Umocněte podle vzorce:

\displaystyle a)\quad {{\left( 0,2x+0,3 \right)}^{2}}=

\displaystyle b)\quad {{\left( 5x+0,5 \right)}^{2}}=

\displaystyle c)\quad {{\left( 0,4a-6 \right)}^{2}}=

\displaystyle d)\quad {{\left( 0,1x-0,1 \right)}^{2}}=

 

5)        Umocněte podle vzorce:

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

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

\displaystyle c)\quad {{\left( \frac{1}{2}c+2d \right)}^{2}}=

\displaystyle d)\quad {{\left( 10-\frac{m}{5} \right)}^{2}}=

\displaystyle e)\quad {{\left( \frac{2}{3}u+\frac{1}{5} \right)}^{2}}=

\displaystyle f)\quad {{\left( \frac{2}{5}x+0,2 \right)}^{2}}=

 

6)        Umocněte podle vzorce:

\displaystyle a)\quad {{\left( \frac{1}{2}a-b \right)}^{2}}=

\displaystyle b)\quad {{\left( 2-\frac{1}{3}x \right)}^{2}}=

\displaystyle c)\quad {{\left( \frac{t}{2}+u \right)}^{2}}=

\displaystyle d)\quad {{\left( \frac{k}{5}+\frac{l}{3} \right)}^{2}}=

\displaystyle e)\quad {{\left( \frac{3}{4}a-\frac{1}{2}b \right)}^{2}}=

\displaystyle f)\quad {{\left( \frac{4}{7}c-d \right)}^{2}}=

\displaystyle g)\quad {{\left( \frac{1}{8}+2a \right)}^{2}}=

\displaystyle h)\quad {{\left( \frac{2}{3}-\frac{1}{4}l \right)}^{2}}=

\displaystyle i)\quad {{\left( rs-\frac{2}{7}t \right)}^{2}}=

\displaystyle j)\quad {{\left( \frac{5}{2}x-2y \right)}^{2}}=

 

7)        Rozložte na součin užitím vhodného vzorce:

\displaystyle a)\quad {{c}^{2}}-49=

\displaystyle b)\quad 64-{{r}^{2}}=

\displaystyle c)\quad -9{{s}^{2}}+64=

\displaystyle d)\quad 1-{{v}^{2}}=

\displaystyle e)\quad 9{{x}^{2}}-4{{y}^{2}}=

\displaystyle f)\quad -81{{b}^{2}}+{{a}^{2}}=

\displaystyle g)\quad {{b}^{2}}-36{{c}^{2}}=

\displaystyle h)\quad 100-4{{m}^{2}}=

\displaystyle i)\quad 16{{m}^{2}}-1=

\displaystyle j)\quad 121{{m}^{2}}-25{{n}^{2}}=

\displaystyle k)\quad 0,16{{r}^{2}}-0,04=

\displaystyle l)\quad -64+\frac{9}{4}{{r}^{2}}=

 

8)        Rozložte na součin užitím vhodného vzorce:

\displaystyle a)\quad 4{{x}^{2}}-16{{y}^{2}}=

\displaystyle b)\quad 25{{a}^{2}}-9{{b}^{2}}=

\displaystyle c)\quad 49{{c}^{2}}-{{d}^{2}}=

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

\displaystyle e)\quad 64-36{{k}^{2}}=

\displaystyle f)\quad {{x}^{4}}-1=

\displaystyle g)\quad 16{{y}^{4}}-81=

\displaystyle h)\quad 75{{m}^{2}}-27{{n}^{2}}=

\displaystyle i)\quad 32{{r}^{2}}-2=

\displaystyle j)\quad \frac{1}{4}-{{x}^{2}}=

\displaystyle k)\quad \frac{1}{9}{{s}^{2}}-\frac{1}{25}{{t}^{2}}=

\displaystyle l)\quad \frac{4}{25}{{a}^{2}}-\frac{9}{16}{{b}^{2}}=

 

9)        Upravte výraz užitím vhodného vzorce:

\displaystyle a)\quad {{a}^{2}}+6a+9=

\displaystyle b)\quad 1-2y+{{y}^{2}}=

\displaystyle c)\quad 9{{x}^{2}}-12xy+4{{y}^{2}}=

\displaystyle d)\quad 16{{u}^{2}}+40u+25=

\displaystyle e)\quad {{t}^{2}}+4tu+4{{u}^{2}}=

\displaystyle f)\quad 4{{v}^{2}}+20v+25=

\displaystyle g)\quad 36{{m}^{2}}+60mn+25{{n}^{2}}=

\displaystyle h)\quad {{x}^{2}}-6xy+9{{y}^{2}}=

 

10)        Upravte výraz užitím vhodného vzorce:

\displaystyle a)\quad 9{{x}^{2}}-6x+1=

\displaystyle b)\quad 16{{b}^{2}}+8bc+{{c}^{2}}=

\displaystyle c)\quad \frac{1}{4}{{e}^{2}}+ef+{{f}^{2}}=

\displaystyle d)\quad 0,01{{a}^{2}}+0,06ab+0,09{{b}^{2}}=

\displaystyle e)\quad 4-36a+81{{a}^{2}}=

\displaystyle f)\quad 100{{r}^{2}}-60rs+9{{s}^{2}}=

\displaystyle g)\quad \frac{1}{36}{{x}^{2}}-\frac{1}{4}xy+\frac{9}{16}{{y}^{2}}=

\displaystyle h)\quad {{b}^{2}}-b+0,25=

 

11)        Doplňte místo teček správné hodnoty:

\displaystyle a)\quad {{\left( \ \ldots \ +\ \ldots \  \right)}^{2}}={{b}^{2}}+\ \ldots \ +16

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

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

\displaystyle d)\quad 9{{a}^{2}}-\ \ldots \ =\left( \ \ldots \ -\ \ldots \  \right)\left( \ \ldots \ +2b \right)

\displaystyle e)\quad {{\left( \ \ldots \ -\ \ldots \  \right)}^{2}}=9{{x}^{2}}-\ \ldots \ +{{y}^{2}}

\displaystyle f)\quad \ \ldots \ -9{{a}^{2}}=\left( \ \ldots \ -\ \ldots \  \right)\left( 1+\ \ldots \  \right)

\displaystyle g)\quad {{\left( 5c+\ \ldots \  \right)}^{2}}=\ \ldots \ +\ \ldots \ +36{{d}^{2}}

\displaystyle h)\quad \ \ldots \ -\ \ldots \ =\left( a-\ \ldots \  \right)\left( \ \ldots \ +\frac{1}{2} \right)

 

12)        Upravte výraz užitím vhodného vzorce:

\displaystyle a)\quad {{z}^{2}}-4z+4=

\displaystyle b)\quad {{a}^{2}}-12a+36=

\displaystyle c)\quad 9-6r+{{r}^{2}}=

\displaystyle d)\quad {{c}^{2}}-\frac{c}{2}+\frac{1}{16}=

\displaystyle e)\quad 4{{u}^{2}}-4uv+{{v}^{2}}=

\displaystyle f)\quad 0,04{{a}^{2}}-2a+25=

\displaystyle g)\quad 36{{x}^{2}}-36xy+9{{y}^{2}}=

\displaystyle h)\quad 144-24a+{{a}^{2}}=