Distributiviteit \((a+r)(b+s)\)

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  1. \((x+\frac{1}{6})(p-\frac{11}{12})\)
  2. \((\frac{-1}{14}+a)(\frac{-2}{3}+p)\)
  3. \((x+\frac{13}{12})(\frac{-10}{4}+q)\)
  4. \(((-19)+b)(\frac{-11}{14}-a)\)
  5. \((\frac{9}{15}+b)(\frac{-20}{19}+a)\)
  6. \((q-\frac{-11}{20})(\frac{-8}{18}-x)\)
  7. \((\frac{1}{8}-p)(\frac{6}{19}-b)\)
  8. \((\frac{2}{13}+p)(a+\frac{-6}{13})\)
  9. \((\frac{6}{13}-p)(\frac{14}{3}-p)\)
  10. \((\frac{12}{9}-x)(b+\frac{20}{10})\)
  11. \((p-\frac{18}{16})(b+\frac{-9}{9})\)
  12. \((x+\frac{14}{11})(\frac{-20}{7}-q)\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{1}{6})(p-\frac{11}{12})& =(\color{red}{x}+\color{orange}{\frac{1}{6}}).(\color{green}{p}+\color{blue}{\frac{-11}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{12})} + \color{orange}{(\frac{1}{6})} . \color{green}{(p)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-11}{12})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{11}{12}x+\frac{1}{6}p-\frac{1}{6}.\frac{11}{12}& \text{Uitwerken } \\ & =px-\frac{11}{12}x+\frac{1}{6}p-\frac{11}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-1}{14}+a)(\frac{-2}{3}+p)& =(\color{red}{a}+\color{orange}{\frac{-1}{14}}).(\color{green}{p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-1}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{14})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{3}a-\frac{1}{14}p+\frac{1}{14}.\frac{2}{3}& \text{Uitwerken } \\ & =ap-\frac{2}{3}a-\frac{1}{14}p+\frac{2}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{2}{3}a-\frac{1}{14}p+\frac{1}{21} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x+\frac{13}{12})(\frac{-10}{4}+q)& =(\color{red}{x}+\color{orange}{\frac{13}{12}}).(\color{green}{q}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{13}{12})} . \color{green}{(q)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{2}x+\frac{13}{12}q-\frac{13}{12}.\frac{5}{2}& \text{Uitwerken } \\ & =qx-\frac{5}{2}x+\frac{13}{12}q-\frac{65}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}((-19)+b)(\frac{-11}{14}-a)& =(\color{red}{b}+\color{orange}{(-19)}).(\color{green}{-a}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(-19)} . \color{green}{(-a)} + \color{orange}{(-19)} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{11}{14}b+19a+19.\frac{11}{14}& \text{Uitwerken } \\ & =-ab-\frac{11}{14}b+19a+\frac{209}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{9}{15}+b)(\frac{-20}{19}+a)& =(\color{red}{b}+\color{orange}{\frac{3}{5}}).(\color{green}{a}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{20}{19}b+\frac{3}{5}a-\frac{3}{5}.\frac{20}{19}& \text{Uitwerken } \\ & =ab-\frac{20}{19}b+\frac{3}{5}a-\frac{60}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{20}{19}b+\frac{3}{5}a-\frac{12}{19} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q-\frac{-11}{20})(\frac{-8}{18}-x)& =(\color{red}{q}+\color{orange}{\frac{11}{20}}).(\color{green}{-x}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{11}{20})} . \color{green}{(-x)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{4}{9}q-\frac{11}{20}x-\frac{11}{20}.\frac{4}{9}& \text{Uitwerken } \\ & =-qx-\frac{4}{9}q-\frac{11}{20}x-\frac{44}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{4}{9}q-\frac{11}{20}x-\frac{11}{45} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{1}{8}-p)(\frac{6}{19}-b)& =(\color{red}{-p}+\color{orange}{\frac{1}{8}}).(\color{green}{-b}+\color{blue}{\frac{6}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{6}{19})} + \color{orange}{(\frac{1}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{6}{19})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{6}{19}p-\frac{1}{8}b+\frac{1}{8}.\frac{6}{19}& \text{Uitwerken } \\ & =bp-\frac{6}{19}p-\frac{1}{8}b+\frac{6}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{6}{19}p-\frac{1}{8}b+\frac{3}{76} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{2}{13}+p)(a+\frac{-6}{13})& =(\color{red}{p}+\color{orange}{\frac{2}{13}}).(\color{green}{a}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(\frac{2}{13})} . \color{green}{(a)} + \color{orange}{(\frac{2}{13})} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{6}{13}p+\frac{2}{13}a-\frac{2}{13}.\frac{6}{13}& \text{Uitwerken } \\ & =ap-\frac{6}{13}p+\frac{2}{13}a-\frac{12}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{6}{13}-p)(\frac{14}{3}-p)& =(\color{red}{-p}+\color{orange}{\frac{6}{13}}).(\color{green}{-p}+\color{blue}{\frac{14}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{14}{3})} + \color{orange}{(\frac{6}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{6}{13})} . \color{blue}{(\frac{14}{3})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{14}{3}p-\frac{6}{13}p+\frac{6}{13}.\frac{14}{3}& \text{Uitwerken } \\ & =p^2+((\frac{-14}{3})+(\frac{-6}{13}))p+\frac{84}{39} & \text{Neem samen} \\ &=p^2-\frac{200}{39}p+\frac{84}{39} & \text{Maak de som} \\ &=p^2-\frac{200}{39}p+\frac{28}{13} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{12}{9}-x)(b+\frac{20}{10})& =(\color{red}{-x}+\color{orange}{\frac{4}{3}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(2)} + \color{orange}{(\frac{4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -bx-2x+\frac{4}{3}b+\frac{4}{3}.2& \text{Uitwerken } \\ & =-bx-2x+\frac{4}{3}b+\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p-\frac{18}{16})(b+\frac{-9}{9})& =(\color{red}{p}+\color{orange}{\frac{-9}{8}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-9}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bp-1p-\frac{9}{8}b+\frac{9}{8}.1& \text{Uitwerken } \\ & =bp-1p-\frac{9}{8}b+\frac{9}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{14}{11})(\frac{-20}{7}-q)& =(\color{red}{x}+\color{orange}{\frac{14}{11}}).(\color{green}{-q}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{14}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{14}{11})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{20}{7}x-\frac{14}{11}q-\frac{14}{11}.\frac{20}{7}& \text{Uitwerken } \\ & =-qx-\frac{20}{7}x-\frac{14}{11}q-\frac{280}{77} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{20}{7}x-\frac{14}{11}q-\frac{40}{11} & \text{Vereenvoudig} \\\end{align}\)
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