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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{-4}{11})(\frac{-7}{4}+q)& =(\color{red}{x}+\color{orange}{\frac{-4}{11}}).(\color{green}{q}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{-4}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{11})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{7}{4}x-\frac{4}{11}q+\frac{4}{11}.\frac{7}{4}& \text{Uitwerken } \\ & =qx-\frac{7}{4}x-\frac{4}{11}q+\frac{28}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{7}{4}x-\frac{4}{11}q+\frac{7}{11} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(x-\frac{-20}{9})(\frac{11}{16}-x)& =(\color{red}{x}+\color{orange}{\frac{20}{9}}).(\color{green}{-x}+\color{blue}{\frac{11}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{11}{16})} + \color{orange}{(\frac{20}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{11}{16})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{11}{16}x-\frac{20}{9}x+\frac{20}{9}.\frac{11}{16}& \text{Uitwerken } \\ & =-x^2+(\frac{11}{16}+(\frac{-20}{9}))x+(\frac{-220}{144}) & \text{Neem samen} \\ &=-x^2-\frac{221}{144}x+(\frac{-220}{144}) & \text{Maak de som} \\ &=-x^2-\frac{221}{144}x+(\frac{-55}{36}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(b+\frac{-19}{10})(\frac{-12}{18}+p)& =(\color{red}{b}+\color{orange}{\frac{-19}{10}}).(\color{green}{p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-19}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{10})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{2}{3}b-\frac{19}{10}p+\frac{19}{10}.\frac{2}{3}& \text{Uitwerken } \\ & =bp-\frac{2}{3}b-\frac{19}{10}p+\frac{38}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{2}{3}b-\frac{19}{10}p+\frac{19}{15} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-6}{16}+x)(\frac{-18}{9}-q)& =(\color{red}{x}+\color{orange}{\frac{-3}{8}}).(\color{green}{-q}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{-3}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -qx-2x+\frac{3}{8}q+\frac{3}{8}.2& \text{Uitwerken } \\ & =-qx-2x+\frac{3}{8}q+\frac{6}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-2x+\frac{3}{8}q+\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a-\frac{4}{11})(\frac{-9}{16}+x)& =(\color{red}{a}+\color{orange}{\frac{-4}{11}}).(\color{green}{x}+\color{blue}{\frac{-9}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{16})} + \color{orange}{(\frac{-4}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{11})} . \color{blue}{(\frac{-9}{16})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{9}{16}a-\frac{4}{11}x+\frac{4}{11}.\frac{9}{16}& \text{Uitwerken } \\ & =ax-\frac{9}{16}a-\frac{4}{11}x+\frac{36}{176} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{9}{16}a-\frac{4}{11}x+\frac{9}{44} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-13}{14}-x)(\frac{7}{19}+a)& =(\color{red}{-x}+\color{orange}{\frac{-13}{14}}).(\color{green}{a}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(\frac{-13}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{7}{19}x-\frac{13}{14}a-\frac{13}{14}.\frac{7}{19}& \text{Uitwerken } \\ & =-ax-\frac{7}{19}x-\frac{13}{14}a-\frac{91}{266} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{7}{19}x-\frac{13}{14}a-\frac{13}{38} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-8}{10}-a)(q+\frac{7}{6})& =(\color{red}{-a}+\color{orange}{\frac{-4}{5}}).(\color{green}{q}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{7}{6}a-\frac{4}{5}q-\frac{4}{5}.\frac{7}{6}& \text{Uitwerken } \\ & =-aq-\frac{7}{6}a-\frac{4}{5}q-\frac{28}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{7}{6}a-\frac{4}{5}q-\frac{14}{15} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-10}{11})(\frac{-10}{20}-b)& =(\color{red}{a}+\color{orange}{\frac{10}{11}}).(\color{green}{-b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{10}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{10}{11})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{2}a-\frac{10}{11}b-\frac{10}{11}.\frac{1}{2}& \text{Uitwerken } \\ & =-ab-\frac{1}{2}a-\frac{10}{11}b-\frac{10}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{1}{2}a-\frac{10}{11}b-\frac{5}{11} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p+\frac{-6}{3})(a+\frac{2}{20})& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{10}p-2a-2.\frac{1}{10}& \text{Uitwerken } \\ & =ap+\frac{1}{10}p-2a-\frac{2}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{1}{10}p-2a-\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-4}{7}-p)(\frac{19}{13}+q)& =(\color{red}{-p}+\color{orange}{\frac{-4}{7}}).(\color{green}{q}+\color{blue}{\frac{19}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{13})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{19}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{19}{13}p-\frac{4}{7}q-\frac{4}{7}.\frac{19}{13}& \text{Uitwerken } \\ & =-pq-\frac{19}{13}p-\frac{4}{7}q-\frac{76}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{5}{13}+a)(x-\frac{-1}{5})& =(\color{red}{a}+\color{orange}{\frac{5}{13}}).(\color{green}{x}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{5}{13})} . \color{green}{(x)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{5}a+\frac{5}{13}x+\frac{5}{13}.\frac{1}{5}& \text{Uitwerken } \\ & =ax+\frac{1}{5}a+\frac{5}{13}x+\frac{5}{65} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{1}{5}a+\frac{5}{13}x+\frac{1}{13} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p+\frac{-13}{6})(\frac{-10}{7}-a)& =(\color{red}{p}+\color{orange}{\frac{-13}{6}}).(\color{green}{-a}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{-13}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-13}{6})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{10}{7}p+\frac{13}{6}a+\frac{13}{6}.\frac{10}{7}& \text{Uitwerken } \\ & =-ap-\frac{10}{7}p+\frac{13}{6}a+\frac{130}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{10}{7}p+\frac{13}{6}a+\frac{65}{21} & \text{Vereenvoudig} \\\end{align}\)
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