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

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  1. \((b+\frac{-17}{18})(\frac{-16}{16}-b)\)
  2. \((\frac{2}{16}-p)(\frac{7}{17}+x)\)
  3. \((\frac{-6}{20}+p)(p-\frac{-3}{18})\)
  4. \((b+\frac{-7}{11})(\frac{-9}{12}-b)\)
  5. \((a+\frac{3}{11})(x+\frac{-1}{6})\)
  6. \((\frac{-14}{20}-q)(p-\frac{10}{2})\)
  7. \((\frac{-13}{13}-b)(\frac{6}{5}+q)\)
  8. \((\frac{-6}{13}+a)(x-\frac{-8}{16})\)
  9. \((\frac{4}{15}-a)(x-\frac{20}{16})\)
  10. \((p+\frac{13}{14})(a+\frac{17}{2})\)
  11. \((p-\frac{-8}{6})(b-\frac{-4}{11})\)
  12. \((\frac{14}{9}-p)(\frac{2}{17}+a)\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-17}{18})(\frac{-16}{16}-b)& =(\color{red}{b}+\color{orange}{\frac{-17}{18}}).(\color{green}{-b}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-17}{18})} . \color{green}{(-b)} + \color{orange}{(\frac{-17}{18})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bb-1b+\frac{17}{18}b+\frac{17}{18}.1& \text{Uitwerken } \\ & =-b^2+((-1)+\frac{17}{18})b+(\frac{-17}{18}) & \text{Neem samen} \\ &=-b^2-\frac{1}{18}b+(\frac{-17}{18}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{2}{16}-p)(\frac{7}{17}+x)& =(\color{red}{-p}+\color{orange}{\frac{1}{8}}).(\color{green}{x}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(\frac{1}{8})} . \color{green}{(x)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{7}{17}p+\frac{1}{8}x+\frac{1}{8}.\frac{7}{17}& \text{Uitwerken } \\ & =-px-\frac{7}{17}p+\frac{1}{8}x+\frac{7}{136} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-6}{20}+p)(p-\frac{-3}{18})& =(\color{red}{p}+\color{orange}{\frac{-3}{10}}).(\color{green}{p}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{6}p-\frac{3}{10}p-\frac{3}{10}.\frac{1}{6}& \text{Uitwerken } \\ & =p^2+(\frac{1}{6}+(\frac{-3}{10}))p-(\frac{-3}{60}) & \text{Neem samen} \\ &=p^2-\frac{4}{30}p-(\frac{-3}{60}) & \text{Maak de som} \\ &=p^2-\frac{2}{15}p+\frac{1}{20} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  4. \(\begin{align}(b+\frac{-7}{11})(\frac{-9}{12}-b)& =(\color{red}{b}+\color{orange}{\frac{-7}{11}}).(\color{green}{-b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-7}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{3}{4}b+\frac{7}{11}b+\frac{7}{11}.\frac{3}{4}& \text{Uitwerken } \\ & =-b^2+((\frac{-3}{4})+\frac{7}{11})b+(\frac{-21}{44}) & \text{Neem samen} \\ &=-b^2-\frac{5}{44}b+(\frac{-21}{44}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(a+\frac{3}{11})(x+\frac{-1}{6})& =(\color{red}{a}+\color{orange}{\frac{3}{11}}).(\color{green}{x}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{3}{11})} . \color{green}{(x)} + \color{orange}{(\frac{3}{11})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{6}a+\frac{3}{11}x-\frac{3}{11}.\frac{1}{6}& \text{Uitwerken } \\ & =ax-\frac{1}{6}a+\frac{3}{11}x-\frac{3}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{1}{6}a+\frac{3}{11}x-\frac{1}{22} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-14}{20}-q)(p-\frac{10}{2})& =(\color{red}{-q}+\color{orange}{\frac{-7}{10}}).(\color{green}{p}+\color{blue}{(-5)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(-5)} + \color{orange}{(\frac{-7}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -pq+5q-\frac{7}{10}p+\frac{7}{10}.5& \text{Uitwerken } \\ & =-pq+5q-\frac{7}{10}p+\frac{35}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+5q-\frac{7}{10}p+\frac{7}{2} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-13}{13}-b)(\frac{6}{5}+q)& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{6}{5}b-1q-1.\frac{6}{5}& \text{Uitwerken } \\ & =-bq-\frac{6}{5}b-1q-\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-6}{13}+a)(x-\frac{-8}{16})& =(\color{red}{a}+\color{orange}{\frac{-6}{13}}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-6}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-6}{13})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{2}a-\frac{6}{13}x-\frac{6}{13}.\frac{1}{2}& \text{Uitwerken } \\ & =ax+\frac{1}{2}a-\frac{6}{13}x-\frac{6}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{1}{2}a-\frac{6}{13}x-\frac{3}{13} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{4}{15}-a)(x-\frac{20}{16})& =(\color{red}{-a}+\color{orange}{\frac{4}{15}}).(\color{green}{x}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{4}{15})} . \color{green}{(x)} + \color{orange}{(\frac{4}{15})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{5}{4}a+\frac{4}{15}x-\frac{4}{15}.\frac{5}{4}& \text{Uitwerken } \\ & =-ax+\frac{5}{4}a+\frac{4}{15}x-\frac{20}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{5}{4}a+\frac{4}{15}x-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p+\frac{13}{14})(a+\frac{17}{2})& =(\color{red}{p}+\color{orange}{\frac{13}{14}}).(\color{green}{a}+\color{blue}{\frac{17}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{17}{2})} + \color{orange}{(\frac{13}{14})} . \color{green}{(a)} + \color{orange}{(\frac{13}{14})} . \color{blue}{(\frac{17}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{17}{2}p+\frac{13}{14}a+\frac{13}{14}.\frac{17}{2}& \text{Uitwerken } \\ & =ap+\frac{17}{2}p+\frac{13}{14}a+\frac{221}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p-\frac{-8}{6})(b-\frac{-4}{11})& =(\color{red}{p}+\color{orange}{\frac{4}{3}}).(\color{green}{b}+\color{blue}{\frac{4}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{4}{11})} + \color{orange}{(\frac{4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{4}{11})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{11}p+\frac{4}{3}b+\frac{4}{3}.\frac{4}{11}& \text{Uitwerken } \\ & =bp+\frac{4}{11}p+\frac{4}{3}b+\frac{16}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{14}{9}-p)(\frac{2}{17}+a)& =(\color{red}{-p}+\color{orange}{\frac{14}{9}}).(\color{green}{a}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{14}{9})} . \color{green}{(a)} + \color{orange}{(\frac{14}{9})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{2}{17}p+\frac{14}{9}a+\frac{14}{9}.\frac{2}{17}& \text{Uitwerken } \\ & =-ap-\frac{2}{17}p+\frac{14}{9}a+\frac{28}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-17 20:13:32
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