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

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

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Verbetersleutel

  1. \(\begin{align}(x-\frac{10}{20})(\frac{-7}{11}+a)& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{-7}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{11})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-7}{11})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{11}x-\frac{1}{2}a+\frac{1}{2}.\frac{7}{11}& \text{Uitwerken } \\ & =ax-\frac{7}{11}x-\frac{1}{2}a+\frac{7}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{-3}{4})(\frac{-15}{15}+a)& =(\color{red}{p}+\color{orange}{\frac{3}{4}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{3}{4})} . \color{green}{(a)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ap-1p+\frac{3}{4}a-\frac{3}{4}.1& \text{Uitwerken } \\ & =ap-1p+\frac{3}{4}a-\frac{3}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{19}{16})(b+\frac{-11}{4})& =(\color{red}{x}+\color{orange}{\frac{19}{16}}).(\color{green}{b}+\color{blue}{\frac{-11}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{4})} + \color{orange}{(\frac{19}{16})} . \color{green}{(b)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(\frac{-11}{4})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{4}x+\frac{19}{16}b-\frac{19}{16}.\frac{11}{4}& \text{Uitwerken } \\ & =bx-\frac{11}{4}x+\frac{19}{16}b-\frac{209}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-7}{4}-a)(\frac{9}{5}-a)& =(\color{red}{-a}+\color{orange}{\frac{-7}{4}}).(\color{green}{-a}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{9}{5}a+\frac{7}{4}a-\frac{7}{4}.\frac{9}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-9}{5})+\frac{7}{4})a-(\frac{-63}{20}) & \text{Neem samen} \\ &=a^2-\frac{1}{20}a-(\frac{-63}{20}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-12}{12})(q+\frac{12}{11})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{12}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{12}{11})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{12}{11})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{12}{11}p+1q+1.\frac{12}{11}& \text{Uitwerken } \\ & =pq+\frac{12}{11}p+1q+\frac{12}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{10}{7}-a)(a+\frac{20}{12})& =(\color{red}{-a}+\color{orange}{\frac{10}{7}}).(\color{green}{a}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{10}{7})} . \color{green}{(a)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{5}{3}a+\frac{10}{7}a+\frac{10}{7}.\frac{5}{3}& \text{Uitwerken } \\ & =-a^2+((\frac{-5}{3})+\frac{10}{7})a+(\frac{-50}{21}) & \text{Neem samen} \\ &=-a^2-\frac{5}{21}a+(\frac{-50}{21}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-10}{19}+b)(p-\frac{-5}{7})& =(\color{red}{b}+\color{orange}{\frac{-10}{19}}).(\color{green}{p}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{-10}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{19})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{7}b-\frac{10}{19}p-\frac{10}{19}.\frac{5}{7}& \text{Uitwerken } \\ & =bp+\frac{5}{7}b-\frac{10}{19}p-\frac{50}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-12}{6})(q-\frac{20}{2})& =(\color{red}{x}+\color{orange}{2}).(\color{green}{q}+\color{blue}{(-10)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-10)} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = qx-10x+2q-2.10& \text{Uitwerken } \\ & =qx-10x+2q-20 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-4}{13}-a)(p-\frac{-20}{8})& =(\color{red}{-a}+\color{orange}{\frac{-4}{13}}).(\color{green}{p}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{5}{2}a-\frac{4}{13}p-\frac{4}{13}.\frac{5}{2}& \text{Uitwerken } \\ & =-ap-\frac{5}{2}a-\frac{4}{13}p-\frac{20}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{5}{2}a-\frac{4}{13}p-\frac{10}{13} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{1}{2}+p)(q-\frac{2}{9})& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{2}{9}p+\frac{1}{2}q-\frac{1}{2}.\frac{2}{9}& \text{Uitwerken } \\ & =pq-\frac{2}{9}p+\frac{1}{2}q-\frac{2}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{2}{9}p+\frac{1}{2}q-\frac{1}{9} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{5}{13}+q)(4-b)& =(\color{red}{q}+\color{orange}{\frac{5}{13}}).(\color{green}{-b}+\color{blue}{4})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(4)} + \color{orange}{(\frac{5}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -bq+4q-\frac{5}{13}b+\frac{5}{13}.4& \text{Uitwerken } \\ & =-bq+4q-\frac{5}{13}b+\frac{20}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-5}{18}-a)(p+\frac{-19}{13})& =(\color{red}{-a}+\color{orange}{\frac{-5}{18}}).(\color{green}{p}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{-5}{18})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{19}{13}a-\frac{5}{18}p+\frac{5}{18}.\frac{19}{13}& \text{Uitwerken } \\ & =-ap+\frac{19}{13}a-\frac{5}{18}p+\frac{95}{234} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-09 05:18:56
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