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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-20}{12})(q+\frac{-16}{7})& =(\color{red}{p}+\color{orange}{\frac{5}{3}}).(\color{green}{q}+\color{blue}{\frac{-16}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{7})} + \color{orange}{(\frac{5}{3})} . \color{green}{(q)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-16}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{16}{7}p+\frac{5}{3}q-\frac{5}{3}.\frac{16}{7}& \text{Uitwerken } \\ & =pq-\frac{16}{7}p+\frac{5}{3}q-\frac{80}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-11}{10})(a-\frac{-10}{20})& =(\color{red}{a}+\color{orange}{\frac{-11}{10}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-11}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{10})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{2}a-\frac{11}{10}a-\frac{11}{10}.\frac{1}{2}& \text{Uitwerken } \\ & =a^2+(\frac{1}{2}+(\frac{-11}{10}))a-(\frac{-11}{20}) & \text{Neem samen} \\ &=a^2-\frac{6}{10}a-(\frac{-11}{20}) & \text{Maak de som} \\ &=a^2-\frac{3}{5}a+\frac{11}{20} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(a+\frac{-15}{9})(p+\frac{8}{2})& =(\color{red}{a}+\color{orange}{\frac{-5}{3}}).(\color{green}{p}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(4)} + \color{orange}{(\frac{-5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = ap+4a-\frac{5}{3}p-\frac{5}{3}.4& \text{Uitwerken } \\ & =ap+4a-\frac{5}{3}p-\frac{20}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{-4}{6})(a-\frac{-4}{9})& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{a}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{4}{9}q+\frac{2}{3}a+\frac{2}{3}.\frac{4}{9}& \text{Uitwerken } \\ & =aq+\frac{4}{9}q+\frac{2}{3}a+\frac{8}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-17}{10}-a)(b+\frac{2}{13})& =(\color{red}{-a}+\color{orange}{\frac{-17}{10}}).(\color{green}{b}+\color{blue}{\frac{2}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{2}{13})} + \color{orange}{(\frac{-17}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(\frac{2}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{2}{13}a-\frac{17}{10}b-\frac{17}{10}.\frac{2}{13}& \text{Uitwerken } \\ & =-ab-\frac{2}{13}a-\frac{17}{10}b-\frac{34}{130} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{2}{13}a-\frac{17}{10}b-\frac{17}{65} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{10}{20}+a)(\frac{17}{4}+b)& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{17}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{17}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{17}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{4}a+\frac{1}{2}b+\frac{1}{2}.\frac{17}{4}& \text{Uitwerken } \\ & =ab+\frac{17}{4}a+\frac{1}{2}b+\frac{17}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x+\frac{16}{11})(\frac{-14}{18}-a)& =(\color{red}{x}+\color{orange}{\frac{16}{11}}).(\color{green}{-a}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{16}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{7}{9}x-\frac{16}{11}a-\frac{16}{11}.\frac{7}{9}& \text{Uitwerken } \\ & =-ax-\frac{7}{9}x-\frac{16}{11}a-\frac{112}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{-1}{15})(p+\frac{-11}{10})& =(\color{red}{q}+\color{orange}{\frac{-1}{15}}).(\color{green}{p}+\color{blue}{\frac{-11}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{10})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{-11}{10})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{11}{10}q-\frac{1}{15}p+\frac{1}{15}.\frac{11}{10}& \text{Uitwerken } \\ & =pq-\frac{11}{10}q-\frac{1}{15}p+\frac{11}{150} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-15}{7}+q)(\frac{-13}{11}+p)& =(\color{red}{q}+\color{orange}{\frac{-15}{7}}).(\color{green}{p}+\color{blue}{\frac{-13}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{11})} + \color{orange}{(\frac{-15}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{7})} . \color{blue}{(\frac{-13}{11})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{13}{11}q-\frac{15}{7}p+\frac{15}{7}.\frac{13}{11}& \text{Uitwerken } \\ & =pq-\frac{13}{11}q-\frac{15}{7}p+\frac{195}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b+\frac{-17}{9})(\frac{-5}{4}+x)& =(\color{red}{b}+\color{orange}{\frac{-17}{9}}).(\color{green}{x}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-17}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{9})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{4}b-\frac{17}{9}x+\frac{17}{9}.\frac{5}{4}& \text{Uitwerken } \\ & =bx-\frac{5}{4}b-\frac{17}{9}x+\frac{85}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x-\frac{20}{3})(a-\frac{13}{9})& =(\color{red}{x}+\color{orange}{\frac{-20}{3}}).(\color{green}{a}+\color{blue}{\frac{-13}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{9})} + \color{orange}{(\frac{-20}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(\frac{-13}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{13}{9}x-\frac{20}{3}a+\frac{20}{3}.\frac{13}{9}& \text{Uitwerken } \\ & =ax-\frac{13}{9}x-\frac{20}{3}a+\frac{260}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-2}{16}+x)(a+\frac{13}{6})& =(\color{red}{x}+\color{orange}{\frac{-1}{8}}).(\color{green}{a}+\color{blue}{\frac{13}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{13}{6})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{13}{6})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{13}{6}x-\frac{1}{8}a-\frac{1}{8}.\frac{13}{6}& \text{Uitwerken } \\ & =ax+\frac{13}{6}x-\frac{1}{8}a-\frac{13}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-18 22:22:26
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