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

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  1. \((q-\frac{-11}{17})(\frac{1}{5}-p)\)
  2. \((q+\frac{-13}{3})(\frac{8}{7}+b)\)
  3. \((a+\frac{-13}{20})(\frac{10}{16}-b)\)
  4. \((\frac{-13}{20}+a)(\frac{-1}{19}+x)\)
  5. \((p-\frac{-8}{3})(x+\frac{15}{4})\)
  6. \((a-\frac{16}{14})(\frac{20}{18}+p)\)
  7. \((b-\frac{17}{3})(p-\frac{-13}{7})\)
  8. \((\frac{10}{9}+p)(a-\frac{-20}{9})\)
  9. \((p-(-17))(p+\frac{4}{19})\)
  10. \((p+\frac{20}{12})(\frac{-15}{15}+p)\)
  11. \((\frac{2}{5}+a)(\frac{18}{20}+p)\)
  12. \((\frac{1}{17}-a)(\frac{5}{8}-x)\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{-11}{17})(\frac{1}{5}-p)& =(\color{red}{q}+\color{orange}{\frac{11}{17}}).(\color{green}{-p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{11}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{5}q-\frac{11}{17}p+\frac{11}{17}.\frac{1}{5}& \text{Uitwerken } \\ & =-pq+\frac{1}{5}q-\frac{11}{17}p+\frac{11}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q+\frac{-13}{3})(\frac{8}{7}+b)& =(\color{red}{q}+\color{orange}{\frac{-13}{3}}).(\color{green}{b}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{-13}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{3})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{8}{7}q-\frac{13}{3}b-\frac{13}{3}.\frac{8}{7}& \text{Uitwerken } \\ & =bq+\frac{8}{7}q-\frac{13}{3}b-\frac{104}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{-13}{20})(\frac{10}{16}-b)& =(\color{red}{a}+\color{orange}{\frac{-13}{20}}).(\color{green}{-b}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(-b)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{5}{8}a+\frac{13}{20}b-\frac{13}{20}.\frac{5}{8}& \text{Uitwerken } \\ & =-ab+\frac{5}{8}a+\frac{13}{20}b-\frac{65}{160} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{5}{8}a+\frac{13}{20}b-\frac{13}{32} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-13}{20}+a)(\frac{-1}{19}+x)& =(\color{red}{a}+\color{orange}{\frac{-13}{20}}).(\color{green}{x}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{19}a-\frac{13}{20}x+\frac{13}{20}.\frac{1}{19}& \text{Uitwerken } \\ & =ax-\frac{1}{19}a-\frac{13}{20}x+\frac{13}{380} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-8}{3})(x+\frac{15}{4})& =(\color{red}{p}+\color{orange}{\frac{8}{3}}).(\color{green}{x}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{8}{3})} . \color{green}{(x)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{15}{4}p+\frac{8}{3}x+\frac{8}{3}.\frac{15}{4}& \text{Uitwerken } \\ & =px+\frac{15}{4}p+\frac{8}{3}x+\frac{120}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{15}{4}p+\frac{8}{3}x+10 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a-\frac{16}{14})(\frac{20}{18}+p)& =(\color{red}{a}+\color{orange}{\frac{-8}{7}}).(\color{green}{p}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{10}{9}a-\frac{8}{7}p-\frac{8}{7}.\frac{10}{9}& \text{Uitwerken } \\ & =ap+\frac{10}{9}a-\frac{8}{7}p-\frac{80}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{17}{3})(p-\frac{-13}{7})& =(\color{red}{b}+\color{orange}{\frac{-17}{3}}).(\color{green}{p}+\color{blue}{\frac{13}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{13}{7})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{13}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{7}b-\frac{17}{3}p-\frac{17}{3}.\frac{13}{7}& \text{Uitwerken } \\ & =bp+\frac{13}{7}b-\frac{17}{3}p-\frac{221}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{10}{9}+p)(a-\frac{-20}{9})& =(\color{red}{p}+\color{orange}{\frac{10}{9}}).(\color{green}{a}+\color{blue}{\frac{20}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{20}{9})} + \color{orange}{(\frac{10}{9})} . \color{green}{(a)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{20}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{20}{9}p+\frac{10}{9}a+\frac{10}{9}.\frac{20}{9}& \text{Uitwerken } \\ & =ap+\frac{20}{9}p+\frac{10}{9}a+\frac{200}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-(-17))(p+\frac{4}{19})& =(\color{red}{p}+\color{orange}{17}).(\color{green}{p}+\color{blue}{\frac{4}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{4}{19})} + \color{orange}{(17)} . \color{green}{(p)} + \color{orange}{(17)} . \color{blue}{(\frac{4}{19})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{4}{19}p+17p+17.\frac{4}{19}& \text{Uitwerken } \\ & =p^2+(\frac{4}{19}+17)p+\frac{68}{19} & \text{Neem samen} \\ &=p^2+\frac{327}{19}p+\frac{68}{19} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(p+\frac{20}{12})(\frac{-15}{15}+p)& =(\color{red}{p}+\color{orange}{\frac{5}{3}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pp-1p+\frac{5}{3}p-\frac{5}{3}.1& \text{Uitwerken } \\ & =p^2+((-1)+\frac{5}{3})p-(\frac{-5}{3}) & \text{Neem samen} \\ &=p^2+\frac{2}{3}p-(\frac{-5}{3}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{2}{5}+a)(\frac{18}{20}+p)& =(\color{red}{a}+\color{orange}{\frac{2}{5}}).(\color{green}{p}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{2}{5})} . \color{green}{(p)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{9}{10}a+\frac{2}{5}p+\frac{2}{5}.\frac{9}{10}& \text{Uitwerken } \\ & =ap+\frac{9}{10}a+\frac{2}{5}p+\frac{18}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{9}{10}a+\frac{2}{5}p+\frac{9}{25} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{1}{17}-a)(\frac{5}{8}-x)& =(\color{red}{-a}+\color{orange}{\frac{1}{17}}).(\color{green}{-x}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{1}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{17})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{8}a-\frac{1}{17}x+\frac{1}{17}.\frac{5}{8}& \text{Uitwerken } \\ & =ax-\frac{5}{8}a-\frac{1}{17}x+\frac{5}{136} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-17 18:57:45
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