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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{4}{5}+b)(a-\frac{10}{8})& =(\color{red}{b}+\color{orange}{\frac{4}{5}}).(\color{green}{a}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{4}{5})} . \color{green}{(a)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{4}b+\frac{4}{5}a-\frac{4}{5}.\frac{5}{4}& \text{Uitwerken } \\ & =ab-\frac{5}{4}b+\frac{4}{5}a-\frac{20}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{5}{4}b+\frac{4}{5}a-1 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p-\frac{17}{11})(x-\frac{20}{19})& =(\color{red}{p}+\color{orange}{\frac{-17}{11}}).(\color{green}{x}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{-17}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{11})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{20}{19}p-\frac{17}{11}x+\frac{17}{11}.\frac{20}{19}& \text{Uitwerken } \\ & =px-\frac{20}{19}p-\frac{17}{11}x+\frac{340}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p+\frac{13}{3})(a+\frac{-20}{18})& =(\color{red}{p}+\color{orange}{\frac{13}{3}}).(\color{green}{a}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{13}{3})} . \color{green}{(a)} + \color{orange}{(\frac{13}{3})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{10}{9}p+\frac{13}{3}a-\frac{13}{3}.\frac{10}{9}& \text{Uitwerken } \\ & =ap-\frac{10}{9}p+\frac{13}{3}a-\frac{130}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{20}{17})(p+\frac{20}{12})& =(\color{red}{a}+\color{orange}{\frac{-20}{17}}).(\color{green}{p}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-20}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-20}{17})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{5}{3}a-\frac{20}{17}p-\frac{20}{17}.\frac{5}{3}& \text{Uitwerken } \\ & =ap+\frac{5}{3}a-\frac{20}{17}p-\frac{100}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b-\frac{-15}{2})(q-\frac{-20}{4})& =(\color{red}{b}+\color{orange}{\frac{15}{2}}).(\color{green}{q}+\color{blue}{5})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(5)} + \color{orange}{(\frac{15}{2})} . \color{green}{(q)} + \color{orange}{(\frac{15}{2})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = bq+5b+\frac{15}{2}q+\frac{15}{2}.5& \text{Uitwerken } \\ & =bq+5b+\frac{15}{2}q+\frac{75}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x-\frac{15}{6})(\frac{19}{7}+p)& =(\color{red}{x}+\color{orange}{\frac{-5}{2}}).(\color{green}{p}+\color{blue}{\frac{19}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{19}{7})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{19}{7})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{19}{7}x-\frac{5}{2}p-\frac{5}{2}.\frac{19}{7}& \text{Uitwerken } \\ & =px+\frac{19}{7}x-\frac{5}{2}p-\frac{95}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{20}{7}+p)(p+(-18))& =(\color{red}{p}+\color{orange}{\frac{20}{7}}).(\color{green}{p}+\color{blue}{(-18)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-18)} + \color{orange}{(\frac{20}{7})} . \color{green}{(p)} + \color{orange}{(\frac{20}{7})} . \color{blue}{(-18)}& \text{Boogjes en uitschrijven} \\ & = pp-18p+\frac{20}{7}p-\frac{20}{7}.18& \text{Uitwerken } \\ & =p^2+((-18)+\frac{20}{7})p-(\frac{-360}{7}) & \text{Neem samen} \\ &=p^2-\frac{106}{7}p-(\frac{-360}{7}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-3}{18})(a+\frac{-9}{12})& =(\color{red}{a}+\color{orange}{\frac{1}{6}}).(\color{green}{a}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{1}{6})} . \color{green}{(a)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{3}{4}a+\frac{1}{6}a-\frac{1}{6}.\frac{3}{4}& \text{Uitwerken } \\ & =a^2+((\frac{-3}{4})+\frac{1}{6})a-(\frac{-3}{24}) & \text{Neem samen} \\ &=a^2-\frac{7}{12}a-(\frac{-3}{24}) & \text{Maak de som} \\ &=a^2-\frac{7}{12}a+\frac{1}{8} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(\frac{-19}{12}+p)(\frac{16}{16}-b)& =(\color{red}{p}+\color{orange}{\frac{-19}{12}}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-19}{12})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bp+1p+\frac{19}{12}b-\frac{19}{12}.1& \text{Uitwerken } \\ & =-bp+1p+\frac{19}{12}b-\frac{19}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q+(-6))(q+\frac{12}{9})& =(\color{red}{q}+\color{orange}{(-6)}).(\color{green}{q}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(-6)} . \color{green}{(q)} + \color{orange}{(-6)} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{4}{3}q-6q-6.\frac{4}{3}& \text{Uitwerken } \\ & =q^2+(\frac{4}{3}+(-6))q-(\frac{-24}{3}) & \text{Neem samen} \\ &=q^2-\frac{14}{3}q-(\frac{-24}{3}) & \text{Maak de som} \\ &=q^2-\frac{14}{3}q+8 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(\frac{11}{20}+a)(a+\frac{19}{11})& =(\color{red}{a}+\color{orange}{\frac{11}{20}}).(\color{green}{a}+\color{blue}{\frac{19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{19}{11})} + \color{orange}{(\frac{11}{20})} . \color{green}{(a)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{19}{11})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{19}{11}a+\frac{11}{20}a+\frac{11}{20}.\frac{19}{11}& \text{Uitwerken } \\ & =a^2+(\frac{19}{11}+\frac{11}{20})a+\frac{209}{220} & \text{Neem samen} \\ &=a^2+\frac{501}{220}a+\frac{209}{220} & \text{Maak de som} \\ &=a^2+\frac{501}{220}a+\frac{19}{20} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(p+\frac{-4}{9})(\frac{14}{16}+x)& =(\color{red}{p}+\color{orange}{\frac{-4}{9}}).(\color{green}{x}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{8}p-\frac{4}{9}x-\frac{4}{9}.\frac{7}{8}& \text{Uitwerken } \\ & =px+\frac{7}{8}p-\frac{4}{9}x-\frac{28}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{7}{8}p-\frac{4}{9}x-\frac{7}{18} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-09 17:06:42
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