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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{9}{6})(\frac{-8}{16}-p)& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{-p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{2}a-\frac{3}{2}p-\frac{3}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =-ap-\frac{1}{2}a-\frac{3}{2}p-\frac{3}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q-\frac{15}{12})(b+\frac{7}{11})& =(\color{red}{q}+\color{orange}{\frac{-5}{4}}).(\color{green}{b}+\color{blue}{\frac{7}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{7}{11})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{7}{11})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{11}q-\frac{5}{4}b-\frac{5}{4}.\frac{7}{11}& \text{Uitwerken } \\ & =bq+\frac{7}{11}q-\frac{5}{4}b-\frac{35}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a-\frac{-11}{13})(x+\frac{1}{3})& =(\color{red}{a}+\color{orange}{\frac{11}{13}}).(\color{green}{x}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{11}{13})} . \color{green}{(x)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{3}a+\frac{11}{13}x+\frac{11}{13}.\frac{1}{3}& \text{Uitwerken } \\ & =ax+\frac{1}{3}a+\frac{11}{13}x+\frac{11}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(12-a)(b+\frac{-12}{11})& =(\color{red}{-a}+\color{orange}{12}).(\color{green}{b}+\color{blue}{\frac{-12}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-12}{11})} + \color{orange}{(12)} . \color{green}{(b)} + \color{orange}{(12)} . \color{blue}{(\frac{-12}{11})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{12}{11}a+12b-12.\frac{12}{11}& \text{Uitwerken } \\ & =-ab+\frac{12}{11}a+12b-\frac{144}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a+\frac{7}{14})(\frac{-13}{6}+p)& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{13}{6}a+\frac{1}{2}p-\frac{1}{2}.\frac{13}{6}& \text{Uitwerken } \\ & =ap-\frac{13}{6}a+\frac{1}{2}p-\frac{13}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(6+b)(\frac{-11}{2}-q)& =(\color{red}{b}+\color{orange}{6}).(\color{green}{-q}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(6)} . \color{green}{(-q)} + \color{orange}{(6)} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{11}{2}b-6q-6.\frac{11}{2}& \text{Uitwerken } \\ & =-bq-\frac{11}{2}b-6q-\frac{66}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{11}{2}b-6q-33 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p+\frac{13}{9})(p+\frac{-18}{16})& =(\color{red}{p}+\color{orange}{\frac{13}{9}}).(\color{green}{p}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{13}{9})} . \color{green}{(p)} + \color{orange}{(\frac{13}{9})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{9}{8}p+\frac{13}{9}p-\frac{13}{9}.\frac{9}{8}& \text{Uitwerken } \\ & =p^2+((\frac{-9}{8})+\frac{13}{9})p-(\frac{-117}{72}) & \text{Neem samen} \\ &=p^2+\frac{23}{72}p-(\frac{-117}{72}) & \text{Maak de som} \\ &=p^2+\frac{23}{72}p+\frac{13}{8} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  8. \(\begin{align}(q+\frac{2}{11})(b+\frac{-18}{16})& =(\color{red}{q}+\color{orange}{\frac{2}{11}}).(\color{green}{b}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{2}{11})} . \color{green}{(b)} + \color{orange}{(\frac{2}{11})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{9}{8}q+\frac{2}{11}b-\frac{2}{11}.\frac{9}{8}& \text{Uitwerken } \\ & =bq-\frac{9}{8}q+\frac{2}{11}b-\frac{18}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{9}{8}q+\frac{2}{11}b-\frac{9}{44} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-4}{7}-q)(\frac{-12}{14}+q)& =(\color{red}{-q}+\color{orange}{\frac{-4}{7}}).(\color{green}{q}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{6}{7}q-\frac{4}{7}q+\frac{4}{7}.\frac{6}{7}& \text{Uitwerken } \\ & =-q^2+(\frac{6}{7}+(\frac{-4}{7}))q+(\frac{-24}{49}) & \text{Neem samen} \\ &=-q^2+\frac{2}{7}q+(\frac{-24}{49}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-11}{17})(\frac{16}{13}-b)& =(\color{red}{b}+\color{orange}{\frac{11}{17}}).(\color{green}{-b}+\color{blue}{\frac{16}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{16}{13})} + \color{orange}{(\frac{11}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{16}{13})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{16}{13}b-\frac{11}{17}b+\frac{11}{17}.\frac{16}{13}& \text{Uitwerken } \\ & =-b^2+(\frac{16}{13}+(\frac{-11}{17}))b+(\frac{-176}{221}) & \text{Neem samen} \\ &=-b^2+\frac{129}{221}b+(\frac{-176}{221}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(p-\frac{2}{17})(a-\frac{-3}{3})& =(\color{red}{p}+\color{orange}{\frac{-2}{17}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-2}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{17})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ap+1p-\frac{2}{17}a-\frac{2}{17}.1& \text{Uitwerken } \\ & =ap+1p-\frac{2}{17}a-\frac{2}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-5}{15})(p-\frac{8}{3})& =(\color{red}{q}+\color{orange}{\frac{-1}{3}}).(\color{green}{p}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{8}{3}q-\frac{1}{3}p+\frac{1}{3}.\frac{8}{3}& \text{Uitwerken } \\ & =pq-\frac{8}{3}q-\frac{1}{3}p+\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-13 15:22:59
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