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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-19}{17}-p)(\frac{2}{13}-p)& =(\color{red}{-p}+\color{orange}{\frac{-19}{17}}).(\color{green}{-p}+\color{blue}{\frac{2}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{2}{13})} + \color{orange}{(\frac{-19}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-19}{17})} . \color{blue}{(\frac{2}{13})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{2}{13}p+\frac{19}{17}p-\frac{19}{17}.\frac{2}{13}& \text{Uitwerken } \\ & =p^2+((\frac{-2}{13})+\frac{19}{17})p-(\frac{-38}{221}) & \text{Neem samen} \\ &=p^2+\frac{213}{221}p-(\frac{-38}{221}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{-13}{3}+q)(a+\frac{3}{2})& =(\color{red}{q}+\color{orange}{\frac{-13}{3}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-13}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{3})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{2}q-\frac{13}{3}a-\frac{13}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =aq+\frac{3}{2}q-\frac{13}{3}a-\frac{39}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{3}{2}q-\frac{13}{3}a-\frac{13}{2} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-5}{18}+a)(\frac{3}{6}-x)& =(\color{red}{a}+\color{orange}{\frac{-5}{18}}).(\color{green}{-x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-5}{18})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{2}a+\frac{5}{18}x-\frac{5}{18}.\frac{1}{2}& \text{Uitwerken } \\ & =-ax+\frac{1}{2}a+\frac{5}{18}x-\frac{5}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{13}{6})(a+(-16))& =(\color{red}{a}+\color{orange}{\frac{13}{6}}).(\color{green}{a}+\color{blue}{(-16)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-16)} + \color{orange}{(\frac{13}{6})} . \color{green}{(a)} + \color{orange}{(\frac{13}{6})} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = aa-16a+\frac{13}{6}a-\frac{13}{6}.16& \text{Uitwerken } \\ & =a^2+((-16)+\frac{13}{6})a-(\frac{-208}{6}) & \text{Neem samen} \\ &=a^2-\frac{83}{6}a-(\frac{-208}{6}) & \text{Maak de som} \\ &=a^2-\frac{83}{6}a+\frac{104}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(\frac{-17}{10}-b)(q-\frac{5}{12})& =(\color{red}{-b}+\color{orange}{\frac{-17}{10}}).(\color{green}{q}+\color{blue}{\frac{-5}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-5}{12})} + \color{orange}{(\frac{-17}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(\frac{-5}{12})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{12}b-\frac{17}{10}q+\frac{17}{10}.\frac{5}{12}& \text{Uitwerken } \\ & =-bq+\frac{5}{12}b-\frac{17}{10}q+\frac{85}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{5}{12}b-\frac{17}{10}q+\frac{17}{24} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-13}{4}-a)(q+\frac{14}{16})& =(\color{red}{-a}+\color{orange}{\frac{-13}{4}}).(\color{green}{q}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-13}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{7}{8}a-\frac{13}{4}q-\frac{13}{4}.\frac{7}{8}& \text{Uitwerken } \\ & =-aq-\frac{7}{8}a-\frac{13}{4}q-\frac{91}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-11}{14}+a)(\frac{-15}{4}-q)& =(\color{red}{a}+\color{orange}{\frac{-11}{14}}).(\color{green}{-q}+\color{blue}{\frac{-15}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{4})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(-q)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{-15}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{15}{4}a+\frac{11}{14}q+\frac{11}{14}.\frac{15}{4}& \text{Uitwerken } \\ & =-aq-\frac{15}{4}a+\frac{11}{14}q+\frac{165}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b+\frac{7}{13})(p-\frac{-16}{18})& =(\color{red}{b}+\color{orange}{\frac{7}{13}}).(\color{green}{p}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{7}{13})} . \color{green}{(p)} + \color{orange}{(\frac{7}{13})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{8}{9}b+\frac{7}{13}p+\frac{7}{13}.\frac{8}{9}& \text{Uitwerken } \\ & =bp+\frac{8}{9}b+\frac{7}{13}p+\frac{56}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-\frac{1}{7})(b-\frac{-6}{15})& =(\color{red}{x}+\color{orange}{\frac{-1}{7}}).(\color{green}{b}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{2}{5}x-\frac{1}{7}b-\frac{1}{7}.\frac{2}{5}& \text{Uitwerken } \\ & =bx+\frac{2}{5}x-\frac{1}{7}b-\frac{2}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{9}{19})(\frac{14}{6}-q)& =(\color{red}{p}+\color{orange}{\frac{-9}{19}}).(\color{green}{-q}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{-9}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{19})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{7}{3}p+\frac{9}{19}q-\frac{9}{19}.\frac{7}{3}& \text{Uitwerken } \\ & =-pq+\frac{7}{3}p+\frac{9}{19}q-\frac{63}{57} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{7}{3}p+\frac{9}{19}q-\frac{21}{19} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-5}{18})(p-\frac{7}{7})& =(\color{red}{a}+\color{orange}{\frac{5}{18}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{5}{18})} . \color{green}{(p)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ap-1a+\frac{5}{18}p-\frac{5}{18}.1& \text{Uitwerken } \\ & =ap-1a+\frac{5}{18}p-\frac{5}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q-\frac{10}{5})(p-\frac{-8}{14})& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{7}q-2p-2.\frac{4}{7}& \text{Uitwerken } \\ & =pq+\frac{4}{7}q-2p-\frac{8}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-09 23:13:57
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