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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-18}{13})(\frac{15}{18}-p)& =(\color{red}{a}+\color{orange}{\frac{-18}{13}}).(\color{green}{-p}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-18}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{-18}{13})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{5}{6}a+\frac{18}{13}p-\frac{18}{13}.\frac{5}{6}& \text{Uitwerken } \\ & =-ap+\frac{5}{6}a+\frac{18}{13}p-\frac{90}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{5}{6}a+\frac{18}{13}p-\frac{15}{13} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-14}{19})(\frac{17}{8}-q)& =(\color{red}{q}+\color{orange}{\frac{14}{19}}).(\color{green}{-q}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(\frac{14}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{14}{19})} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{17}{8}q-\frac{14}{19}q+\frac{14}{19}.\frac{17}{8}& \text{Uitwerken } \\ & =-q^2+(\frac{17}{8}+(\frac{-14}{19}))q+(\frac{-238}{152}) & \text{Neem samen} \\ &=-q^2+\frac{211}{152}q+(\frac{-238}{152}) & \text{Maak de som} \\ &=-q^2+\frac{211}{152}q+(\frac{-119}{76}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{-3}{8}+x)(\frac{18}{12}+a)& =(\color{red}{x}+\color{orange}{\frac{-3}{8}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{2}x-\frac{3}{8}a-\frac{3}{8}.\frac{3}{2}& \text{Uitwerken } \\ & =ax+\frac{3}{2}x-\frac{3}{8}a-\frac{9}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{-2}{7})(b-\frac{-1}{20})& =(\color{red}{q}+\color{orange}{\frac{2}{7}}).(\color{green}{b}+\color{blue}{\frac{1}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{20})} + \color{orange}{(\frac{2}{7})} . \color{green}{(b)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{1}{20})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{20}q+\frac{2}{7}b+\frac{2}{7}.\frac{1}{20}& \text{Uitwerken } \\ & =bq+\frac{1}{20}q+\frac{2}{7}b+\frac{2}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{1}{20}q+\frac{2}{7}b+\frac{1}{70} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(q-\frac{14}{2})(x+\frac{20}{8})& =(\color{red}{q}+\color{orange}{(-7)}).(\color{green}{x}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(-7)} . \color{green}{(x)} + \color{orange}{(-7)} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{2}q-7x-7.\frac{5}{2}& \text{Uitwerken } \\ & =qx+\frac{5}{2}q-7x-\frac{35}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-2}{11}-q)(b-\frac{-6}{16})& =(\color{red}{-q}+\color{orange}{\frac{-2}{11}}).(\color{green}{b}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{-2}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{3}{8}q-\frac{2}{11}b-\frac{2}{11}.\frac{3}{8}& \text{Uitwerken } \\ & =-bq-\frac{3}{8}q-\frac{2}{11}b-\frac{6}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{3}{8}q-\frac{2}{11}b-\frac{3}{44} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b+\frac{3}{2})(q+\frac{-6}{13})& =(\color{red}{b}+\color{orange}{\frac{3}{2}}).(\color{green}{q}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(\frac{3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{6}{13}b+\frac{3}{2}q-\frac{3}{2}.\frac{6}{13}& \text{Uitwerken } \\ & =bq-\frac{6}{13}b+\frac{3}{2}q-\frac{18}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{6}{13}b+\frac{3}{2}q-\frac{9}{13} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(a+\frac{10}{12})(x-\frac{-11}{14})& =(\color{red}{a}+\color{orange}{\frac{5}{6}}).(\color{green}{x}+\color{blue}{\frac{11}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{11}{14})} + \color{orange}{(\frac{5}{6})} . \color{green}{(x)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{11}{14})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{11}{14}a+\frac{5}{6}x+\frac{5}{6}.\frac{11}{14}& \text{Uitwerken } \\ & =ax+\frac{11}{14}a+\frac{5}{6}x+\frac{55}{84} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-12}{14}-x)(p-\frac{7}{3})& =(\color{red}{-x}+\color{orange}{\frac{-6}{7}}).(\color{green}{p}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{7}{3}x-\frac{6}{7}p+\frac{6}{7}.\frac{7}{3}& \text{Uitwerken } \\ & =-px+\frac{7}{3}x-\frac{6}{7}p+\frac{42}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{7}{3}x-\frac{6}{7}p+2 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(17-b)(\frac{10}{15}-b)& =(\color{red}{-b}+\color{orange}{17}).(\color{green}{-b}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(17)} . \color{green}{(-b)} + \color{orange}{(17)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{2}{3}b-17b+17.\frac{2}{3}& \text{Uitwerken } \\ & =b^2+((\frac{-2}{3})+(-17))b+\frac{34}{3} & \text{Neem samen} \\ &=b^2-\frac{53}{3}b+\frac{34}{3} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{1}{7}-q)(p-\frac{-9}{9})& =(\color{red}{-q}+\color{orange}{\frac{1}{7}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{7})} . \color{green}{(p)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -pq-1q+\frac{1}{7}p+\frac{1}{7}.1& \text{Uitwerken } \\ & =-pq-1q+\frac{1}{7}p+\frac{1}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q-4)(b-\frac{6}{9})& =(\color{red}{q}+\color{orange}{(-4)}).(\color{green}{b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(-4)} . \color{green}{(b)} + \color{orange}{(-4)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{2}{3}q-4b+4.\frac{2}{3}& \text{Uitwerken } \\ & =bq-\frac{2}{3}q-4b+\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-16 12:46:26
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