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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{11}{14}-q)(\frac{-7}{5}+x)& =(\color{red}{-q}+\color{orange}{\frac{11}{14}}).(\color{green}{x}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{11}{14})} . \color{green}{(x)} + \color{orange}{(\frac{11}{14})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{7}{5}q+\frac{11}{14}x-\frac{11}{14}.\frac{7}{5}& \text{Uitwerken } \\ & =-qx+\frac{7}{5}q+\frac{11}{14}x-\frac{77}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{7}{5}q+\frac{11}{14}x-\frac{11}{10} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-4}{11}+x)(\frac{-9}{14}-b)& =(\color{red}{x}+\color{orange}{\frac{-4}{11}}).(\color{green}{-b}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(\frac{-4}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{-4}{11})} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{9}{14}x+\frac{4}{11}b+\frac{4}{11}.\frac{9}{14}& \text{Uitwerken } \\ & =-bx-\frac{9}{14}x+\frac{4}{11}b+\frac{36}{154} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{9}{14}x+\frac{4}{11}b+\frac{18}{77} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-3}{3}-x)(p-\frac{-4}{11})& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{4}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{4}{11})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{4}{11})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{4}{11}x-1p-1.\frac{4}{11}& \text{Uitwerken } \\ & =-px-\frac{4}{11}x-1p-\frac{4}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{2}{9})(p+\frac{-11}{3})& =(\color{red}{a}+\color{orange}{\frac{-2}{9}}).(\color{green}{p}+\color{blue}{\frac{-11}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{3})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{-11}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{11}{3}a-\frac{2}{9}p+\frac{2}{9}.\frac{11}{3}& \text{Uitwerken } \\ & =ap-\frac{11}{3}a-\frac{2}{9}p+\frac{22}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{14}{5}+b)(q+\frac{-15}{18})& =(\color{red}{b}+\color{orange}{\frac{14}{5}}).(\color{green}{q}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{14}{5})} . \color{green}{(q)} + \color{orange}{(\frac{14}{5})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{6}b+\frac{14}{5}q-\frac{14}{5}.\frac{5}{6}& \text{Uitwerken } \\ & =bq-\frac{5}{6}b+\frac{14}{5}q-\frac{70}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{5}{6}b+\frac{14}{5}q-\frac{7}{3} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-7}{13}+b)(\frac{9}{13}-b)& =(\color{red}{b}+\color{orange}{\frac{-7}{13}}).(\color{green}{-b}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{-7}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{13})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{9}{13}b+\frac{7}{13}b-\frac{7}{13}.\frac{9}{13}& \text{Uitwerken } \\ & =-b^2+(\frac{9}{13}+\frac{7}{13})b-\frac{63}{169} & \text{Neem samen} \\ &=-b^2+\frac{16}{13}b-\frac{63}{169} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(b+\frac{2}{14})(\frac{-15}{11}-q)& =(\color{red}{b}+\color{orange}{\frac{1}{7}}).(\color{green}{-q}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(\frac{1}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{15}{11}b-\frac{1}{7}q-\frac{1}{7}.\frac{15}{11}& \text{Uitwerken } \\ & =-bq-\frac{15}{11}b-\frac{1}{7}q-\frac{15}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{5}{8}+a)(\frac{-19}{8}+p)& =(\color{red}{a}+\color{orange}{\frac{5}{8}}).(\color{green}{p}+\color{blue}{\frac{-19}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{8})} + \color{orange}{(\frac{5}{8})} . \color{green}{(p)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{-19}{8})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{8}a+\frac{5}{8}p-\frac{5}{8}.\frac{19}{8}& \text{Uitwerken } \\ & =ap-\frac{19}{8}a+\frac{5}{8}p-\frac{95}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{3}{11})(\frac{-2}{19}-a)& =(\color{red}{b}+\color{orange}{\frac{-3}{11}}).(\color{green}{-a}+\color{blue}{\frac{-2}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{19})} + \color{orange}{(\frac{-3}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{11})} . \color{blue}{(\frac{-2}{19})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{2}{19}b+\frac{3}{11}a+\frac{3}{11}.\frac{2}{19}& \text{Uitwerken } \\ & =-ab-\frac{2}{19}b+\frac{3}{11}a+\frac{6}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{9}{2}+q)(p-\frac{12}{9})& =(\color{red}{q}+\color{orange}{\frac{9}{2}}).(\color{green}{p}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{9}{2})} . \color{green}{(p)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{4}{3}q+\frac{9}{2}p-\frac{9}{2}.\frac{4}{3}& \text{Uitwerken } \\ & =pq-\frac{4}{3}q+\frac{9}{2}p-\frac{36}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{4}{3}q+\frac{9}{2}p-6 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-11}{15}+q)((-18)-q)& =(\color{red}{q}+\color{orange}{\frac{-11}{15}}).(\color{green}{-q}+\color{blue}{(-18)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(-18)} + \color{orange}{(\frac{-11}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(-18)}& \text{Boogjes en uitschrijven} \\ & = -qq-18q+\frac{11}{15}q+\frac{11}{15}.18& \text{Uitwerken } \\ & =-q^2+((-18)+\frac{11}{15})q+(\frac{-198}{15}) & \text{Neem samen} \\ &=-q^2-\frac{259}{15}q+(\frac{-198}{15}) & \text{Maak de som} \\ &=-q^2-\frac{259}{15}q+(\frac{-66}{5}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(x+\frac{-10}{15})(p-\frac{-5}{18})& =(\color{red}{x}+\color{orange}{\frac{-2}{3}}).(\color{green}{p}+\color{blue}{\frac{5}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{5}{18})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{5}{18})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{18}x-\frac{2}{3}p-\frac{2}{3}.\frac{5}{18}& \text{Uitwerken } \\ & =px+\frac{5}{18}x-\frac{2}{3}p-\frac{10}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{5}{18}x-\frac{2}{3}p-\frac{5}{27} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-06 22:12:33
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