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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{6}{11})(b+\frac{20}{6})& =(\color{red}{x}+\color{orange}{\frac{-6}{11}}).(\color{green}{b}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{10}{3}x-\frac{6}{11}b-\frac{6}{11}.\frac{10}{3}& \text{Uitwerken } \\ & =bx+\frac{10}{3}x-\frac{6}{11}b-\frac{60}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{10}{3}x-\frac{6}{11}b-\frac{20}{11} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-9}{7})(\frac{14}{18}-b)& =(\color{red}{q}+\color{orange}{\frac{9}{7}}).(\color{green}{-b}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{9}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{7}{9}q-\frac{9}{7}b+\frac{9}{7}.\frac{7}{9}& \text{Uitwerken } \\ & =-bq+\frac{7}{9}q-\frac{9}{7}b+\frac{63}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{7}{9}q-\frac{9}{7}b+1 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p+\frac{12}{12})(x+\frac{17}{2})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{17}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{17}{2})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{17}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{17}{2}p+1x+1.\frac{17}{2}& \text{Uitwerken } \\ & =px+\frac{17}{2}p+1x+\frac{17}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x+\frac{-10}{8})(a+\frac{7}{9})& =(\color{red}{x}+\color{orange}{\frac{-5}{4}}).(\color{green}{a}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{9}x-\frac{5}{4}a-\frac{5}{4}.\frac{7}{9}& \text{Uitwerken } \\ & =ax+\frac{7}{9}x-\frac{5}{4}a-\frac{35}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b+\frac{-19}{20})(\frac{2}{7}+a)& =(\color{red}{b}+\color{orange}{\frac{-19}{20}}).(\color{green}{a}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{-19}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{7}b-\frac{19}{20}a-\frac{19}{20}.\frac{2}{7}& \text{Uitwerken } \\ & =ab+\frac{2}{7}b-\frac{19}{20}a-\frac{38}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{2}{7}b-\frac{19}{20}a-\frac{19}{70} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q+\frac{16}{17})(x+\frac{-4}{9})& =(\color{red}{q}+\color{orange}{\frac{16}{17}}).(\color{green}{x}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{16}{17})} . \color{green}{(x)} + \color{orange}{(\frac{16}{17})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{4}{9}q+\frac{16}{17}x-\frac{16}{17}.\frac{4}{9}& \text{Uitwerken } \\ & =qx-\frac{4}{9}q+\frac{16}{17}x-\frac{64}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-4}{11})(b-\frac{-14}{20})& =(\color{red}{b}+\color{orange}{\frac{4}{11}}).(\color{green}{b}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{4}{11})} . \color{green}{(b)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{7}{10}b+\frac{4}{11}b+\frac{4}{11}.\frac{7}{10}& \text{Uitwerken } \\ & =b^2+(\frac{7}{10}+\frac{4}{11})b+\frac{28}{110} & \text{Neem samen} \\ &=b^2+\frac{117}{110}b+\frac{28}{110} & \text{Maak de som} \\ &=b^2+\frac{117}{110}b+\frac{14}{55} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{6}{14}+p)(\frac{-14}{18}-x)& =(\color{red}{p}+\color{orange}{\frac{3}{7}}).(\color{green}{-x}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{3}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{7}{9}p-\frac{3}{7}x-\frac{3}{7}.\frac{7}{9}& \text{Uitwerken } \\ & =-px-\frac{7}{9}p-\frac{3}{7}x-\frac{21}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{7}{9}p-\frac{3}{7}x-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(q-\frac{16}{2})(b-\frac{17}{2})& =(\color{red}{q}+\color{orange}{(-8)}).(\color{green}{b}+\color{blue}{\frac{-17}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{2})} + \color{orange}{(-8)} . \color{green}{(b)} + \color{orange}{(-8)} . \color{blue}{(\frac{-17}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{17}{2}q-8b+8.\frac{17}{2}& \text{Uitwerken } \\ & =bq-\frac{17}{2}q-8b+\frac{136}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{17}{2}q-8b+68 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{8}{15}-a)(q+\frac{-20}{20})& =(\color{red}{-a}+\color{orange}{\frac{8}{15}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(-1)} + \color{orange}{(\frac{8}{15})} . \color{green}{(q)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -aq+1a+\frac{8}{15}q-\frac{8}{15}.1& \text{Uitwerken } \\ & =-aq+1a+\frac{8}{15}q-\frac{8}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-2}{17})(\frac{-2}{6}+b)& =(\color{red}{a}+\color{orange}{\frac{2}{17}}).(\color{green}{b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{2}{17})} . \color{green}{(b)} + \color{orange}{(\frac{2}{17})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{3}a+\frac{2}{17}b-\frac{2}{17}.\frac{1}{3}& \text{Uitwerken } \\ & =ab-\frac{1}{3}a+\frac{2}{17}b-\frac{2}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{19}{12})(\frac{-14}{9}+a)& =(\color{red}{p}+\color{orange}{\frac{-19}{12}}).(\color{green}{a}+\color{blue}{\frac{-14}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{9})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{-14}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{14}{9}p-\frac{19}{12}a+\frac{19}{12}.\frac{14}{9}& \text{Uitwerken } \\ & =ap-\frac{14}{9}p-\frac{19}{12}a+\frac{266}{108} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{14}{9}p-\frac{19}{12}a+\frac{133}{54} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-07 06:32:39
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