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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-14)(\frac{16}{16}-a)& =(\color{red}{a}+\color{orange}{(-14)}).(\color{green}{-a}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(-14)} . \color{green}{(-a)} + \color{orange}{(-14)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -aa+1a+14a-14.1& \text{Uitwerken } \\ & =-a^2+(1+14)a-14 & \text{Neem samen} \\ &=-a^2+15a-14 & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{-7}{20}+q)(\frac{-10}{16}+a)& =(\color{red}{q}+\color{orange}{\frac{-7}{20}}).(\color{green}{a}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{-7}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{8}q-\frac{7}{20}a+\frac{7}{20}.\frac{5}{8}& \text{Uitwerken } \\ & =aq-\frac{5}{8}q-\frac{7}{20}a+\frac{35}{160} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{5}{8}q-\frac{7}{20}a+\frac{7}{32} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x-\frac{19}{7})(\frac{12}{13}-x)& =(\color{red}{x}+\color{orange}{\frac{-19}{7}}).(\color{green}{-x}+\color{blue}{\frac{12}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{12}{13})} + \color{orange}{(\frac{-19}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{7})} . \color{blue}{(\frac{12}{13})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{12}{13}x+\frac{19}{7}x-\frac{19}{7}.\frac{12}{13}& \text{Uitwerken } \\ & =-x^2+(\frac{12}{13}+\frac{19}{7})x-\frac{228}{91} & \text{Neem samen} \\ &=-x^2+\frac{331}{91}x-\frac{228}{91} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(b+\frac{20}{5})(b-\frac{-4}{10})& =(\color{red}{b}+\color{orange}{4}).(\color{green}{b}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(4)} . \color{green}{(b)} + \color{orange}{(4)} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{2}{5}b+4b+4.\frac{2}{5}& \text{Uitwerken } \\ & =b^2+(\frac{2}{5}+4)b+\frac{8}{5} & \text{Neem samen} \\ &=b^2+\frac{22}{5}b+\frac{8}{5} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}((-4)-p)(a-\frac{20}{4})& =(\color{red}{-p}+\color{orange}{(-4)}).(\color{green}{a}+\color{blue}{(-5)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(-5)} + \color{orange}{(-4)} . \color{green}{(a)} + \color{orange}{(-4)} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -ap+5p-4a+4.5& \text{Uitwerken } \\ & =-ap+5p-4a+20 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{7}{7}-b)(\frac{-8}{8}-q)& =(\color{red}{-b}+\color{orange}{1}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(-1)} + \color{orange}{(1)} . \color{green}{(-q)} + \color{orange}{(1)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bq+1b-1q-1.1& \text{Uitwerken } \\ & =bq+1b-1q-1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-15}{8}+p)(q+\frac{-7}{9})& =(\color{red}{p}+\color{orange}{\frac{-15}{8}}).(\color{green}{q}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{-15}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{8})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{7}{9}p-\frac{15}{8}q+\frac{15}{8}.\frac{7}{9}& \text{Uitwerken } \\ & =pq-\frac{7}{9}p-\frac{15}{8}q+\frac{105}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{7}{9}p-\frac{15}{8}q+\frac{35}{24} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-19}{18})(x+\frac{11}{16})& =(\color{red}{x}+\color{orange}{\frac{19}{18}}).(\color{green}{x}+\color{blue}{\frac{11}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{11}{16})} + \color{orange}{(\frac{19}{18})} . \color{green}{(x)} + \color{orange}{(\frac{19}{18})} . \color{blue}{(\frac{11}{16})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{11}{16}x+\frac{19}{18}x+\frac{19}{18}.\frac{11}{16}& \text{Uitwerken } \\ & =x^2+(\frac{11}{16}+\frac{19}{18})x+\frac{209}{288} & \text{Neem samen} \\ &=x^2+\frac{251}{144}x+\frac{209}{288} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(x+18)(b-\frac{-1}{4})& =(\color{red}{x}+\color{orange}{18}).(\color{green}{b}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(18)} . \color{green}{(b)} + \color{orange}{(18)} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{4}x+18b+18.\frac{1}{4}& \text{Uitwerken } \\ & =bx+\frac{1}{4}x+18b+\frac{18}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{1}{4}x+18b+\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-16}{5}+p)(b+\frac{-17}{19})& =(\color{red}{p}+\color{orange}{\frac{-16}{5}}).(\color{green}{b}+\color{blue}{\frac{-17}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{19})} + \color{orange}{(\frac{-16}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{5})} . \color{blue}{(\frac{-17}{19})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{17}{19}p-\frac{16}{5}b+\frac{16}{5}.\frac{17}{19}& \text{Uitwerken } \\ & =bp-\frac{17}{19}p-\frac{16}{5}b+\frac{272}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{20}{2}-q)(x-\frac{-17}{11})& =(\color{red}{-q}+\color{orange}{10}).(\color{green}{x}+\color{blue}{\frac{17}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{17}{11})} + \color{orange}{(10)} . \color{green}{(x)} + \color{orange}{(10)} . \color{blue}{(\frac{17}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{17}{11}q+10x+10.\frac{17}{11}& \text{Uitwerken } \\ & =-qx-\frac{17}{11}q+10x+\frac{170}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q-\frac{-20}{20})(\frac{9}{18}-x)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{-x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(1)} . \color{green}{(-x)} + \color{orange}{(1)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{2}q-1x+1.\frac{1}{2}& \text{Uitwerken } \\ & =-qx+\frac{1}{2}q-1x+\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-02 14:38:44
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