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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{-16}{11})(a-\frac{-9}{11})& =(\color{red}{x}+\color{orange}{\frac{-16}{11}}).(\color{green}{a}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{-16}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{11})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{11}x-\frac{16}{11}a-\frac{16}{11}.\frac{9}{11}& \text{Uitwerken } \\ & =ax+\frac{9}{11}x-\frac{16}{11}a-\frac{144}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-6}{4})(p-\frac{4}{12})& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{3}b-\frac{3}{2}p+\frac{3}{2}.\frac{1}{3}& \text{Uitwerken } \\ & =bp-\frac{1}{3}b-\frac{3}{2}p+\frac{3}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{1}{3}b-\frac{3}{2}p+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(a-\frac{11}{13})(a-\frac{-7}{3})& =(\color{red}{a}+\color{orange}{\frac{-11}{13}}).(\color{green}{a}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{7}{3}a-\frac{11}{13}a-\frac{11}{13}.\frac{7}{3}& \text{Uitwerken } \\ & =a^2+(\frac{7}{3}+(\frac{-11}{13}))a-(\frac{-77}{39}) & \text{Neem samen} \\ &=a^2+\frac{58}{39}a-(\frac{-77}{39}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-4}{19}-x)(\frac{-10}{8}+x)& =(\color{red}{-x}+\color{orange}{\frac{-4}{19}}).(\color{green}{x}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-4}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{19})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{5}{4}x-\frac{4}{19}x+\frac{4}{19}.\frac{5}{4}& \text{Uitwerken } \\ & =-x^2+(\frac{5}{4}+(\frac{-4}{19}))x+(\frac{-20}{76}) & \text{Neem samen} \\ &=-x^2+\frac{79}{76}x+(\frac{-20}{76}) & \text{Maak de som} \\ &=-x^2+\frac{79}{76}x+(\frac{-5}{19}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(8+p)(x-\frac{3}{13})& =(\color{red}{p}+\color{orange}{8}).(\color{green}{x}+\color{blue}{\frac{-3}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{13})} + \color{orange}{(8)} . \color{green}{(x)} + \color{orange}{(8)} . \color{blue}{(\frac{-3}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{3}{13}p+8x-8.\frac{3}{13}& \text{Uitwerken } \\ & =px-\frac{3}{13}p+8x-\frac{24}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-18}{10})(\frac{3}{9}+a)& =(\color{red}{p}+\color{orange}{\frac{-9}{5}}).(\color{green}{a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{3}p-\frac{9}{5}a-\frac{9}{5}.\frac{1}{3}& \text{Uitwerken } \\ & =ap+\frac{1}{3}p-\frac{9}{5}a-\frac{9}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{1}{3}p-\frac{9}{5}a-\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p+\frac{12}{5})(p+\frac{-13}{15})& =(\color{red}{p}+\color{orange}{\frac{12}{5}}).(\color{green}{p}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{12}{5})} . \color{green}{(p)} + \color{orange}{(\frac{12}{5})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{13}{15}p+\frac{12}{5}p-\frac{12}{5}.\frac{13}{15}& \text{Uitwerken } \\ & =p^2+((\frac{-13}{15})+\frac{12}{5})p-(\frac{-156}{75}) & \text{Neem samen} \\ &=p^2+\frac{23}{15}p-(\frac{-156}{75}) & \text{Maak de som} \\ &=p^2+\frac{23}{15}p+\frac{52}{25} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  8. \(\begin{align}(a-\frac{2}{6})(\frac{6}{5}-p)& =(\color{red}{a}+\color{orange}{\frac{-1}{3}}).(\color{green}{-p}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{6}{5}a+\frac{1}{3}p-\frac{1}{3}.\frac{6}{5}& \text{Uitwerken } \\ & =-ap+\frac{6}{5}a+\frac{1}{3}p-\frac{6}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{6}{5}a+\frac{1}{3}p-\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}((-15)-q)(\frac{18}{5}-b)& =(\color{red}{-q}+\color{orange}{(-15)}).(\color{green}{-b}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(-15)} . \color{green}{(-b)} + \color{orange}{(-15)} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{18}{5}q+15b-15.\frac{18}{5}& \text{Uitwerken } \\ & =bq-\frac{18}{5}q+15b-\frac{270}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{18}{5}q+15b-54 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p-\frac{11}{15})(b-\frac{9}{15})& =(\color{red}{p}+\color{orange}{\frac{-11}{15}}).(\color{green}{b}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{5}p-\frac{11}{15}b+\frac{11}{15}.\frac{3}{5}& \text{Uitwerken } \\ & =bp-\frac{3}{5}p-\frac{11}{15}b+\frac{33}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{3}{5}p-\frac{11}{15}b+\frac{11}{25} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-12}{11})(x-\frac{1}{19})& =(\color{red}{a}+\color{orange}{\frac{12}{11}}).(\color{green}{x}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{12}{11})} . \color{green}{(x)} + \color{orange}{(\frac{12}{11})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{19}a+\frac{12}{11}x-\frac{12}{11}.\frac{1}{19}& \text{Uitwerken } \\ & =ax-\frac{1}{19}a+\frac{12}{11}x-\frac{12}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-17}{10})(\frac{13}{15}+q)& =(\color{red}{a}+\color{orange}{\frac{-17}{10}}).(\color{green}{q}+\color{blue}{\frac{13}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{13}{15})} + \color{orange}{(\frac{-17}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(\frac{13}{15})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{13}{15}a-\frac{17}{10}q-\frac{17}{10}.\frac{13}{15}& \text{Uitwerken } \\ & =aq+\frac{13}{15}a-\frac{17}{10}q-\frac{221}{150} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-19 17:40:57
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