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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{-14}{4})(\frac{2}{7}-x)& =(\color{red}{a}+\color{orange}{\frac{7}{2}}).(\color{green}{-x}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{7}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{2}{7}a-\frac{7}{2}x+\frac{7}{2}.\frac{2}{7}& \text{Uitwerken } \\ & =-ax+\frac{2}{7}a-\frac{7}{2}x+\frac{14}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{2}{7}a-\frac{7}{2}x+1 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a-\frac{6}{11})(\frac{-9}{16}+b)& =(\color{red}{a}+\color{orange}{\frac{-6}{11}}).(\color{green}{b}+\color{blue}{\frac{-9}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{16})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{-9}{16})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{9}{16}a-\frac{6}{11}b+\frac{6}{11}.\frac{9}{16}& \text{Uitwerken } \\ & =ab-\frac{9}{16}a-\frac{6}{11}b+\frac{54}{176} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{9}{16}a-\frac{6}{11}b+\frac{27}{88} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x-\frac{-20}{13})(x+\frac{-14}{19})& =(\color{red}{x}+\color{orange}{\frac{20}{13}}).(\color{green}{x}+\color{blue}{\frac{-14}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{19})} + \color{orange}{(\frac{20}{13})} . \color{green}{(x)} + \color{orange}{(\frac{20}{13})} . \color{blue}{(\frac{-14}{19})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{14}{19}x+\frac{20}{13}x-\frac{20}{13}.\frac{14}{19}& \text{Uitwerken } \\ & =x^2+((\frac{-14}{19})+\frac{20}{13})x-(\frac{-280}{247}) & \text{Neem samen} \\ &=x^2+\frac{198}{247}x-(\frac{-280}{247}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(7-a)(\frac{-4}{9}-x)& =(\color{red}{-a}+\color{orange}{7}).(\color{green}{-x}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(7)} . \color{green}{(-x)} + \color{orange}{(7)} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{4}{9}a-7x-7.\frac{4}{9}& \text{Uitwerken } \\ & =ax+\frac{4}{9}a-7x-\frac{28}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{-18}{15})(x+\frac{-5}{19})& =(\color{red}{a}+\color{orange}{\frac{6}{5}}).(\color{green}{x}+\color{blue}{\frac{-5}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{19})} + \color{orange}{(\frac{6}{5})} . \color{green}{(x)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-5}{19})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{19}a+\frac{6}{5}x-\frac{6}{5}.\frac{5}{19}& \text{Uitwerken } \\ & =ax-\frac{5}{19}a+\frac{6}{5}x-\frac{30}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{5}{19}a+\frac{6}{5}x-\frac{6}{19} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-9}{15}-p)(a+\frac{16}{20})& =(\color{red}{-p}+\color{orange}{\frac{-3}{5}}).(\color{green}{a}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{4}{5}p-\frac{3}{5}a-\frac{3}{5}.\frac{4}{5}& \text{Uitwerken } \\ & =-ap-\frac{4}{5}p-\frac{3}{5}a-\frac{12}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{17}{12}+p)(\frac{20}{8}+x)& =(\color{red}{p}+\color{orange}{\frac{17}{12}}).(\color{green}{x}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{17}{12})} . \color{green}{(x)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{2}p+\frac{17}{12}x+\frac{17}{12}.\frac{5}{2}& \text{Uitwerken } \\ & =px+\frac{5}{2}p+\frac{17}{12}x+\frac{85}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a-\frac{-6}{5})(18-x)& =(\color{red}{a}+\color{orange}{\frac{6}{5}}).(\color{green}{-x}+\color{blue}{18})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(18)} + \color{orange}{(\frac{6}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(18)}& \text{Boogjes en uitschrijven} \\ & = -ax+18a-\frac{6}{5}x+\frac{6}{5}.18& \text{Uitwerken } \\ & =-ax+18a-\frac{6}{5}x+\frac{108}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}((-20)-x)(x+\frac{6}{20})& =(\color{red}{-x}+\color{orange}{(-20)}).(\color{green}{x}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(-20)} . \color{green}{(x)} + \color{orange}{(-20)} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{3}{10}x-20x-20.\frac{3}{10}& \text{Uitwerken } \\ & =-x^2+((\frac{-3}{10})+(-20))x-\frac{60}{10} & \text{Neem samen} \\ &=-x^2-\frac{203}{10}x-\frac{60}{10} & \text{Maak de som} \\ &=-x^2-\frac{203}{10}x-6 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{-12}{6}-x)(\frac{-14}{15}-q)& =(\color{red}{-x}+\color{orange}{(-2)}).(\color{green}{-q}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(-2)} . \color{green}{(-q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{14}{15}x+2q+2.\frac{14}{15}& \text{Uitwerken } \\ & =qx+\frac{14}{15}x+2q+\frac{28}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q-\frac{3}{11})(\frac{11}{16}-b)& =(\color{red}{q}+\color{orange}{\frac{-3}{11}}).(\color{green}{-b}+\color{blue}{\frac{11}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{11}{16})} + \color{orange}{(\frac{-3}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{11})} . \color{blue}{(\frac{11}{16})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{11}{16}q+\frac{3}{11}b-\frac{3}{11}.\frac{11}{16}& \text{Uitwerken } \\ & =-bq+\frac{11}{16}q+\frac{3}{11}b-\frac{33}{176} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{11}{16}q+\frac{3}{11}b-\frac{3}{16} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{9}{4}+a)(p-\frac{-13}{17})& =(\color{red}{a}+\color{orange}{\frac{9}{4}}).(\color{green}{p}+\color{blue}{\frac{13}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{13}{17})} + \color{orange}{(\frac{9}{4})} . \color{green}{(p)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{13}{17})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{17}a+\frac{9}{4}p+\frac{9}{4}.\frac{13}{17}& \text{Uitwerken } \\ & =ap+\frac{13}{17}a+\frac{9}{4}p+\frac{117}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-16 11:49:56
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