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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-18}{10}-b)(\frac{4}{14}+x)& =(\color{red}{-b}+\color{orange}{\frac{-9}{5}}).(\color{green}{x}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{2}{7}b-\frac{9}{5}x-\frac{9}{5}.\frac{2}{7}& \text{Uitwerken } \\ & =-bx-\frac{2}{7}b-\frac{9}{5}x-\frac{18}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x+\frac{20}{3})(\frac{18}{16}-b)& =(\color{red}{x}+\color{orange}{\frac{20}{3}}).(\color{green}{-b}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{20}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{20}{3})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{9}{8}x-\frac{20}{3}b+\frac{20}{3}.\frac{9}{8}& \text{Uitwerken } \\ & =-bx+\frac{9}{8}x-\frac{20}{3}b+\frac{180}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{9}{8}x-\frac{20}{3}b+\frac{15}{2} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x-\frac{9}{19})(a-\frac{10}{6})& =(\color{red}{x}+\color{orange}{\frac{-9}{19}}).(\color{green}{a}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-9}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{19})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{3}x-\frac{9}{19}a+\frac{9}{19}.\frac{5}{3}& \text{Uitwerken } \\ & =ax-\frac{5}{3}x-\frac{9}{19}a+\frac{45}{57} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{5}{3}x-\frac{9}{19}a+\frac{15}{19} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{1}{12}+q)(b+\frac{-1}{5})& =(\color{red}{q}+\color{orange}{\frac{1}{12}}).(\color{green}{b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{1}{12})} . \color{green}{(b)} + \color{orange}{(\frac{1}{12})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{5}q+\frac{1}{12}b-\frac{1}{12}.\frac{1}{5}& \text{Uitwerken } \\ & =bq-\frac{1}{5}q+\frac{1}{12}b-\frac{1}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p+\frac{-20}{17})(\frac{12}{17}+b)& =(\color{red}{p}+\color{orange}{\frac{-20}{17}}).(\color{green}{b}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{-20}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-20}{17})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{12}{17}p-\frac{20}{17}b-\frac{20}{17}.\frac{12}{17}& \text{Uitwerken } \\ & =bp+\frac{12}{17}p-\frac{20}{17}b-\frac{240}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{18}{16})(x-\frac{-4}{7})& =(\color{red}{b}+\color{orange}{\frac{9}{8}}).(\color{green}{x}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{9}{8})} . \color{green}{(x)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{4}{7}b+\frac{9}{8}x+\frac{9}{8}.\frac{4}{7}& \text{Uitwerken } \\ & =bx+\frac{4}{7}b+\frac{9}{8}x+\frac{36}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{4}{7}b+\frac{9}{8}x+\frac{9}{14} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q-\frac{5}{11})(p+\frac{-20}{7})& =(\color{red}{q}+\color{orange}{\frac{-5}{11}}).(\color{green}{p}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{-5}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{20}{7}q-\frac{5}{11}p+\frac{5}{11}.\frac{20}{7}& \text{Uitwerken } \\ & =pq-\frac{20}{7}q-\frac{5}{11}p+\frac{100}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{15}{12})(\frac{-2}{13}+x)& =(\color{red}{q}+\color{orange}{\frac{5}{4}}).(\color{green}{x}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(\frac{5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{2}{13}q+\frac{5}{4}x-\frac{5}{4}.\frac{2}{13}& \text{Uitwerken } \\ & =qx-\frac{2}{13}q+\frac{5}{4}x-\frac{10}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{2}{13}q+\frac{5}{4}x-\frac{5}{26} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{20}{14}+a)(b+\frac{6}{5})& =(\color{red}{a}+\color{orange}{\frac{10}{7}}).(\color{green}{b}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{10}{7})} . \color{green}{(b)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{6}{5}a+\frac{10}{7}b+\frac{10}{7}.\frac{6}{5}& \text{Uitwerken } \\ & =ab+\frac{6}{5}a+\frac{10}{7}b+\frac{60}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{6}{5}a+\frac{10}{7}b+\frac{12}{7} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-12}{11}-p)(\frac{3}{14}-p)& =(\color{red}{-p}+\color{orange}{\frac{-12}{11}}).(\color{green}{-p}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(\frac{-12}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-12}{11})} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{3}{14}p+\frac{12}{11}p-\frac{12}{11}.\frac{3}{14}& \text{Uitwerken } \\ & =p^2+((\frac{-3}{14})+\frac{12}{11})p-(\frac{-36}{154}) & \text{Neem samen} \\ &=p^2+\frac{135}{154}p-(\frac{-36}{154}) & \text{Maak de som} \\ &=p^2+\frac{135}{154}p+\frac{18}{77} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(p+\frac{10}{16})(\frac{18}{15}+x)& =(\color{red}{p}+\color{orange}{\frac{5}{8}}).(\color{green}{x}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{5}{8})} . \color{green}{(x)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{6}{5}p+\frac{5}{8}x+\frac{5}{8}.\frac{6}{5}& \text{Uitwerken } \\ & =px+\frac{6}{5}p+\frac{5}{8}x+\frac{30}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{6}{5}p+\frac{5}{8}x+\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-2}{20}+b)(\frac{11}{11}+q)& =(\color{red}{b}+\color{orange}{\frac{-1}{10}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-1}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1b-\frac{1}{10}q-\frac{1}{10}.1& \text{Uitwerken } \\ & =bq+1b-\frac{1}{10}q-\frac{1}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-20 19:09:05
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