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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{7}{9})(x+\frac{3}{15})& =(\color{red}{a}+\color{orange}{\frac{-7}{9}}).(\color{green}{x}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{5}a-\frac{7}{9}x-\frac{7}{9}.\frac{1}{5}& \text{Uitwerken } \\ & =ax+\frac{1}{5}a-\frac{7}{9}x-\frac{7}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{2}{8}-b)(q+\frac{-9}{6})& =(\color{red}{-b}+\color{orange}{\frac{1}{4}}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{3}{2}b+\frac{1}{4}q-\frac{1}{4}.\frac{3}{2}& \text{Uitwerken } \\ & =-bq+\frac{3}{2}b+\frac{1}{4}q-\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{17}{12}-x)(\frac{-15}{11}+q)& =(\color{red}{-x}+\color{orange}{\frac{17}{12}}).(\color{green}{q}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(\frac{17}{12})} . \color{green}{(q)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{15}{11}x+\frac{17}{12}q-\frac{17}{12}.\frac{15}{11}& \text{Uitwerken } \\ & =-qx+\frac{15}{11}x+\frac{17}{12}q-\frac{255}{132} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{15}{11}x+\frac{17}{12}q-\frac{85}{44} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x+\frac{13}{15})(x+\frac{-17}{10})& =(\color{red}{x}+\color{orange}{\frac{13}{15}}).(\color{green}{x}+\color{blue}{\frac{-17}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{10})} + \color{orange}{(\frac{13}{15})} . \color{green}{(x)} + \color{orange}{(\frac{13}{15})} . \color{blue}{(\frac{-17}{10})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{17}{10}x+\frac{13}{15}x-\frac{13}{15}.\frac{17}{10}& \text{Uitwerken } \\ & =x^2+((\frac{-17}{10})+\frac{13}{15})x-(\frac{-221}{150}) & \text{Neem samen} \\ &=x^2-\frac{25}{30}x-(\frac{-221}{150}) & \text{Maak de som} \\ &=x^2-\frac{5}{6}x+\frac{221}{150} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(p+\frac{20}{9})(b+\frac{13}{20})& =(\color{red}{p}+\color{orange}{\frac{20}{9}}).(\color{green}{b}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{20}{9})} . \color{green}{(b)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{20}p+\frac{20}{9}b+\frac{20}{9}.\frac{13}{20}& \text{Uitwerken } \\ & =bp+\frac{13}{20}p+\frac{20}{9}b+\frac{260}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{13}{20}p+\frac{20}{9}b+\frac{13}{9} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-20}{2}+a)(p-\frac{9}{2})& =(\color{red}{a}+\color{orange}{(-10)}).(\color{green}{p}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(-10)} . \color{green}{(p)} + \color{orange}{(-10)} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{9}{2}a-10p+10.\frac{9}{2}& \text{Uitwerken } \\ & =ap-\frac{9}{2}a-10p+\frac{90}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{9}{2}a-10p+45 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-20}{18}-p)(\frac{-4}{9}-b)& =(\color{red}{-p}+\color{orange}{\frac{-10}{9}}).(\color{green}{-b}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{9}p+\frac{10}{9}b+\frac{10}{9}.\frac{4}{9}& \text{Uitwerken } \\ & =bp+\frac{4}{9}p+\frac{10}{9}b+\frac{40}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-9}{17}-p)(x+\frac{20}{18})& =(\color{red}{-p}+\color{orange}{\frac{-9}{17}}).(\color{green}{x}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{-9}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{17})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{10}{9}p-\frac{9}{17}x-\frac{9}{17}.\frac{10}{9}& \text{Uitwerken } \\ & =-px-\frac{10}{9}p-\frac{9}{17}x-\frac{90}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{10}{9}p-\frac{9}{17}x-\frac{10}{17} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p-\frac{-18}{15})(\frac{7}{19}+x)& =(\color{red}{p}+\color{orange}{\frac{6}{5}}).(\color{green}{x}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(\frac{6}{5})} . \color{green}{(x)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{19}p+\frac{6}{5}x+\frac{6}{5}.\frac{7}{19}& \text{Uitwerken } \\ & =px+\frac{7}{19}p+\frac{6}{5}x+\frac{42}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-15}{8}-p)(\frac{9}{6}-b)& =(\color{red}{-p}+\color{orange}{\frac{-15}{8}}).(\color{green}{-b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-15}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{-15}{8})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{2}p+\frac{15}{8}b-\frac{15}{8}.\frac{3}{2}& \text{Uitwerken } \\ & =bp-\frac{3}{2}p+\frac{15}{8}b-\frac{45}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q+\frac{-2}{8})(p-\frac{13}{8})& =(\color{red}{q}+\color{orange}{\frac{-1}{4}}).(\color{green}{p}+\color{blue}{\frac{-13}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{8})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-13}{8})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{13}{8}q-\frac{1}{4}p+\frac{1}{4}.\frac{13}{8}& \text{Uitwerken } \\ & =pq-\frac{13}{8}q-\frac{1}{4}p+\frac{13}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{10}{12}+a)(\frac{15}{6}-x)& =(\color{red}{a}+\color{orange}{\frac{5}{6}}).(\color{green}{-x}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{5}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{5}{2}a-\frac{5}{6}x+\frac{5}{6}.\frac{5}{2}& \text{Uitwerken } \\ & =-ax+\frac{5}{2}a-\frac{5}{6}x+\frac{25}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-07 19:46:59
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