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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{12}{2})(p+\frac{20}{5})& =(\color{red}{a}+\color{orange}{6}).(\color{green}{p}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(4)} + \color{orange}{(6)} . \color{green}{(p)} + \color{orange}{(6)} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = ap+4a+6p+6.4& \text{Uitwerken } \\ & =ap+4a+6p+24 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{12}{10}-a)(\frac{6}{16}+x)& =(\color{red}{-a}+\color{orange}{\frac{6}{5}}).(\color{green}{x}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{6}{5})} . \color{green}{(x)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{3}{8}a+\frac{6}{5}x+\frac{6}{5}.\frac{3}{8}& \text{Uitwerken } \\ & =-ax-\frac{3}{8}a+\frac{6}{5}x+\frac{18}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{3}{8}a+\frac{6}{5}x+\frac{9}{20} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x-\frac{-17}{9})(\frac{17}{12}+a)& =(\color{red}{x}+\color{orange}{\frac{17}{9}}).(\color{green}{a}+\color{blue}{\frac{17}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{17}{12})} + \color{orange}{(\frac{17}{9})} . \color{green}{(a)} + \color{orange}{(\frac{17}{9})} . \color{blue}{(\frac{17}{12})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{12}x+\frac{17}{9}a+\frac{17}{9}.\frac{17}{12}& \text{Uitwerken } \\ & =ax+\frac{17}{12}x+\frac{17}{9}a+\frac{289}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-(-3))(x-\frac{11}{20})& =(\color{red}{q}+\color{orange}{3}).(\color{green}{x}+\color{blue}{\frac{-11}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{20})} + \color{orange}{(3)} . \color{green}{(x)} + \color{orange}{(3)} . \color{blue}{(\frac{-11}{20})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{11}{20}q+3x-3.\frac{11}{20}& \text{Uitwerken } \\ & =qx-\frac{11}{20}q+3x-\frac{33}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p+\frac{-20}{5})(a-\frac{-19}{3})& =(\color{red}{p}+\color{orange}{(-4)}).(\color{green}{a}+\color{blue}{\frac{19}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{19}{3})} + \color{orange}{(-4)} . \color{green}{(a)} + \color{orange}{(-4)} . \color{blue}{(\frac{19}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{19}{3}p-4a-4.\frac{19}{3}& \text{Uitwerken } \\ & =ap+\frac{19}{3}p-4a-\frac{76}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-1}{16}+a)(p+\frac{16}{20})& =(\color{red}{a}+\color{orange}{\frac{-1}{16}}).(\color{green}{p}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-1}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{16})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{4}{5}a-\frac{1}{16}p-\frac{1}{16}.\frac{4}{5}& \text{Uitwerken } \\ & =ap+\frac{4}{5}a-\frac{1}{16}p-\frac{4}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{4}{5}a-\frac{1}{16}p-\frac{1}{20} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q-\frac{13}{8})(\frac{16}{15}+b)& =(\color{red}{q}+\color{orange}{\frac{-13}{8}}).(\color{green}{b}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{-13}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{8})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{16}{15}q-\frac{13}{8}b-\frac{13}{8}.\frac{16}{15}& \text{Uitwerken } \\ & =bq+\frac{16}{15}q-\frac{13}{8}b-\frac{208}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{16}{15}q-\frac{13}{8}b-\frac{26}{15} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-20}{2}-p)(x-\frac{4}{10})& =(\color{red}{-p}+\color{orange}{(-10)}).(\color{green}{x}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(-10)} . \color{green}{(x)} + \color{orange}{(-10)} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{2}{5}p-10x+10.\frac{2}{5}& \text{Uitwerken } \\ & =-px+\frac{2}{5}p-10x+\frac{20}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{2}{5}p-10x+4 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{9}{17}+a)(p-\frac{-9}{20})& =(\color{red}{a}+\color{orange}{\frac{9}{17}}).(\color{green}{p}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(\frac{9}{17})} . \color{green}{(p)} + \color{orange}{(\frac{9}{17})} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{9}{20}a+\frac{9}{17}p+\frac{9}{17}.\frac{9}{20}& \text{Uitwerken } \\ & =ap+\frac{9}{20}a+\frac{9}{17}p+\frac{81}{340} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{19}{6}+a)(a-\frac{2}{7})& =(\color{red}{a}+\color{orange}{\frac{19}{6}}).(\color{green}{a}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{19}{6})} . \color{green}{(a)} + \color{orange}{(\frac{19}{6})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{2}{7}a+\frac{19}{6}a-\frac{19}{6}.\frac{2}{7}& \text{Uitwerken } \\ & =a^2+((\frac{-2}{7})+\frac{19}{6})a-(\frac{-38}{42}) & \text{Neem samen} \\ &=a^2+\frac{121}{42}a-(\frac{-38}{42}) & \text{Maak de som} \\ &=a^2+\frac{121}{42}a+\frac{19}{21} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(\frac{15}{10}+a)(b+\frac{-18}{20})& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{b}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{9}{10}a+\frac{3}{2}b-\frac{3}{2}.\frac{9}{10}& \text{Uitwerken } \\ & =ab-\frac{9}{10}a+\frac{3}{2}b-\frac{27}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{1}{12}+q)(p+\frac{17}{10})& =(\color{red}{q}+\color{orange}{\frac{1}{12}}).(\color{green}{p}+\color{blue}{\frac{17}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{17}{10})} + \color{orange}{(\frac{1}{12})} . \color{green}{(p)} + \color{orange}{(\frac{1}{12})} . \color{blue}{(\frac{17}{10})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{17}{10}q+\frac{1}{12}p+\frac{1}{12}.\frac{17}{10}& \text{Uitwerken } \\ & =pq+\frac{17}{10}q+\frac{1}{12}p+\frac{17}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-18 09:20:58
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