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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{10}{2})(\frac{2}{18}+b)& =(\color{red}{q}+\color{orange}{(-5)}).(\color{green}{b}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(-5)} . \color{green}{(b)} + \color{orange}{(-5)} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{9}q-5b-5.\frac{1}{9}& \text{Uitwerken } \\ & =bq+\frac{1}{9}q-5b-\frac{5}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x-\frac{-20}{3})(\frac{-6}{6}-b)& =(\color{red}{x}+\color{orange}{\frac{20}{3}}).(\color{green}{-b}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{20}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{20}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bx-1x-\frac{20}{3}b-\frac{20}{3}.1& \text{Uitwerken } \\ & =-bx-1x-\frac{20}{3}b-\frac{20}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{-3}{15})(x+\frac{-6}{3})& =(\color{red}{q}+\color{orange}{\frac{1}{5}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{1}{5})} . \color{green}{(x)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = qx-2q+\frac{1}{5}x-\frac{1}{5}.2& \text{Uitwerken } \\ & =qx-2q+\frac{1}{5}x-\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x+\frac{-12}{9})(\frac{-19}{8}+x)& =(\color{red}{x}+\color{orange}{\frac{-4}{3}}).(\color{green}{x}+\color{blue}{\frac{-19}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{8})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-19}{8})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{19}{8}x-\frac{4}{3}x+\frac{4}{3}.\frac{19}{8}& \text{Uitwerken } \\ & =x^2+((\frac{-19}{8})+(\frac{-4}{3}))x+\frac{76}{24} & \text{Neem samen} \\ &=x^2-\frac{89}{24}x+\frac{76}{24} & \text{Maak de som} \\ &=x^2-\frac{89}{24}x+\frac{19}{6} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{6}{4}+a)(a-\frac{-4}{18})& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{2}{9}a+\frac{3}{2}a+\frac{3}{2}.\frac{2}{9}& \text{Uitwerken } \\ & =a^2+(\frac{2}{9}+\frac{3}{2})a+\frac{6}{18} & \text{Neem samen} \\ &=a^2+\frac{31}{18}a+\frac{6}{18} & \text{Maak de som} \\ &=a^2+\frac{31}{18}a+\frac{1}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(x-\frac{-16}{9})(\frac{18}{20}+b)& =(\color{red}{x}+\color{orange}{\frac{16}{9}}).(\color{green}{b}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{16}{9})} . \color{green}{(b)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{9}{10}x+\frac{16}{9}b+\frac{16}{9}.\frac{9}{10}& \text{Uitwerken } \\ & =bx+\frac{9}{10}x+\frac{16}{9}b+\frac{144}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{9}{10}x+\frac{16}{9}b+\frac{8}{5} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-14}{16})(x+\frac{-16}{19})& =(\color{red}{b}+\color{orange}{\frac{-7}{8}}).(\color{green}{x}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{16}{19}b-\frac{7}{8}x+\frac{7}{8}.\frac{16}{19}& \text{Uitwerken } \\ & =bx-\frac{16}{19}b-\frac{7}{8}x+\frac{112}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{16}{19}b-\frac{7}{8}x+\frac{14}{19} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x-\frac{11}{16})(p-\frac{-9}{7})& =(\color{red}{x}+\color{orange}{\frac{-11}{16}}).(\color{green}{p}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{9}{7}x-\frac{11}{16}p-\frac{11}{16}.\frac{9}{7}& \text{Uitwerken } \\ & =px+\frac{9}{7}x-\frac{11}{16}p-\frac{99}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{16}{15}-a)(\frac{-19}{15}-q)& =(\color{red}{-a}+\color{orange}{\frac{16}{15}}).(\color{green}{-q}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(\frac{16}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{16}{15})} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{19}{15}a-\frac{16}{15}q-\frac{16}{15}.\frac{19}{15}& \text{Uitwerken } \\ & =aq+\frac{19}{15}a-\frac{16}{15}q-\frac{304}{225} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-10}{14}-x)(a+\frac{-10}{20})& =(\color{red}{-x}+\color{orange}{\frac{-5}{7}}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{2}x-\frac{5}{7}a+\frac{5}{7}.\frac{1}{2}& \text{Uitwerken } \\ & =-ax+\frac{1}{2}x-\frac{5}{7}a+\frac{5}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-12}{8}+q)(x-\frac{-15}{9})& =(\color{red}{q}+\color{orange}{\frac{-3}{2}}).(\color{green}{x}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{3}q-\frac{3}{2}x-\frac{3}{2}.\frac{5}{3}& \text{Uitwerken } \\ & =qx+\frac{5}{3}q-\frac{3}{2}x-\frac{15}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{5}{3}q-\frac{3}{2}x-\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{7}{11}+b)(\frac{6}{9}-x)& =(\color{red}{b}+\color{orange}{\frac{7}{11}}).(\color{green}{-x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{7}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{11})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{2}{3}b-\frac{7}{11}x+\frac{7}{11}.\frac{2}{3}& \text{Uitwerken } \\ & =-bx+\frac{2}{3}b-\frac{7}{11}x+\frac{14}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-20 02:04:38
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