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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-18}{15}+b)(\frac{3}{15}-x)& =(\color{red}{b}+\color{orange}{\frac{-6}{5}}).(\color{green}{-x}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{5}b+\frac{6}{5}x-\frac{6}{5}.\frac{1}{5}& \text{Uitwerken } \\ & =-bx+\frac{1}{5}b+\frac{6}{5}x-\frac{6}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x-\frac{-8}{20})(q+\frac{-10}{8})& =(\color{red}{x}+\color{orange}{\frac{2}{5}}).(\color{green}{q}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{4}x+\frac{2}{5}q-\frac{2}{5}.\frac{5}{4}& \text{Uitwerken } \\ & =qx-\frac{5}{4}x+\frac{2}{5}q-\frac{10}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{5}{4}x+\frac{2}{5}q-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q+\frac{-1}{2})(p+\frac{-4}{10})& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{2}{5}q-\frac{1}{2}p+\frac{1}{2}.\frac{2}{5}& \text{Uitwerken } \\ & =pq-\frac{2}{5}q-\frac{1}{2}p+\frac{2}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{2}{5}q-\frac{1}{2}p+\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-17}{2}+x)(\frac{18}{20}-p)& =(\color{red}{x}+\color{orange}{\frac{-17}{2}}).(\color{green}{-p}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-17}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-17}{2})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{9}{10}x+\frac{17}{2}p-\frac{17}{2}.\frac{9}{10}& \text{Uitwerken } \\ & =-px+\frac{9}{10}x+\frac{17}{2}p-\frac{153}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{8}{3}+a)(p+\frac{3}{11})& =(\color{red}{a}+\color{orange}{\frac{8}{3}}).(\color{green}{p}+\color{blue}{\frac{3}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{3}{11})} + \color{orange}{(\frac{8}{3})} . \color{green}{(p)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{3}{11})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{11}a+\frac{8}{3}p+\frac{8}{3}.\frac{3}{11}& \text{Uitwerken } \\ & =ap+\frac{3}{11}a+\frac{8}{3}p+\frac{24}{33} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{3}{11}a+\frac{8}{3}p+\frac{8}{11} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-20}{5})(p+\frac{3}{4})& =(\color{red}{a}+\color{orange}{(-4)}).(\color{green}{p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(-4)} . \color{green}{(p)} + \color{orange}{(-4)} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{4}a-4p-4.\frac{3}{4}& \text{Uitwerken } \\ & =ap+\frac{3}{4}a-4p-\frac{12}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{3}{4}a-4p-3 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{1}{13}-a)(p+\frac{-10}{13})& =(\color{red}{-a}+\color{orange}{\frac{1}{13}}).(\color{green}{p}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{1}{13})} . \color{green}{(p)} + \color{orange}{(\frac{1}{13})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{10}{13}a+\frac{1}{13}p-\frac{1}{13}.\frac{10}{13}& \text{Uitwerken } \\ & =-ap+\frac{10}{13}a+\frac{1}{13}p-\frac{10}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-17}{20}-a)(\frac{-7}{8}+a)& =(\color{red}{-a}+\color{orange}{\frac{-17}{20}}).(\color{green}{a}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{-17}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{20})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{7}{8}a-\frac{17}{20}a+\frac{17}{20}.\frac{7}{8}& \text{Uitwerken } \\ & =-a^2+(\frac{7}{8}+(\frac{-17}{20}))a+(\frac{-119}{160}) & \text{Neem samen} \\ &=-a^2+\frac{1}{40}a+(\frac{-119}{160}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-3}{18}-b)(a+\frac{-1}{7})& =(\color{red}{-b}+\color{orange}{\frac{-1}{6}}).(\color{green}{a}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{7}b-\frac{1}{6}a+\frac{1}{6}.\frac{1}{7}& \text{Uitwerken } \\ & =-ab+\frac{1}{7}b-\frac{1}{6}a+\frac{1}{42} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{10}{17}+q)(9+a)& =(\color{red}{q}+\color{orange}{\frac{10}{17}}).(\color{green}{a}+\color{blue}{9})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(9)} + \color{orange}{(\frac{10}{17})} . \color{green}{(a)} + \color{orange}{(\frac{10}{17})} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = aq+9q+\frac{10}{17}a+\frac{10}{17}.9& \text{Uitwerken } \\ & =aq+9q+\frac{10}{17}a+\frac{90}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x-\frac{12}{14})(\frac{2}{4}+q)& =(\color{red}{x}+\color{orange}{\frac{-6}{7}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{2}x-\frac{6}{7}q-\frac{6}{7}.\frac{1}{2}& \text{Uitwerken } \\ & =qx+\frac{1}{2}x-\frac{6}{7}q-\frac{6}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{1}{2}x-\frac{6}{7}q-\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{9}{3}+x)(x+\frac{-5}{8})& =(\color{red}{x}+\color{orange}{3}).(\color{green}{x}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(3)} . \color{green}{(x)} + \color{orange}{(3)} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{5}{8}x+3x-3.\frac{5}{8}& \text{Uitwerken } \\ & =x^2+((\frac{-5}{8})+3)x-(\frac{-15}{8}) & \text{Neem samen} \\ &=x^2+\frac{19}{8}x-(\frac{-15}{8}) & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-12 15:29:57
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