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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-4}{19}-b)(\frac{-1}{15}+a)& =(\color{red}{-b}+\color{orange}{\frac{-4}{19}}).(\color{green}{a}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(\frac{-4}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{19})} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{15}b-\frac{4}{19}a+\frac{4}{19}.\frac{1}{15}& \text{Uitwerken } \\ & =-ab+\frac{1}{15}b-\frac{4}{19}a+\frac{4}{285} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-17}{14}-x)(\frac{-5}{13}+p)& =(\color{red}{-x}+\color{orange}{\frac{-17}{14}}).(\color{green}{p}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{13})} + \color{orange}{(\frac{-17}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{14})} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{5}{13}x-\frac{17}{14}p+\frac{17}{14}.\frac{5}{13}& \text{Uitwerken } \\ & =-px+\frac{5}{13}x-\frac{17}{14}p+\frac{85}{182} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-14}{10})(a+\frac{20}{2})& =(\color{red}{x}+\color{orange}{\frac{-7}{5}}).(\color{green}{a}+\color{blue}{10})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(10)} + \color{orange}{(\frac{-7}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = ax+10x-\frac{7}{5}a-\frac{7}{5}.10& \text{Uitwerken } \\ & =ax+10x-\frac{7}{5}a-\frac{70}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+10x-\frac{7}{5}a-14 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-8}{6}+b)(b-\frac{14}{15})& =(\color{red}{b}+\color{orange}{\frac{-4}{3}}).(\color{green}{b}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{14}{15}b-\frac{4}{3}b+\frac{4}{3}.\frac{14}{15}& \text{Uitwerken } \\ & =b^2+((\frac{-14}{15})+(\frac{-4}{3}))b+\frac{56}{45} & \text{Neem samen} \\ &=b^2-\frac{34}{15}b+\frac{56}{45} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-7}{14}+x)(x-\frac{5}{14})& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{5}{14}x-\frac{1}{2}x+\frac{1}{2}.\frac{5}{14}& \text{Uitwerken } \\ & =x^2+((\frac{-5}{14})+(\frac{-1}{2}))x+\frac{5}{28} & \text{Neem samen} \\ &=x^2-\frac{12}{14}x+\frac{5}{28} & \text{Maak de som} \\ &=x^2-\frac{6}{7}x+\frac{5}{28} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(x+\frac{18}{11})(q+\frac{-11}{6})& =(\color{red}{x}+\color{orange}{\frac{18}{11}}).(\color{green}{q}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{18}{11})} . \color{green}{(q)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{11}{6}x+\frac{18}{11}q-\frac{18}{11}.\frac{11}{6}& \text{Uitwerken } \\ & =qx-\frac{11}{6}x+\frac{18}{11}q-\frac{198}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{11}{6}x+\frac{18}{11}q-3 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-18}{4}+p)(\frac{-14}{7}+x)& =(\color{red}{p}+\color{orange}{\frac{-9}{2}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-9}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = px-2p-\frac{9}{2}x+\frac{9}{2}.2& \text{Uitwerken } \\ & =px-2p-\frac{9}{2}x+\frac{18}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-2p-\frac{9}{2}x+9 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-3}{2}-b)(\frac{-4}{18}-p)& =(\color{red}{-b}+\color{orange}{\frac{-3}{2}}).(\color{green}{-p}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{9}b+\frac{3}{2}p+\frac{3}{2}.\frac{2}{9}& \text{Uitwerken } \\ & =bp+\frac{2}{9}b+\frac{3}{2}p+\frac{6}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{2}{9}b+\frac{3}{2}p+\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-10}{20}+b)(\frac{-5}{13}-a)& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{-a}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{13})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{5}{13}b+\frac{1}{2}a+\frac{1}{2}.\frac{5}{13}& \text{Uitwerken } \\ & =-ab-\frac{5}{13}b+\frac{1}{2}a+\frac{5}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{-19}{16})(\frac{-16}{15}+x)& =(\color{red}{a}+\color{orange}{\frac{19}{16}}).(\color{green}{x}+\color{blue}{\frac{-16}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{15})} + \color{orange}{(\frac{19}{16})} . \color{green}{(x)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(\frac{-16}{15})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{16}{15}a+\frac{19}{16}x-\frac{19}{16}.\frac{16}{15}& \text{Uitwerken } \\ & =ax-\frac{16}{15}a+\frac{19}{16}x-\frac{304}{240} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{16}{15}a+\frac{19}{16}x-\frac{19}{15} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(p-\frac{-9}{20})(\frac{9}{8}+p)& =(\color{red}{p}+\color{orange}{\frac{9}{20}}).(\color{green}{p}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{9}{20})} . \color{green}{(p)} + \color{orange}{(\frac{9}{20})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{9}{8}p+\frac{9}{20}p+\frac{9}{20}.\frac{9}{8}& \text{Uitwerken } \\ & =p^2+(\frac{9}{8}+\frac{9}{20})p+\frac{81}{160} & \text{Neem samen} \\ &=p^2+\frac{63}{40}p+\frac{81}{160} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{8}{5}+a)(x+\frac{-20}{14})& =(\color{red}{a}+\color{orange}{\frac{8}{5}}).(\color{green}{x}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{8}{5})} . \color{green}{(x)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{10}{7}a+\frac{8}{5}x-\frac{8}{5}.\frac{10}{7}& \text{Uitwerken } \\ & =ax-\frac{10}{7}a+\frac{8}{5}x-\frac{80}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{10}{7}a+\frac{8}{5}x-\frac{16}{7} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-19 20:29:16
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