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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{-8}{11})(b+\frac{-3}{8})& =(\color{red}{p}+\color{orange}{\frac{-8}{11}}).(\color{green}{b}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{-8}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{11})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{8}p-\frac{8}{11}b+\frac{8}{11}.\frac{3}{8}& \text{Uitwerken } \\ & =bp-\frac{3}{8}p-\frac{8}{11}b+\frac{24}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{3}{8}p-\frac{8}{11}b+\frac{3}{11} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{12}{19}-a)(\frac{20}{13}+p)& =(\color{red}{-a}+\color{orange}{\frac{12}{19}}).(\color{green}{p}+\color{blue}{\frac{20}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{20}{13})} + \color{orange}{(\frac{12}{19})} . \color{green}{(p)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(\frac{20}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{20}{13}a+\frac{12}{19}p+\frac{12}{19}.\frac{20}{13}& \text{Uitwerken } \\ & =-ap-\frac{20}{13}a+\frac{12}{19}p+\frac{240}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{13}{8}-x)(a+\frac{-8}{18})& =(\color{red}{-x}+\color{orange}{\frac{13}{8}}).(\color{green}{a}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{13}{8})} . \color{green}{(a)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{4}{9}x+\frac{13}{8}a-\frac{13}{8}.\frac{4}{9}& \text{Uitwerken } \\ & =-ax+\frac{4}{9}x+\frac{13}{8}a-\frac{52}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{4}{9}x+\frac{13}{8}a-\frac{13}{18} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-15}{4}-a)(q-\frac{-11}{16})& =(\color{red}{-a}+\color{orange}{\frac{-15}{4}}).(\color{green}{q}+\color{blue}{\frac{11}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{16})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{11}{16})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{11}{16}a-\frac{15}{4}q-\frac{15}{4}.\frac{11}{16}& \text{Uitwerken } \\ & =-aq-\frac{11}{16}a-\frac{15}{4}q-\frac{165}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{5}{12}+p)(\frac{-20}{5}-q)& =(\color{red}{p}+\color{orange}{\frac{5}{12}}).(\color{green}{-q}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(-4)} + \color{orange}{(\frac{5}{12})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{12})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -pq-4p-\frac{5}{12}q-\frac{5}{12}.4& \text{Uitwerken } \\ & =-pq-4p-\frac{5}{12}q-\frac{20}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-4p-\frac{5}{12}q-\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b-\frac{8}{18})(a+\frac{-20}{20})& =(\color{red}{b}+\color{orange}{\frac{-4}{9}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-4}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab-1b-\frac{4}{9}a+\frac{4}{9}.1& \text{Uitwerken } \\ & =ab-1b-\frac{4}{9}a+\frac{4}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x-\frac{10}{6})(\frac{-6}{10}+x)& =(\color{red}{x}+\color{orange}{\frac{-5}{3}}).(\color{green}{x}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{3}{5}x-\frac{5}{3}x+\frac{5}{3}.\frac{3}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-3}{5})+(\frac{-5}{3}))x+\frac{15}{15} & \text{Neem samen} \\ &=x^2-\frac{34}{15}x+\frac{15}{15} & \text{Maak de som} \\ &=x^2-\frac{34}{15}x+1 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{-6}{9}+a)(q-\frac{9}{6})& =(\color{red}{a}+\color{orange}{\frac{-2}{3}}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{3}{2}a-\frac{2}{3}q+\frac{2}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =aq-\frac{3}{2}a-\frac{2}{3}q+\frac{6}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{3}{2}a-\frac{2}{3}q+1 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x+\frac{-15}{10})(\frac{-9}{14}-b)& =(\color{red}{x}+\color{orange}{\frac{-3}{2}}).(\color{green}{-b}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{9}{14}x+\frac{3}{2}b+\frac{3}{2}.\frac{9}{14}& \text{Uitwerken } \\ & =-bx-\frac{9}{14}x+\frac{3}{2}b+\frac{27}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{18}{12}+a)(\frac{8}{8}+a)& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = aa+1a+\frac{3}{2}a+\frac{3}{2}.1& \text{Uitwerken } \\ & =a^2+(1+\frac{3}{2})a+\frac{3}{2} & \text{Neem samen} \\ &=a^2+\frac{5}{2}a+\frac{3}{2} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{-7}{18}-a)(x+\frac{20}{5})& =(\color{red}{-a}+\color{orange}{\frac{-7}{18}}).(\color{green}{x}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(4)} + \color{orange}{(\frac{-7}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{18})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -ax-4a-\frac{7}{18}x-\frac{7}{18}.4& \text{Uitwerken } \\ & =-ax-4a-\frac{7}{18}x-\frac{28}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-4a-\frac{7}{18}x-\frac{14}{9} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p-\frac{-19}{12})(p-\frac{12}{12})& =(\color{red}{p}+\color{orange}{\frac{19}{12}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{19}{12})} . \color{green}{(p)} + \color{orange}{(\frac{19}{12})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pp-1p+\frac{19}{12}p-\frac{19}{12}.1& \text{Uitwerken } \\ & =p^2+((-1)+\frac{19}{12})p-(\frac{-19}{12}) & \text{Neem samen} \\ &=p^2+\frac{7}{12}p-(\frac{-19}{12}) & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-22 22:18:32
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