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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-11}{9}+a)(\frac{-16}{5}-p)& =(\color{red}{a}+\color{orange}{\frac{-11}{9}}).(\color{green}{-p}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{-11}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{16}{5}a+\frac{11}{9}p+\frac{11}{9}.\frac{16}{5}& \text{Uitwerken } \\ & =-ap-\frac{16}{5}a+\frac{11}{9}p+\frac{176}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{1}{4}-a)(p+\frac{-4}{8})& =(\color{red}{-a}+\color{orange}{\frac{1}{4}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{2}a+\frac{1}{4}p-\frac{1}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =-ap+\frac{1}{2}a+\frac{1}{4}p-\frac{1}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-5}{16}+a)((-5)+a)& =(\color{red}{a}+\color{orange}{\frac{-5}{16}}).(\color{green}{a}+\color{blue}{(-5)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-5)} + \color{orange}{(\frac{-5}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{16})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = aa-5a-\frac{5}{16}a+\frac{5}{16}.5& \text{Uitwerken } \\ & =a^2+((-5)+(\frac{-5}{16}))a+\frac{25}{16} & \text{Neem samen} \\ &=a^2-\frac{85}{16}a+\frac{25}{16} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(a+\frac{4}{17})(\frac{-12}{14}+q)& =(\color{red}{a}+\color{orange}{\frac{4}{17}}).(\color{green}{q}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{4}{17})} . \color{green}{(q)} + \color{orange}{(\frac{4}{17})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{6}{7}a+\frac{4}{17}q-\frac{4}{17}.\frac{6}{7}& \text{Uitwerken } \\ & =aq-\frac{6}{7}a+\frac{4}{17}q-\frac{24}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{20}{16}-p)(b-\frac{14}{8})& =(\color{red}{-p}+\color{orange}{\frac{5}{4}}).(\color{green}{b}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{7}{4}p+\frac{5}{4}b-\frac{5}{4}.\frac{7}{4}& \text{Uitwerken } \\ & =-bp+\frac{7}{4}p+\frac{5}{4}b-\frac{35}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{6}{3}-b)(\frac{6}{17}-b)& =(\color{red}{-b}+\color{orange}{2}).(\color{green}{-b}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(2)} . \color{green}{(-b)} + \color{orange}{(2)} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{6}{17}b-2b+2.\frac{6}{17}& \text{Uitwerken } \\ & =b^2+((\frac{-6}{17})+(-2))b+\frac{12}{17} & \text{Neem samen} \\ &=b^2-\frac{40}{17}b+\frac{12}{17} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-12}{11}-b)(b-\frac{13}{18})& =(\color{red}{-b}+\color{orange}{\frac{-12}{11}}).(\color{green}{b}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(\frac{-12}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-12}{11})} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{13}{18}b-\frac{12}{11}b+\frac{12}{11}.\frac{13}{18}& \text{Uitwerken } \\ & =-b^2+(\frac{13}{18}+(\frac{-12}{11}))b+(\frac{-156}{198}) & \text{Neem samen} \\ &=-b^2-\frac{73}{198}b+(\frac{-156}{198}) & \text{Maak de som} \\ &=-b^2-\frac{73}{198}b+(\frac{-26}{33}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-14}{15})(q+\frac{18}{11})& =(\color{red}{b}+\color{orange}{\frac{-14}{15}}).(\color{green}{q}+\color{blue}{\frac{18}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{18}{11})} + \color{orange}{(\frac{-14}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-14}{15})} . \color{blue}{(\frac{18}{11})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{18}{11}b-\frac{14}{15}q-\frac{14}{15}.\frac{18}{11}& \text{Uitwerken } \\ & =bq+\frac{18}{11}b-\frac{14}{15}q-\frac{252}{165} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{18}{11}b-\frac{14}{15}q-\frac{84}{55} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{18}{11}+x)(q+\frac{7}{11})& =(\color{red}{x}+\color{orange}{\frac{18}{11}}).(\color{green}{q}+\color{blue}{\frac{7}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{7}{11})} + \color{orange}{(\frac{18}{11})} . \color{green}{(q)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{7}{11})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{7}{11}x+\frac{18}{11}q+\frac{18}{11}.\frac{7}{11}& \text{Uitwerken } \\ & =qx+\frac{7}{11}x+\frac{18}{11}q+\frac{126}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-13}{14}-x)(\frac{20}{13}-a)& =(\color{red}{-x}+\color{orange}{\frac{-13}{14}}).(\color{green}{-a}+\color{blue}{\frac{20}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{20}{13})} + \color{orange}{(\frac{-13}{14})} . \color{green}{(-a)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(\frac{20}{13})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{20}{13}x+\frac{13}{14}a-\frac{13}{14}.\frac{20}{13}& \text{Uitwerken } \\ & =ax-\frac{20}{13}x+\frac{13}{14}a-\frac{260}{182} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{20}{13}x+\frac{13}{14}a-\frac{10}{7} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-14}{3}+q)(q+\frac{-15}{2})& =(\color{red}{q}+\color{orange}{\frac{-14}{3}}).(\color{green}{q}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{-14}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-14}{3})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{15}{2}q-\frac{14}{3}q+\frac{14}{3}.\frac{15}{2}& \text{Uitwerken } \\ & =q^2+((\frac{-15}{2})+(\frac{-14}{3}))q+\frac{210}{6} & \text{Neem samen} \\ &=q^2-\frac{73}{6}q+\frac{210}{6} & \text{Maak de som} \\ &=q^2-\frac{73}{6}q+35 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(x+\frac{11}{19})(a-\frac{-4}{18})& =(\color{red}{x}+\color{orange}{\frac{11}{19}}).(\color{green}{a}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{11}{19})} . \color{green}{(a)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{9}x+\frac{11}{19}a+\frac{11}{19}.\frac{2}{9}& \text{Uitwerken } \\ & =ax+\frac{2}{9}x+\frac{11}{19}a+\frac{22}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-15 22:05:19
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