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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{8}{13})(\frac{5}{2}+a)& =(\color{red}{b}+\color{orange}{\frac{8}{13}}).(\color{green}{a}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{8}{13})} . \color{green}{(a)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{2}b+\frac{8}{13}a+\frac{8}{13}.\frac{5}{2}& \text{Uitwerken } \\ & =ab+\frac{5}{2}b+\frac{8}{13}a+\frac{40}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{5}{2}b+\frac{8}{13}a+\frac{20}{13} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b+\frac{20}{17})(\frac{-9}{9}-a)& =(\color{red}{b}+\color{orange}{\frac{20}{17}}).(\color{green}{-a}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{20}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{20}{17})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ab-1b-\frac{20}{17}a-\frac{20}{17}.1& \text{Uitwerken } \\ & =-ab-1b-\frac{20}{17}a-\frac{20}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{15}{20}-b)(b-\frac{6}{10})& =(\color{red}{-b}+\color{orange}{\frac{3}{4}}).(\color{green}{b}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{3}{5}b+\frac{3}{4}b-\frac{3}{4}.\frac{3}{5}& \text{Uitwerken } \\ & =-b^2+(\frac{3}{5}+\frac{3}{4})b-\frac{9}{20} & \text{Neem samen} \\ &=-b^2+\frac{27}{20}b-\frac{9}{20} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-7}{13}-a)(p-\frac{-6}{4})& =(\color{red}{-a}+\color{orange}{\frac{-7}{13}}).(\color{green}{p}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-7}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{13})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{3}{2}a-\frac{7}{13}p-\frac{7}{13}.\frac{3}{2}& \text{Uitwerken } \\ & =-ap-\frac{3}{2}a-\frac{7}{13}p-\frac{21}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{11}{15}-q)(\frac{6}{11}+b)& =(\color{red}{-q}+\color{orange}{\frac{11}{15}}).(\color{green}{b}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{11}{15})} . \color{green}{(b)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{6}{11}q+\frac{11}{15}b+\frac{11}{15}.\frac{6}{11}& \text{Uitwerken } \\ & =-bq-\frac{6}{11}q+\frac{11}{15}b+\frac{66}{165} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{6}{11}q+\frac{11}{15}b+\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{2}{15}-x)(\frac{-20}{2}+q)& =(\color{red}{-x}+\color{orange}{\frac{2}{15}}).(\color{green}{q}+\color{blue}{(-10)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(-10)} + \color{orange}{(\frac{2}{15})} . \color{green}{(q)} + \color{orange}{(\frac{2}{15})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -qx+10x+\frac{2}{15}q-\frac{2}{15}.10& \text{Uitwerken } \\ & =-qx+10x+\frac{2}{15}q-\frac{20}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+10x+\frac{2}{15}q-\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{7}{9}-a)(a-\frac{15}{20})& =(\color{red}{-a}+\color{orange}{\frac{7}{9}}).(\color{green}{a}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{7}{9})} . \color{green}{(a)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{3}{4}a+\frac{7}{9}a-\frac{7}{9}.\frac{3}{4}& \text{Uitwerken } \\ & =-a^2+(\frac{3}{4}+\frac{7}{9})a-\frac{21}{36} & \text{Neem samen} \\ &=-a^2+\frac{55}{36}a-\frac{21}{36} & \text{Maak de som} \\ &=-a^2+\frac{55}{36}a-\frac{7}{12} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{4}{7}-a)(x-\frac{7}{18})& =(\color{red}{-a}+\color{orange}{\frac{4}{7}}).(\color{green}{x}+\color{blue}{\frac{-7}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{18})} + \color{orange}{(\frac{4}{7})} . \color{green}{(x)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{-7}{18})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{7}{18}a+\frac{4}{7}x-\frac{4}{7}.\frac{7}{18}& \text{Uitwerken } \\ & =-ax+\frac{7}{18}a+\frac{4}{7}x-\frac{28}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{7}{18}a+\frac{4}{7}x-\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(q+\frac{-19}{9})(\frac{16}{14}-p)& =(\color{red}{q}+\color{orange}{\frac{-19}{9}}).(\color{green}{-p}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{-19}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{8}{7}q+\frac{19}{9}p-\frac{19}{9}.\frac{8}{7}& \text{Uitwerken } \\ & =-pq+\frac{8}{7}q+\frac{19}{9}p-\frac{152}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x-\frac{6}{20})(\frac{11}{19}-q)& =(\color{red}{x}+\color{orange}{\frac{-3}{10}}).(\color{green}{-q}+\color{blue}{\frac{11}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{11}{19})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{11}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{11}{19}x+\frac{3}{10}q-\frac{3}{10}.\frac{11}{19}& \text{Uitwerken } \\ & =-qx+\frac{11}{19}x+\frac{3}{10}q-\frac{33}{190} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-7}{15}+b)(q-\frac{15}{18})& =(\color{red}{b}+\color{orange}{\frac{-7}{15}}).(\color{green}{q}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{-7}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{6}b-\frac{7}{15}q+\frac{7}{15}.\frac{5}{6}& \text{Uitwerken } \\ & =bq-\frac{5}{6}b-\frac{7}{15}q+\frac{35}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{5}{6}b-\frac{7}{15}q+\frac{7}{18} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b+\frac{1}{11})(p-\frac{15}{7})& =(\color{red}{b}+\color{orange}{\frac{1}{11}}).(\color{green}{p}+\color{blue}{\frac{-15}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{7})} + \color{orange}{(\frac{1}{11})} . \color{green}{(p)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(\frac{-15}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{15}{7}b+\frac{1}{11}p-\frac{1}{11}.\frac{15}{7}& \text{Uitwerken } \\ & =bp-\frac{15}{7}b+\frac{1}{11}p-\frac{15}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-26 19:30:56
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