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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-3}{16})(a+\frac{-1}{18})& =(\color{red}{b}+\color{orange}{\frac{-3}{16}}).(\color{green}{a}+\color{blue}{\frac{-1}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{18})} + \color{orange}{(\frac{-3}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{16})} . \color{blue}{(\frac{-1}{18})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{18}b-\frac{3}{16}a+\frac{3}{16}.\frac{1}{18}& \text{Uitwerken } \\ & =ab-\frac{1}{18}b-\frac{3}{16}a+\frac{3}{288} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{1}{18}b-\frac{3}{16}a+\frac{1}{96} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a+\frac{-17}{9})(x-\frac{-5}{13})& =(\color{red}{a}+\color{orange}{\frac{-17}{9}}).(\color{green}{x}+\color{blue}{\frac{5}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{5}{13})} + \color{orange}{(\frac{-17}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{9})} . \color{blue}{(\frac{5}{13})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{5}{13}a-\frac{17}{9}x-\frac{17}{9}.\frac{5}{13}& \text{Uitwerken } \\ & =ax+\frac{5}{13}a-\frac{17}{9}x-\frac{85}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-11}{5}-x)(p-\frac{-11}{12})& =(\color{red}{-x}+\color{orange}{\frac{-11}{5}}).(\color{green}{p}+\color{blue}{\frac{11}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{11}{12})} + \color{orange}{(\frac{-11}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{5})} . \color{blue}{(\frac{11}{12})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{11}{12}x-\frac{11}{5}p-\frac{11}{5}.\frac{11}{12}& \text{Uitwerken } \\ & =-px-\frac{11}{12}x-\frac{11}{5}p-\frac{121}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{20}{20}+p)(p-\frac{17}{11})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-17}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{11})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-17}{11})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{17}{11}p+1p-1.\frac{17}{11}& \text{Uitwerken } \\ & =p^2+((\frac{-17}{11})+1)p-(\frac{-17}{11}) & \text{Neem samen} \\ &=p^2-\frac{6}{11}p-(\frac{-17}{11}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(q-\frac{-11}{9})(\frac{-7}{2}+x)& =(\color{red}{q}+\color{orange}{\frac{11}{9}}).(\color{green}{x}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{11}{9})} . \color{green}{(x)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{7}{2}q+\frac{11}{9}x-\frac{11}{9}.\frac{7}{2}& \text{Uitwerken } \\ & =qx-\frac{7}{2}q+\frac{11}{9}x-\frac{77}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{12}{14})(b-\frac{8}{15})& =(\color{red}{p}+\color{orange}{\frac{-6}{7}}).(\color{green}{b}+\color{blue}{\frac{-8}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{15})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{-8}{15})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{8}{15}p-\frac{6}{7}b+\frac{6}{7}.\frac{8}{15}& \text{Uitwerken } \\ & =bp-\frac{8}{15}p-\frac{6}{7}b+\frac{48}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{8}{15}p-\frac{6}{7}b+\frac{16}{35} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b-\frac{13}{16})(a-\frac{11}{14})& =(\color{red}{b}+\color{orange}{\frac{-13}{16}}).(\color{green}{a}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{11}{14}b-\frac{13}{16}a+\frac{13}{16}.\frac{11}{14}& \text{Uitwerken } \\ & =ab-\frac{11}{14}b-\frac{13}{16}a+\frac{143}{224} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{11}{8}-p)(q-\frac{-18}{20})& =(\color{red}{-p}+\color{orange}{\frac{11}{8}}).(\color{green}{q}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{11}{8})} . \color{green}{(q)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{9}{10}p+\frac{11}{8}q+\frac{11}{8}.\frac{9}{10}& \text{Uitwerken } \\ & =-pq-\frac{9}{10}p+\frac{11}{8}q+\frac{99}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b+\frac{10}{2})(\frac{-20}{19}+x)& =(\color{red}{b}+\color{orange}{5}).(\color{green}{x}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(5)} . \color{green}{(x)} + \color{orange}{(5)} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{20}{19}b+5x-5.\frac{20}{19}& \text{Uitwerken } \\ & =bx-\frac{20}{19}b+5x-\frac{100}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b+\frac{10}{4})(\frac{20}{15}+b)& =(\color{red}{b}+\color{orange}{\frac{5}{2}}).(\color{green}{b}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{4}{3}b+\frac{5}{2}b+\frac{5}{2}.\frac{4}{3}& \text{Uitwerken } \\ & =b^2+(\frac{4}{3}+\frac{5}{2})b+\frac{20}{6} & \text{Neem samen} \\ &=b^2+\frac{23}{6}b+\frac{20}{6} & \text{Maak de som} \\ &=b^2+\frac{23}{6}b+\frac{10}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{-6}{8}+b)(b-\frac{16}{8})& =(\color{red}{b}+\color{orange}{\frac{-3}{4}}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bb-2b-\frac{3}{4}b+\frac{3}{4}.2& \text{Uitwerken } \\ & =b^2+((-2)+(\frac{-3}{4}))b+\frac{6}{4} & \text{Neem samen} \\ &=b^2-\frac{11}{4}b+\frac{6}{4} & \text{Maak de som} \\ &=b^2-\frac{11}{4}b+\frac{3}{2} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-17}{15})(b-\frac{6}{11})& =(\color{red}{a}+\color{orange}{\frac{-17}{15}}).(\color{green}{b}+\color{blue}{\frac{-6}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-6}{11})} + \color{orange}{(\frac{-17}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{15})} . \color{blue}{(\frac{-6}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{6}{11}a-\frac{17}{15}b+\frac{17}{15}.\frac{6}{11}& \text{Uitwerken } \\ & =ab-\frac{6}{11}a-\frac{17}{15}b+\frac{102}{165} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{6}{11}a-\frac{17}{15}b+\frac{34}{55} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-23 01:30:17
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