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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{5}{11}+a)(\frac{-19}{18}+q)& =(\color{red}{a}+\color{orange}{\frac{5}{11}}).(\color{green}{q}+\color{blue}{\frac{-19}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{18})} + \color{orange}{(\frac{5}{11})} . \color{green}{(q)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(\frac{-19}{18})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{19}{18}a+\frac{5}{11}q-\frac{5}{11}.\frac{19}{18}& \text{Uitwerken } \\ & =aq-\frac{19}{18}a+\frac{5}{11}q-\frac{95}{198} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-12}{16})(\frac{15}{4}-q)& =(\color{red}{p}+\color{orange}{\frac{-3}{4}}).(\color{green}{-q}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{15}{4}p+\frac{3}{4}q-\frac{3}{4}.\frac{15}{4}& \text{Uitwerken } \\ & =-pq+\frac{15}{4}p+\frac{3}{4}q-\frac{45}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b+(-17))(b-\frac{12}{5})& =(\color{red}{b}+\color{orange}{(-17)}).(\color{green}{b}+\color{blue}{\frac{-12}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-12}{5})} + \color{orange}{(-17)} . \color{green}{(b)} + \color{orange}{(-17)} . \color{blue}{(\frac{-12}{5})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{12}{5}b-17b+17.\frac{12}{5}& \text{Uitwerken } \\ & =b^2+((\frac{-12}{5})+(-17))b+\frac{204}{5} & \text{Neem samen} \\ &=b^2-\frac{97}{5}b+\frac{204}{5} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(p+\frac{-2}{11})(x-\frac{-16}{12})& =(\color{red}{p}+\color{orange}{\frac{-2}{11}}).(\color{green}{x}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-2}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{4}{3}p-\frac{2}{11}x-\frac{2}{11}.\frac{4}{3}& \text{Uitwerken } \\ & =px+\frac{4}{3}p-\frac{2}{11}x-\frac{8}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{13}{5}-b)(\frac{5}{6}+p)& =(\color{red}{-b}+\color{orange}{\frac{13}{5}}).(\color{green}{p}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{13}{5})} . \color{green}{(p)} + \color{orange}{(\frac{13}{5})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{5}{6}b+\frac{13}{5}p+\frac{13}{5}.\frac{5}{6}& \text{Uitwerken } \\ & =-bp-\frac{5}{6}b+\frac{13}{5}p+\frac{65}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{5}{6}b+\frac{13}{5}p+\frac{13}{6} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q-\frac{20}{20})(a-18)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{(-18)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-18)} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(-18)}& \text{Boogjes en uitschrijven} \\ & = aq-18q-1a+1.18& \text{Uitwerken } \\ & =aq-18q-1a+18 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-\frac{-3}{16})(x-\frac{-1}{11})& =(\color{red}{q}+\color{orange}{\frac{3}{16}}).(\color{green}{x}+\color{blue}{\frac{1}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{11})} + \color{orange}{(\frac{3}{16})} . \color{green}{(x)} + \color{orange}{(\frac{3}{16})} . \color{blue}{(\frac{1}{11})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{11}q+\frac{3}{16}x+\frac{3}{16}.\frac{1}{11}& \text{Uitwerken } \\ & =qx+\frac{1}{11}q+\frac{3}{16}x+\frac{3}{176} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{11}{8}+b)(x+\frac{-19}{2})& =(\color{red}{b}+\color{orange}{\frac{11}{8}}).(\color{green}{x}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(\frac{11}{8})} . \color{green}{(x)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{2}b+\frac{11}{8}x-\frac{11}{8}.\frac{19}{2}& \text{Uitwerken } \\ & =bx-\frac{19}{2}b+\frac{11}{8}x-\frac{209}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}((-5)-q)(b-\frac{5}{10})& =(\color{red}{-q}+\color{orange}{(-5)}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(-5)} . \color{green}{(b)} + \color{orange}{(-5)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{2}q-5b+5.\frac{1}{2}& \text{Uitwerken } \\ & =-bq+\frac{1}{2}q-5b+\frac{5}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-18}{18})(\frac{6}{17}+a)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{6}{17}b+1a+1.\frac{6}{17}& \text{Uitwerken } \\ & =ab+\frac{6}{17}b+1a+\frac{6}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b+\frac{10}{2})(\frac{-5}{4}+p)& =(\color{red}{b}+\color{orange}{5}).(\color{green}{p}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(5)} . \color{green}{(p)} + \color{orange}{(5)} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{4}b+5p-5.\frac{5}{4}& \text{Uitwerken } \\ & =bp-\frac{5}{4}b+5p-\frac{25}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p+\frac{9}{9})(\frac{19}{10}-b)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{19}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{19}{10})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{19}{10})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{19}{10}p-1b+1.\frac{19}{10}& \text{Uitwerken } \\ & =-bp+\frac{19}{10}p-1b+\frac{19}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-05 08:38:27
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