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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{17}{8})(b-\frac{-11}{17})& =(\color{red}{a}+\color{orange}{\frac{17}{8}}).(\color{green}{b}+\color{blue}{\frac{11}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{11}{17})} + \color{orange}{(\frac{17}{8})} . \color{green}{(b)} + \color{orange}{(\frac{17}{8})} . \color{blue}{(\frac{11}{17})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{11}{17}a+\frac{17}{8}b+\frac{17}{8}.\frac{11}{17}& \text{Uitwerken } \\ & =ab+\frac{11}{17}a+\frac{17}{8}b+\frac{187}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{11}{17}a+\frac{17}{8}b+\frac{11}{8} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-20}{18})(a+\frac{20}{8})& =(\color{red}{p}+\color{orange}{\frac{-10}{9}}).(\color{green}{a}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{5}{2}p-\frac{10}{9}a-\frac{10}{9}.\frac{5}{2}& \text{Uitwerken } \\ & =ap+\frac{5}{2}p-\frac{10}{9}a-\frac{50}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{5}{2}p-\frac{10}{9}a-\frac{25}{9} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q+\frac{20}{11})(x+\frac{-2}{19})& =(\color{red}{q}+\color{orange}{\frac{20}{11}}).(\color{green}{x}+\color{blue}{\frac{-2}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{19})} + \color{orange}{(\frac{20}{11})} . \color{green}{(x)} + \color{orange}{(\frac{20}{11})} . \color{blue}{(\frac{-2}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{2}{19}q+\frac{20}{11}x-\frac{20}{11}.\frac{2}{19}& \text{Uitwerken } \\ & =qx-\frac{2}{19}q+\frac{20}{11}x-\frac{40}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-3}{3}+x)(x-\frac{19}{11})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{19}{11}x-1x+1.\frac{19}{11}& \text{Uitwerken } \\ & =x^2+((\frac{-19}{11})+(-1))x+\frac{19}{11} & \text{Neem samen} \\ &=x^2-\frac{30}{11}x+\frac{19}{11} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{17}{6}-b)(p+\frac{2}{7})& =(\color{red}{-b}+\color{orange}{\frac{17}{6}}).(\color{green}{p}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{17}{6})} . \color{green}{(p)} + \color{orange}{(\frac{17}{6})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{2}{7}b+\frac{17}{6}p+\frac{17}{6}.\frac{2}{7}& \text{Uitwerken } \\ & =-bp-\frac{2}{7}b+\frac{17}{6}p+\frac{34}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{2}{7}b+\frac{17}{6}p+\frac{17}{21} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{18}{16}+q)(a-\frac{12}{3})& =(\color{red}{q}+\color{orange}{\frac{9}{8}}).(\color{green}{a}+\color{blue}{(-4)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-4)} + \color{orange}{(\frac{9}{8})} . \color{green}{(a)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = aq-4q+\frac{9}{8}a-\frac{9}{8}.4& \text{Uitwerken } \\ & =aq-4q+\frac{9}{8}a-\frac{36}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-4q+\frac{9}{8}a-\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{5}{17}+b)(\frac{-9}{6}+b)& =(\color{red}{b}+\color{orange}{\frac{5}{17}}).(\color{green}{b}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{5}{17})} . \color{green}{(b)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{3}{2}b+\frac{5}{17}b-\frac{5}{17}.\frac{3}{2}& \text{Uitwerken } \\ & =b^2+((\frac{-3}{2})+\frac{5}{17})b-(\frac{-15}{34}) & \text{Neem samen} \\ &=b^2-\frac{41}{34}b-(\frac{-15}{34}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-4}{2}-p)(x-\frac{-2}{11})& =(\color{red}{-p}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{2}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{2}{11})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{2}{11})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{2}{11}p-2x-2.\frac{2}{11}& \text{Uitwerken } \\ & =-px-\frac{2}{11}p-2x-\frac{4}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{2}{14}-b)(\frac{-13}{11}+b)& =(\color{red}{-b}+\color{orange}{\frac{1}{7}}).(\color{green}{b}+\color{blue}{\frac{-13}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-13}{11})} + \color{orange}{(\frac{1}{7})} . \color{green}{(b)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{-13}{11})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{13}{11}b+\frac{1}{7}b-\frac{1}{7}.\frac{13}{11}& \text{Uitwerken } \\ & =-b^2+(\frac{13}{11}+\frac{1}{7})b-\frac{13}{77} & \text{Neem samen} \\ &=-b^2+\frac{102}{77}b-\frac{13}{77} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(x-\frac{13}{15})(b-\frac{17}{15})& =(\color{red}{x}+\color{orange}{\frac{-13}{15}}).(\color{green}{b}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{-13}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{15})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{17}{15}x-\frac{13}{15}b+\frac{13}{15}.\frac{17}{15}& \text{Uitwerken } \\ & =bx-\frac{17}{15}x-\frac{13}{15}b+\frac{221}{225} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p+\frac{-16}{14})(q-\frac{-1}{20})& =(\color{red}{p}+\color{orange}{\frac{-8}{7}}).(\color{green}{q}+\color{blue}{\frac{1}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{20})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{1}{20})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{20}p-\frac{8}{7}q-\frac{8}{7}.\frac{1}{20}& \text{Uitwerken } \\ & =pq+\frac{1}{20}p-\frac{8}{7}q-\frac{8}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{1}{20}p-\frac{8}{7}q-\frac{2}{35} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{14}{12}-p)(\frac{-7}{4}-x)& =(\color{red}{-p}+\color{orange}{\frac{7}{6}}).(\color{green}{-x}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{7}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{4}p-\frac{7}{6}x-\frac{7}{6}.\frac{7}{4}& \text{Uitwerken } \\ & =px+\frac{7}{4}p-\frac{7}{6}x-\frac{49}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-05-30 04:43:59