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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{-4}{6})(\frac{10}{7}-x)& =(\color{red}{a}+\color{orange}{\frac{2}{3}}).(\color{green}{-x}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{2}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{10}{7}a-\frac{2}{3}x+\frac{2}{3}.\frac{10}{7}& \text{Uitwerken } \\ & =-ax+\frac{10}{7}a-\frac{2}{3}x+\frac{20}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-18}{17}-p)(\frac{-19}{9}-q)& =(\color{red}{-p}+\color{orange}{\frac{-18}{17}}).(\color{green}{-q}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{19}{9}p+\frac{18}{17}q+\frac{18}{17}.\frac{19}{9}& \text{Uitwerken } \\ & =pq+\frac{19}{9}p+\frac{18}{17}q+\frac{342}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{19}{9}p+\frac{18}{17}q+\frac{38}{17} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x-\frac{13}{19})(a-\frac{10}{19})& =(\color{red}{x}+\color{orange}{\frac{-13}{19}}).(\color{green}{a}+\color{blue}{\frac{-10}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{19})} + \color{orange}{(\frac{-13}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{19})} . \color{blue}{(\frac{-10}{19})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{10}{19}x-\frac{13}{19}a+\frac{13}{19}.\frac{10}{19}& \text{Uitwerken } \\ & =ax-\frac{10}{19}x-\frac{13}{19}a+\frac{130}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-20}{6}+p)(b-\frac{5}{8})& =(\color{red}{p}+\color{orange}{\frac{-10}{3}}).(\color{green}{b}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{8}p-\frac{10}{3}b+\frac{10}{3}.\frac{5}{8}& \text{Uitwerken } \\ & =bp-\frac{5}{8}p-\frac{10}{3}b+\frac{50}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{5}{8}p-\frac{10}{3}b+\frac{25}{12} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-4}{11}+b)(\frac{18}{14}-b)& =(\color{red}{b}+\color{orange}{\frac{-4}{11}}).(\color{green}{-b}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{-4}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{-4}{11})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{9}{7}b+\frac{4}{11}b-\frac{4}{11}.\frac{9}{7}& \text{Uitwerken } \\ & =-b^2+(\frac{9}{7}+\frac{4}{11})b-\frac{36}{77} & \text{Neem samen} \\ &=-b^2+\frac{127}{77}b-\frac{36}{77} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(x-\frac{-20}{10})(\frac{12}{7}-x)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{-x}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(2)} . \color{green}{(-x)} + \color{orange}{(2)} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{12}{7}x-2x+2.\frac{12}{7}& \text{Uitwerken } \\ & =-x^2+(\frac{12}{7}+(-2))x+(\frac{-24}{7}) & \text{Neem samen} \\ &=-x^2-\frac{2}{7}x+(\frac{-24}{7}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-14}{12})(\frac{13}{13}+q)& =(\color{red}{b}+\color{orange}{\frac{7}{6}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{7}{6})} . \color{green}{(q)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1b+\frac{7}{6}q+\frac{7}{6}.1& \text{Uitwerken } \\ & =bq+1b+\frac{7}{6}q+\frac{7}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-6}{16}+q)(x+\frac{5}{20})& =(\color{red}{q}+\color{orange}{\frac{-3}{8}}).(\color{green}{x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{4}q-\frac{3}{8}x-\frac{3}{8}.\frac{1}{4}& \text{Uitwerken } \\ & =qx+\frac{1}{4}q-\frac{3}{8}x-\frac{3}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{5}{18}+b)(\frac{6}{13}-a)& =(\color{red}{b}+\color{orange}{\frac{5}{18}}).(\color{green}{-a}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{5}{18})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{6}{13}b-\frac{5}{18}a+\frac{5}{18}.\frac{6}{13}& \text{Uitwerken } \\ & =-ab+\frac{6}{13}b-\frac{5}{18}a+\frac{30}{234} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{6}{13}b-\frac{5}{18}a+\frac{5}{39} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-18}{10}-x)(\frac{9}{2}-b)& =(\color{red}{-x}+\color{orange}{\frac{-9}{5}}).(\color{green}{-b}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{9}{2}x+\frac{9}{5}b-\frac{9}{5}.\frac{9}{2}& \text{Uitwerken } \\ & =bx-\frac{9}{2}x+\frac{9}{5}b-\frac{81}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-11}{16}+a)(\frac{10}{3}+p)& =(\color{red}{a}+\color{orange}{\frac{-11}{16}}).(\color{green}{p}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{10}{3}a-\frac{11}{16}p-\frac{11}{16}.\frac{10}{3}& \text{Uitwerken } \\ & =ap+\frac{10}{3}a-\frac{11}{16}p-\frac{110}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{10}{3}a-\frac{11}{16}p-\frac{55}{24} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p+\frac{-3}{18})(\frac{2}{18}+x)& =(\color{red}{p}+\color{orange}{\frac{-1}{6}}).(\color{green}{x}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{9}p-\frac{1}{6}x-\frac{1}{6}.\frac{1}{9}& \text{Uitwerken } \\ & =px+\frac{1}{9}p-\frac{1}{6}x-\frac{1}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-07 16:06:43