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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{18}{17})(q-\frac{16}{14})& =(\color{red}{x}+\color{orange}{\frac{18}{17}}).(\color{green}{q}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{18}{17})} . \color{green}{(q)} + \color{orange}{(\frac{18}{17})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{8}{7}x+\frac{18}{17}q-\frac{18}{17}.\frac{8}{7}& \text{Uitwerken } \\ & =qx-\frac{8}{7}x+\frac{18}{17}q-\frac{144}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-1}{6}+x)(\frac{17}{14}-p)& =(\color{red}{x}+\color{orange}{\frac{-1}{6}}).(\color{green}{-p}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{17}{14}x+\frac{1}{6}p-\frac{1}{6}.\frac{17}{14}& \text{Uitwerken } \\ & =-px+\frac{17}{14}x+\frac{1}{6}p-\frac{17}{84} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-15}{9}+b)(\frac{-18}{17}+x)& =(\color{red}{b}+\color{orange}{\frac{-5}{3}}).(\color{green}{x}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{18}{17}b-\frac{5}{3}x+\frac{5}{3}.\frac{18}{17}& \text{Uitwerken } \\ & =bx-\frac{18}{17}b-\frac{5}{3}x+\frac{90}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{18}{17}b-\frac{5}{3}x+\frac{30}{17} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q+\frac{8}{8})(\frac{-10}{4}+q)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{5}{2}q+1q-1.\frac{5}{2}& \text{Uitwerken } \\ & =q^2+((\frac{-5}{2})+1)q-(\frac{-5}{2}) & \text{Neem samen} \\ &=q^2-\frac{3}{2}q-(\frac{-5}{2}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{20}{11}-b)(q+\frac{-20}{9})& =(\color{red}{-b}+\color{orange}{\frac{20}{11}}).(\color{green}{q}+\color{blue}{\frac{-20}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-20}{9})} + \color{orange}{(\frac{20}{11})} . \color{green}{(q)} + \color{orange}{(\frac{20}{11})} . \color{blue}{(\frac{-20}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{20}{9}b+\frac{20}{11}q-\frac{20}{11}.\frac{20}{9}& \text{Uitwerken } \\ & =-bq+\frac{20}{9}b+\frac{20}{11}q-\frac{400}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{1}{20}+a)(p+\frac{15}{5})& =(\color{red}{a}+\color{orange}{\frac{1}{20}}).(\color{green}{p}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(3)} + \color{orange}{(\frac{1}{20})} . \color{green}{(p)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ap+3a+\frac{1}{20}p+\frac{1}{20}.3& \text{Uitwerken } \\ & =ap+3a+\frac{1}{20}p+\frac{3}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x-\frac{7}{17})(\frac{15}{12}-b)& =(\color{red}{x}+\color{orange}{\frac{-7}{17}}).(\color{green}{-b}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-7}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{5}{4}x+\frac{7}{17}b-\frac{7}{17}.\frac{5}{4}& \text{Uitwerken } \\ & =-bx+\frac{5}{4}x+\frac{7}{17}b-\frac{35}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b+\frac{12}{18})(q-\frac{10}{4})& =(\color{red}{b}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{2}b+\frac{2}{3}q-\frac{2}{3}.\frac{5}{2}& \text{Uitwerken } \\ & =bq-\frac{5}{2}b+\frac{2}{3}q-\frac{10}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{5}{2}b+\frac{2}{3}q-\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{2}{4}-p)(\frac{-17}{3}-q)& =(\color{red}{-p}+\color{orange}{\frac{1}{2}}).(\color{green}{-q}+\color{blue}{\frac{-17}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{-17}{3})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-17}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{17}{3}p-\frac{1}{2}q-\frac{1}{2}.\frac{17}{3}& \text{Uitwerken } \\ & =pq+\frac{17}{3}p-\frac{1}{2}q-\frac{17}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x-\frac{10}{20})(p+\frac{-6}{5})& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{6}{5}x-\frac{1}{2}p+\frac{1}{2}.\frac{6}{5}& \text{Uitwerken } \\ & =px-\frac{6}{5}x-\frac{1}{2}p+\frac{6}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{6}{5}x-\frac{1}{2}p+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-4}{16}+a)(\frac{13}{14}-q)& =(\color{red}{a}+\color{orange}{\frac{-1}{4}}).(\color{green}{-q}+\color{blue}{\frac{13}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{13}{14})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{13}{14})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{13}{14}a+\frac{1}{4}q-\frac{1}{4}.\frac{13}{14}& \text{Uitwerken } \\ & =-aq+\frac{13}{14}a+\frac{1}{4}q-\frac{13}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-11}{10})(\frac{-10}{7}-q)& =(\color{red}{a}+\color{orange}{\frac{-11}{10}}).(\color{green}{-q}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{-11}{10})} . \color{green}{(-q)} + \color{orange}{(\frac{-11}{10})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{10}{7}a+\frac{11}{10}q+\frac{11}{10}.\frac{10}{7}& \text{Uitwerken } \\ & =-aq-\frac{10}{7}a+\frac{11}{10}q+\frac{110}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{10}{7}a+\frac{11}{10}q+\frac{11}{7} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-19 19:20:29
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