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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{13}{14})(p-\frac{-16}{18})& =(\color{red}{q}+\color{orange}{\frac{-13}{14}}).(\color{green}{p}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{-13}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{8}{9}q-\frac{13}{14}p-\frac{13}{14}.\frac{8}{9}& \text{Uitwerken } \\ & =pq+\frac{8}{9}q-\frac{13}{14}p-\frac{104}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{8}{9}q-\frac{13}{14}p-\frac{52}{63} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{14}{3}-x)(p+\frac{2}{17})& =(\color{red}{-x}+\color{orange}{\frac{14}{3}}).(\color{green}{p}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{14}{3})} . \color{green}{(p)} + \color{orange}{(\frac{14}{3})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{2}{17}x+\frac{14}{3}p+\frac{14}{3}.\frac{2}{17}& \text{Uitwerken } \\ & =-px-\frac{2}{17}x+\frac{14}{3}p+\frac{28}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{-15}{20})(\frac{-15}{7}-x)& =(\color{red}{q}+\color{orange}{\frac{3}{4}}).(\color{green}{-x}+\color{blue}{\frac{-15}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{7})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-15}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{15}{7}q-\frac{3}{4}x-\frac{3}{4}.\frac{15}{7}& \text{Uitwerken } \\ & =-qx-\frac{15}{7}q-\frac{3}{4}x-\frac{45}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{4}{16})(x+\frac{1}{4})& =(\color{red}{q}+\color{orange}{\frac{-1}{4}}).(\color{green}{x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{4}q-\frac{1}{4}x-\frac{1}{4}.\frac{1}{4}& \text{Uitwerken } \\ & =qx+\frac{1}{4}q-\frac{1}{4}x-\frac{1}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x+\frac{-20}{12})(\frac{11}{17}+a)& =(\color{red}{x}+\color{orange}{\frac{-5}{3}}).(\color{green}{a}+\color{blue}{\frac{11}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{11}{17})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{11}{17})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{11}{17}x-\frac{5}{3}a-\frac{5}{3}.\frac{11}{17}& \text{Uitwerken } \\ & =ax+\frac{11}{17}x-\frac{5}{3}a-\frac{55}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q+\frac{12}{16})(\frac{20}{14}-a)& =(\color{red}{q}+\color{orange}{\frac{3}{4}}).(\color{green}{-a}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{10}{7}q-\frac{3}{4}a+\frac{3}{4}.\frac{10}{7}& \text{Uitwerken } \\ & =-aq+\frac{10}{7}q-\frac{3}{4}a+\frac{30}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{10}{7}q-\frac{3}{4}a+\frac{15}{14} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-9}{18}+q)(\frac{4}{18}+x)& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{2}{9}q-\frac{1}{2}x-\frac{1}{2}.\frac{2}{9}& \text{Uitwerken } \\ & =qx+\frac{2}{9}q-\frac{1}{2}x-\frac{2}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{2}{9}q-\frac{1}{2}x-\frac{1}{9} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{3}{6}-x)(p+\frac{-2}{17})& =(\color{red}{-x}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{2}{17}x+\frac{1}{2}p-\frac{1}{2}.\frac{2}{17}& \text{Uitwerken } \\ & =-px+\frac{2}{17}x+\frac{1}{2}p-\frac{2}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{2}{17}x+\frac{1}{2}p-\frac{1}{17} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-19}{18}+x)(x-\frac{11}{8})& =(\color{red}{x}+\color{orange}{\frac{-19}{18}}).(\color{green}{x}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{-19}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{18})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{11}{8}x-\frac{19}{18}x+\frac{19}{18}.\frac{11}{8}& \text{Uitwerken } \\ & =x^2+((\frac{-11}{8})+(\frac{-19}{18}))x+\frac{209}{144} & \text{Neem samen} \\ &=x^2-\frac{175}{72}x+\frac{209}{144} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{-13}{2}+b)(q+\frac{19}{8})& =(\color{red}{b}+\color{orange}{\frac{-13}{2}}).(\color{green}{q}+\color{blue}{\frac{19}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{19}{8})} + \color{orange}{(\frac{-13}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{2})} . \color{blue}{(\frac{19}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{19}{8}b-\frac{13}{2}q-\frac{13}{2}.\frac{19}{8}& \text{Uitwerken } \\ & =bq+\frac{19}{8}b-\frac{13}{2}q-\frac{247}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p+\frac{5}{11})(\frac{-13}{20}+p)& =(\color{red}{p}+\color{orange}{\frac{5}{11}}).(\color{green}{p}+\color{blue}{\frac{-13}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{20})} + \color{orange}{(\frac{5}{11})} . \color{green}{(p)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(\frac{-13}{20})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{13}{20}p+\frac{5}{11}p-\frac{5}{11}.\frac{13}{20}& \text{Uitwerken } \\ & =p^2+((\frac{-13}{20})+\frac{5}{11})p-(\frac{-65}{220}) & \text{Neem samen} \\ &=p^2-\frac{43}{220}p-(\frac{-65}{220}) & \text{Maak de som} \\ &=p^2-\frac{43}{220}p+\frac{13}{44} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{-4}{3}-b)(b-\frac{20}{7})& =(\color{red}{-b}+\color{orange}{\frac{-4}{3}}).(\color{green}{b}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{20}{7}b-\frac{4}{3}b+\frac{4}{3}.\frac{20}{7}& \text{Uitwerken } \\ & =-b^2+(\frac{20}{7}+(\frac{-4}{3}))b+(\frac{-80}{21}) & \text{Neem samen} \\ &=-b^2+\frac{32}{21}b+(\frac{-80}{21}) & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-01 08:36:22
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