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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{4}{13}-q)(x-\frac{-6}{8})& =(\color{red}{-q}+\color{orange}{\frac{4}{13}}).(\color{green}{x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{4}{13})} . \color{green}{(x)} + \color{orange}{(\frac{4}{13})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{3}{4}q+\frac{4}{13}x+\frac{4}{13}.\frac{3}{4}& \text{Uitwerken } \\ & =-qx-\frac{3}{4}q+\frac{4}{13}x+\frac{12}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{3}{4}q+\frac{4}{13}x+\frac{3}{13} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{7}{3}-b)(q+\frac{-1}{19})& =(\color{red}{-b}+\color{orange}{\frac{7}{3}}).(\color{green}{q}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{7}{3})} . \color{green}{(q)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{19}b+\frac{7}{3}q-\frac{7}{3}.\frac{1}{19}& \text{Uitwerken } \\ & =-bq+\frac{1}{19}b+\frac{7}{3}q-\frac{7}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{-5}{14})(p+\frac{-16}{14})& =(\color{red}{q}+\color{orange}{\frac{5}{14}}).(\color{green}{p}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{5}{14})} . \color{green}{(p)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{8}{7}q+\frac{5}{14}p-\frac{5}{14}.\frac{8}{7}& \text{Uitwerken } \\ & =pq-\frac{8}{7}q+\frac{5}{14}p-\frac{40}{98} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{8}{7}q+\frac{5}{14}p-\frac{20}{49} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x+\frac{13}{19})(\frac{-1}{9}-b)& =(\color{red}{x}+\color{orange}{\frac{13}{19}}).(\color{green}{-b}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{13}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{9}x-\frac{13}{19}b-\frac{13}{19}.\frac{1}{9}& \text{Uitwerken } \\ & =-bx-\frac{1}{9}x-\frac{13}{19}b-\frac{13}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{-20}{6})((-5)-x)& =(\color{red}{a}+\color{orange}{\frac{10}{3}}).(\color{green}{-x}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(-5)} + \color{orange}{(\frac{10}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -ax-5a-\frac{10}{3}x-\frac{10}{3}.5& \text{Uitwerken } \\ & =-ax-5a-\frac{10}{3}x-\frac{50}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{17}{12}+b)(x-\frac{-18}{17})& =(\color{red}{b}+\color{orange}{\frac{17}{12}}).(\color{green}{x}+\color{blue}{\frac{18}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{18}{17})} + \color{orange}{(\frac{17}{12})} . \color{green}{(x)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{18}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{18}{17}b+\frac{17}{12}x+\frac{17}{12}.\frac{18}{17}& \text{Uitwerken } \\ & =bx+\frac{18}{17}b+\frac{17}{12}x+\frac{306}{204} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{18}{17}b+\frac{17}{12}x+\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{9}{15}+p)(a+\frac{10}{8})& =(\color{red}{p}+\color{orange}{\frac{3}{5}}).(\color{green}{a}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{5}{4}p+\frac{3}{5}a+\frac{3}{5}.\frac{5}{4}& \text{Uitwerken } \\ & =ap+\frac{5}{4}p+\frac{3}{5}a+\frac{15}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{5}{4}p+\frac{3}{5}a+\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-4}{18}-b)(\frac{-18}{17}-q)& =(\color{red}{-b}+\color{orange}{\frac{-2}{9}}).(\color{green}{-q}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{18}{17}b+\frac{2}{9}q+\frac{2}{9}.\frac{18}{17}& \text{Uitwerken } \\ & =bq+\frac{18}{17}b+\frac{2}{9}q+\frac{36}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{18}{17}b+\frac{2}{9}q+\frac{4}{17} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(q+\frac{-15}{2})(\frac{5}{2}+a)& =(\color{red}{q}+\color{orange}{\frac{-15}{2}}).(\color{green}{a}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-15}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{2}q-\frac{15}{2}a-\frac{15}{2}.\frac{5}{2}& \text{Uitwerken } \\ & =aq+\frac{5}{2}q-\frac{15}{2}a-\frac{75}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{19}{6})(\frac{-12}{17}-b)& =(\color{red}{p}+\color{orange}{\frac{-19}{6}}).(\color{green}{-b}+\color{blue}{\frac{-12}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-12}{17})} + \color{orange}{(\frac{-19}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{6})} . \color{blue}{(\frac{-12}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{12}{17}p+\frac{19}{6}b+\frac{19}{6}.\frac{12}{17}& \text{Uitwerken } \\ & =-bp-\frac{12}{17}p+\frac{19}{6}b+\frac{228}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{12}{17}p+\frac{19}{6}b+\frac{38}{17} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q+\frac{13}{19})(a-\frac{1}{16})& =(\color{red}{q}+\color{orange}{\frac{13}{19}}).(\color{green}{a}+\color{blue}{\frac{-1}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{16})} + \color{orange}{(\frac{13}{19})} . \color{green}{(a)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{-1}{16})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{16}q+\frac{13}{19}a-\frac{13}{19}.\frac{1}{16}& \text{Uitwerken } \\ & =aq-\frac{1}{16}q+\frac{13}{19}a-\frac{13}{304} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-4}{17}-p)(q+19)& =(\color{red}{-p}+\color{orange}{\frac{-4}{17}}).(\color{green}{q}+\color{blue}{19})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(19)} + \color{orange}{(\frac{-4}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{17})} . \color{blue}{(19)}& \text{Boogjes en uitschrijven} \\ & = -pq-19p-\frac{4}{17}q-\frac{4}{17}.19& \text{Uitwerken } \\ & =-pq-19p-\frac{4}{17}q-\frac{76}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-11-13 21:49:28
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