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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{4}{19})(b+\frac{-3}{18})& =(\color{red}{x}+\color{orange}{\frac{-4}{19}}).(\color{green}{b}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-4}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{19})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{6}x-\frac{4}{19}b+\frac{4}{19}.\frac{1}{6}& \text{Uitwerken } \\ & =bx-\frac{1}{6}x-\frac{4}{19}b+\frac{4}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{1}{6}x-\frac{4}{19}b+\frac{2}{57} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{11}{13}-q)(\frac{-19}{20}-x)& =(\color{red}{-q}+\color{orange}{\frac{11}{13}}).(\color{green}{-x}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(\frac{11}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{19}{20}q-\frac{11}{13}x-\frac{11}{13}.\frac{19}{20}& \text{Uitwerken } \\ & =qx+\frac{19}{20}q-\frac{11}{13}x-\frac{209}{260} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-18}{8}+b)(q+\frac{17}{17})& =(\color{red}{b}+\color{orange}{\frac{-9}{4}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-9}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1b-\frac{9}{4}q-\frac{9}{4}.1& \text{Uitwerken } \\ & =bq+1b-\frac{9}{4}q-\frac{9}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-8}{20}+x)(\frac{-12}{17}+b)& =(\color{red}{x}+\color{orange}{\frac{-2}{5}}).(\color{green}{b}+\color{blue}{\frac{-12}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-12}{17})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-12}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{12}{17}x-\frac{2}{5}b+\frac{2}{5}.\frac{12}{17}& \text{Uitwerken } \\ & =bx-\frac{12}{17}x-\frac{2}{5}b+\frac{24}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p+\frac{14}{15})(\frac{-14}{20}-x)& =(\color{red}{p}+\color{orange}{\frac{14}{15}}).(\color{green}{-x}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{14}{15})} . \color{green}{(-x)} + \color{orange}{(\frac{14}{15})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{7}{10}p-\frac{14}{15}x-\frac{14}{15}.\frac{7}{10}& \text{Uitwerken } \\ & =-px-\frac{7}{10}p-\frac{14}{15}x-\frac{98}{150} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{7}{10}p-\frac{14}{15}x-\frac{49}{75} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b-\frac{2}{12})(\frac{10}{17}+b)& =(\color{red}{b}+\color{orange}{\frac{-1}{6}}).(\color{green}{b}+\color{blue}{\frac{10}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{10}{17})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{10}{17})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{10}{17}b-\frac{1}{6}b-\frac{1}{6}.\frac{10}{17}& \text{Uitwerken } \\ & =b^2+(\frac{10}{17}+(\frac{-1}{6}))b-(\frac{-10}{102}) & \text{Neem samen} \\ &=b^2+\frac{43}{102}b-(\frac{-10}{102}) & \text{Maak de som} \\ &=b^2+\frac{43}{102}b+\frac{5}{51} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-15}{13})(a-\frac{16}{19})& =(\color{red}{b}+\color{orange}{\frac{-15}{13}}).(\color{green}{a}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{16}{19}b-\frac{15}{13}a+\frac{15}{13}.\frac{16}{19}& \text{Uitwerken } \\ & =ab-\frac{16}{19}b-\frac{15}{13}a+\frac{240}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-14}{8}-a)(p-\frac{8}{14})& =(\color{red}{-a}+\color{orange}{\frac{-7}{4}}).(\color{green}{p}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{4}{7}a-\frac{7}{4}p+\frac{7}{4}.\frac{4}{7}& \text{Uitwerken } \\ & =-ap+\frac{4}{7}a-\frac{7}{4}p+\frac{28}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{4}{7}a-\frac{7}{4}p+1 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-17}{10})(x-\frac{4}{8})& =(\color{red}{a}+\color{orange}{\frac{-17}{10}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-17}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{2}a-\frac{17}{10}x+\frac{17}{10}.\frac{1}{2}& \text{Uitwerken } \\ & =ax-\frac{1}{2}a-\frac{17}{10}x+\frac{17}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{20}{18}-b)(\frac{-9}{5}-q)& =(\color{red}{-b}+\color{orange}{\frac{10}{9}}).(\color{green}{-q}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{10}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{9}{5}b-\frac{10}{9}q-\frac{10}{9}.\frac{9}{5}& \text{Uitwerken } \\ & =bq+\frac{9}{5}b-\frac{10}{9}q-\frac{90}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{9}{5}b-\frac{10}{9}q-2 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q-\frac{-4}{19})(\frac{-11}{16}+x)& =(\color{red}{q}+\color{orange}{\frac{4}{19}}).(\color{green}{x}+\color{blue}{\frac{-11}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{16})} + \color{orange}{(\frac{4}{19})} . \color{green}{(x)} + \color{orange}{(\frac{4}{19})} . \color{blue}{(\frac{-11}{16})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{11}{16}q+\frac{4}{19}x-\frac{4}{19}.\frac{11}{16}& \text{Uitwerken } \\ & =qx-\frac{11}{16}q+\frac{4}{19}x-\frac{44}{304} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{11}{16}q+\frac{4}{19}x-\frac{11}{76} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{1}{11}-q)(\frac{10}{10}-q)& =(\color{red}{-q}+\color{orange}{\frac{1}{11}}).(\color{green}{-q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = qq-1q-\frac{1}{11}q+\frac{1}{11}.1& \text{Uitwerken } \\ & =q^2+((-1)+(\frac{-1}{11}))q+\frac{1}{11} & \text{Neem samen} \\ &=q^2-\frac{12}{11}q+\frac{1}{11} & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-11-03 06:58:01
Een site van Busleyden Atheneum Mechelen