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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{-12}{17})(q-\frac{-10}{13})& =(\color{red}{b}+\color{orange}{\frac{12}{17}}).(\color{green}{q}+\color{blue}{\frac{10}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{10}{13})} + \color{orange}{(\frac{12}{17})} . \color{green}{(q)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{10}{13})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{10}{13}b+\frac{12}{17}q+\frac{12}{17}.\frac{10}{13}& \text{Uitwerken } \\ & =bq+\frac{10}{13}b+\frac{12}{17}q+\frac{120}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p+\frac{1}{17})(q+\frac{-3}{14})& =(\color{red}{p}+\color{orange}{\frac{1}{17}}).(\color{green}{q}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{1}{17})} . \color{green}{(q)} + \color{orange}{(\frac{1}{17})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{14}p+\frac{1}{17}q-\frac{1}{17}.\frac{3}{14}& \text{Uitwerken } \\ & =pq-\frac{3}{14}p+\frac{1}{17}q-\frac{3}{238} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-8}{14}+x)(x-\frac{-9}{8})& =(\color{red}{x}+\color{orange}{\frac{-4}{7}}).(\color{green}{x}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{9}{8}x-\frac{4}{7}x-\frac{4}{7}.\frac{9}{8}& \text{Uitwerken } \\ & =x^2+(\frac{9}{8}+(\frac{-4}{7}))x-(\frac{-36}{56}) & \text{Neem samen} \\ &=x^2+\frac{31}{56}x-(\frac{-36}{56}) & \text{Maak de som} \\ &=x^2+\frac{31}{56}x+\frac{9}{14} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  4. \(\begin{align}(p-\frac{20}{12})(\frac{4}{12}-b)& =(\color{red}{p}+\color{orange}{\frac{-5}{3}}).(\color{green}{-b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{3}p+\frac{5}{3}b-\frac{5}{3}.\frac{1}{3}& \text{Uitwerken } \\ & =-bp+\frac{1}{3}p+\frac{5}{3}b-\frac{5}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{5}{13}-x)(x-\frac{13}{15})& =(\color{red}{-x}+\color{orange}{\frac{5}{13}}).(\color{green}{x}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{5}{13})} . \color{green}{(x)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{13}{15}x+\frac{5}{13}x-\frac{5}{13}.\frac{13}{15}& \text{Uitwerken } \\ & =-x^2+(\frac{13}{15}+\frac{5}{13})x-\frac{65}{195} & \text{Neem samen} \\ &=-x^2+\frac{244}{195}x-\frac{65}{195} & \text{Maak de som} \\ &=-x^2+\frac{244}{195}x-\frac{1}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{1}{2}-a)(p-\frac{-2}{5})& =(\color{red}{-a}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{2}{5}a+\frac{1}{2}p+\frac{1}{2}.\frac{2}{5}& \text{Uitwerken } \\ & =-ap-\frac{2}{5}a+\frac{1}{2}p+\frac{2}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{2}{5}a+\frac{1}{2}p+\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-8}{4}-x)(\frac{9}{4}-p)& =(\color{red}{-x}+\color{orange}{(-2)}).(\color{green}{-p}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(-2)} . \color{green}{(-p)} + \color{orange}{(-2)} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{9}{4}x+2p-2.\frac{9}{4}& \text{Uitwerken } \\ & =px-\frac{9}{4}x+2p-\frac{18}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{9}{4}x+2p-\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-13}{3}-a)(x+\frac{-9}{7})& =(\color{red}{-a}+\color{orange}{\frac{-13}{3}}).(\color{green}{x}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{-13}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{3})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{9}{7}a-\frac{13}{3}x+\frac{13}{3}.\frac{9}{7}& \text{Uitwerken } \\ & =-ax+\frac{9}{7}a-\frac{13}{3}x+\frac{117}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{9}{7}a-\frac{13}{3}x+\frac{39}{7} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{11}{20}-b)(b+\frac{-11}{8})& =(\color{red}{-b}+\color{orange}{\frac{11}{20}}).(\color{green}{b}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{11}{20})} . \color{green}{(b)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{11}{8}b+\frac{11}{20}b-\frac{11}{20}.\frac{11}{8}& \text{Uitwerken } \\ & =-b^2+(\frac{11}{8}+\frac{11}{20})b-\frac{121}{160} & \text{Neem samen} \\ &=-b^2+\frac{77}{40}b-\frac{121}{160} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(q+\frac{9}{10})(\frac{-17}{19}-x)& =(\color{red}{q}+\color{orange}{\frac{9}{10}}).(\color{green}{-x}+\color{blue}{\frac{-17}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{19})} + \color{orange}{(\frac{9}{10})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{-17}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{17}{19}q-\frac{9}{10}x-\frac{9}{10}.\frac{17}{19}& \text{Uitwerken } \\ & =-qx-\frac{17}{19}q-\frac{9}{10}x-\frac{153}{190} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{-8}{2})(b-\frac{-13}{13})& =(\color{red}{b}+\color{orange}{4}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(4)} . \color{green}{(b)} + \color{orange}{(4)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bb+1b+4b+4.1& \text{Uitwerken } \\ & =b^2+(1+4)b+4 & \text{Neem samen} \\ &=b^2+5b+4 & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-19}{11})(\frac{-8}{4}-a)& =(\color{red}{q}+\color{orange}{\frac{-19}{11}}).(\color{green}{-a}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{-19}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -aq-2q+\frac{19}{11}a+\frac{19}{11}.2& \text{Uitwerken } \\ & =-aq-2q+\frac{19}{11}a+\frac{38}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-03-13 21:01:09
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