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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{6}{12})(q-\frac{18}{19})& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{-18}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{19})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-18}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{18}{19}x-\frac{1}{2}q+\frac{1}{2}.\frac{18}{19}& \text{Uitwerken } \\ & =qx-\frac{18}{19}x-\frac{1}{2}q+\frac{18}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{18}{19}x-\frac{1}{2}q+\frac{9}{19} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(x-\frac{-7}{13})(\frac{-18}{18}+a)& =(\color{red}{x}+\color{orange}{\frac{7}{13}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{7}{13})} . \color{green}{(a)} + \color{orange}{(\frac{7}{13})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1x+\frac{7}{13}a-\frac{7}{13}.1& \text{Uitwerken } \\ & =ax-1x+\frac{7}{13}a-\frac{7}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p-\frac{3}{6})(x-\frac{-1}{19})& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{19}p-\frac{1}{2}x-\frac{1}{2}.\frac{1}{19}& \text{Uitwerken } \\ & =px+\frac{1}{19}p-\frac{1}{2}x-\frac{1}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-1}{13}-q)(b-\frac{12}{9})& =(\color{red}{-q}+\color{orange}{\frac{-1}{13}}).(\color{green}{b}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-1}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{13})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{4}{3}q-\frac{1}{13}b+\frac{1}{13}.\frac{4}{3}& \text{Uitwerken } \\ & =-bq+\frac{4}{3}q-\frac{1}{13}b+\frac{4}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q-\frac{1}{13})(\frac{-1}{15}-q)& =(\color{red}{q}+\color{orange}{\frac{-1}{13}}).(\color{green}{-q}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(\frac{-1}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{13})} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{1}{15}q+\frac{1}{13}q+\frac{1}{13}.\frac{1}{15}& \text{Uitwerken } \\ & =-q^2+((\frac{-1}{15})+\frac{1}{13})q+(\frac{-1}{195}) & \text{Neem samen} \\ &=-q^2+\frac{2}{195}q+(\frac{-1}{195}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(a+\frac{11}{20})(\frac{20}{19}+p)& =(\color{red}{a}+\color{orange}{\frac{11}{20}}).(\color{green}{p}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{11}{20})} . \color{green}{(p)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{20}{19}a+\frac{11}{20}p+\frac{11}{20}.\frac{20}{19}& \text{Uitwerken } \\ & =ap+\frac{20}{19}a+\frac{11}{20}p+\frac{220}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{20}{19}a+\frac{11}{20}p+\frac{11}{19} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{9}{16}-a)(x-\frac{-3}{2})& =(\color{red}{-a}+\color{orange}{\frac{9}{16}}).(\color{green}{x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{9}{16})} . \color{green}{(x)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{3}{2}a+\frac{9}{16}x+\frac{9}{16}.\frac{3}{2}& \text{Uitwerken } \\ & =-ax-\frac{3}{2}a+\frac{9}{16}x+\frac{27}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b+\frac{7}{11})(\frac{-13}{19}-p)& =(\color{red}{b}+\color{orange}{\frac{7}{11}}).(\color{green}{-p}+\color{blue}{\frac{-13}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{19})} + \color{orange}{(\frac{7}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{7}{11})} . \color{blue}{(\frac{-13}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{13}{19}b-\frac{7}{11}p-\frac{7}{11}.\frac{13}{19}& \text{Uitwerken } \\ & =-bp-\frac{13}{19}b-\frac{7}{11}p-\frac{91}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-7}{12}-q)(\frac{4}{13}-b)& =(\color{red}{-q}+\color{orange}{\frac{-7}{12}}).(\color{green}{-b}+\color{blue}{\frac{4}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{4}{13})} + \color{orange}{(\frac{-7}{12})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{12})} . \color{blue}{(\frac{4}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{4}{13}q+\frac{7}{12}b-\frac{7}{12}.\frac{4}{13}& \text{Uitwerken } \\ & =bq-\frac{4}{13}q+\frac{7}{12}b-\frac{28}{156} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{4}{13}q+\frac{7}{12}b-\frac{7}{39} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p-\frac{13}{7})(a-\frac{7}{3})& =(\color{red}{p}+\color{orange}{\frac{-13}{7}}).(\color{green}{a}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{-13}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{7})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{3}p-\frac{13}{7}a+\frac{13}{7}.\frac{7}{3}& \text{Uitwerken } \\ & =ap-\frac{7}{3}p-\frac{13}{7}a+\frac{91}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{7}{3}p-\frac{13}{7}a+\frac{13}{3} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-5}{11})(\frac{-4}{6}-p)& =(\color{red}{a}+\color{orange}{\frac{5}{11}}).(\color{green}{-p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{5}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{2}{3}a-\frac{5}{11}p-\frac{5}{11}.\frac{2}{3}& \text{Uitwerken } \\ & =-ap-\frac{2}{3}a-\frac{5}{11}p-\frac{10}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x-\frac{10}{7})(p+\frac{-5}{14})& =(\color{red}{x}+\color{orange}{\frac{-10}{7}}).(\color{green}{p}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{5}{14}x-\frac{10}{7}p+\frac{10}{7}.\frac{5}{14}& \text{Uitwerken } \\ & =px-\frac{5}{14}x-\frac{10}{7}p+\frac{50}{98} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{5}{14}x-\frac{10}{7}p+\frac{25}{49} & \text{Vereenvoudig} \\\end{align}\)
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