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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-18}{11}-q)(16+q)& =(\color{red}{-q}+\color{orange}{\frac{-18}{11}}).(\color{green}{q}+\color{blue}{16})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(16)} + \color{orange}{(\frac{-18}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-18}{11})} . \color{blue}{(16)}& \text{Boogjes en uitschrijven} \\ & = -qq-16q-\frac{18}{11}q-\frac{18}{11}.16& \text{Uitwerken } \\ & =-q^2+((-16)+(\frac{-18}{11}))q-\frac{288}{11} & \text{Neem samen} \\ &=-q^2-\frac{194}{11}q-\frac{288}{11} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{4}{5}-a)(\frac{7}{17}-x)& =(\color{red}{-a}+\color{orange}{\frac{4}{5}}).(\color{green}{-x}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(\frac{4}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{17}a-\frac{4}{5}x+\frac{4}{5}.\frac{7}{17}& \text{Uitwerken } \\ & =ax-\frac{7}{17}a-\frac{4}{5}x+\frac{28}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b+\frac{-18}{8})(\frac{6}{8}-q)& =(\color{red}{b}+\color{orange}{\frac{-9}{4}}).(\color{green}{-q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{3}{4}b+\frac{9}{4}q-\frac{9}{4}.\frac{3}{4}& \text{Uitwerken } \\ & =-bq+\frac{3}{4}b+\frac{9}{4}q-\frac{27}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{-14}{8})(\frac{-18}{15}-x)& =(\color{red}{q}+\color{orange}{\frac{-7}{4}}).(\color{green}{-x}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{6}{5}q+\frac{7}{4}x+\frac{7}{4}.\frac{6}{5}& \text{Uitwerken } \\ & =-qx-\frac{6}{5}q+\frac{7}{4}x+\frac{42}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{6}{5}q+\frac{7}{4}x+\frac{21}{10} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{2}{18}+b)(a-\frac{-2}{3})& =(\color{red}{b}+\color{orange}{\frac{1}{9}}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{1}{9})} . \color{green}{(a)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{3}b+\frac{1}{9}a+\frac{1}{9}.\frac{2}{3}& \text{Uitwerken } \\ & =ab+\frac{2}{3}b+\frac{1}{9}a+\frac{2}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{20}{19}-p)(p+\frac{-1}{18})& =(\color{red}{-p}+\color{orange}{\frac{20}{19}}).(\color{green}{p}+\color{blue}{\frac{-1}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{18})} + \color{orange}{(\frac{20}{19})} . \color{green}{(p)} + \color{orange}{(\frac{20}{19})} . \color{blue}{(\frac{-1}{18})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{1}{18}p+\frac{20}{19}p-\frac{20}{19}.\frac{1}{18}& \text{Uitwerken } \\ & =-p^2+(\frac{1}{18}+\frac{20}{19})p-\frac{20}{342} & \text{Neem samen} \\ &=-p^2+\frac{379}{342}p-\frac{20}{342} & \text{Maak de som} \\ &=-p^2+\frac{379}{342}p-\frac{10}{171} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{-10}{12}-p)(p-\frac{-2}{14})& =(\color{red}{-p}+\color{orange}{\frac{-5}{6}}).(\color{green}{p}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{1}{7}p-\frac{5}{6}p-\frac{5}{6}.\frac{1}{7}& \text{Uitwerken } \\ & =-p^2+((\frac{-1}{7})+(\frac{-5}{6}))p-\frac{5}{42} & \text{Neem samen} \\ &=-p^2-\frac{41}{42}p-\frac{5}{42} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(p+\frac{11}{7})((-11)+b)& =(\color{red}{p}+\color{orange}{\frac{11}{7}}).(\color{green}{b}+\color{blue}{(-11)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-11)} + \color{orange}{(\frac{11}{7})} . \color{green}{(b)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(-11)}& \text{Boogjes en uitschrijven} \\ & = bp-11p+\frac{11}{7}b-\frac{11}{7}.11& \text{Uitwerken } \\ & =bp-11p+\frac{11}{7}b-\frac{121}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{14}{9}-p)(p+\frac{-11}{16})& =(\color{red}{-p}+\color{orange}{\frac{14}{9}}).(\color{green}{p}+\color{blue}{\frac{-11}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-11}{16})} + \color{orange}{(\frac{14}{9})} . \color{green}{(p)} + \color{orange}{(\frac{14}{9})} . \color{blue}{(\frac{-11}{16})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{11}{16}p+\frac{14}{9}p-\frac{14}{9}.\frac{11}{16}& \text{Uitwerken } \\ & =-p^2+(\frac{11}{16}+\frac{14}{9})p-\frac{154}{144} & \text{Neem samen} \\ &=-p^2+\frac{323}{144}p-\frac{154}{144} & \text{Maak de som} \\ &=-p^2+\frac{323}{144}p-\frac{77}{72} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{-1}{13}+q)(b+\frac{-20}{4})& =(\color{red}{q}+\color{orange}{\frac{-1}{13}}).(\color{green}{b}+\color{blue}{(-5)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-5)} + \color{orange}{(\frac{-1}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{13})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = bq-5q-\frac{1}{13}b+\frac{1}{13}.5& \text{Uitwerken } \\ & =bq-5q-\frac{1}{13}b+\frac{5}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{-13}{19})(q-\frac{-4}{20})& =(\color{red}{b}+\color{orange}{\frac{13}{19}}).(\color{green}{q}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{13}{19})} . \color{green}{(q)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{5}b+\frac{13}{19}q+\frac{13}{19}.\frac{1}{5}& \text{Uitwerken } \\ & =bq+\frac{1}{5}b+\frac{13}{19}q+\frac{13}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{-17}{5})(\frac{-17}{2}-q)& =(\color{red}{p}+\color{orange}{\frac{17}{5}}).(\color{green}{-q}+\color{blue}{\frac{-17}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{2})} + \color{orange}{(\frac{17}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{-17}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{17}{2}p-\frac{17}{5}q-\frac{17}{5}.\frac{17}{2}& \text{Uitwerken } \\ & =-pq-\frac{17}{2}p-\frac{17}{5}q-\frac{289}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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