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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}((-19)+b)(x+\frac{15}{16})& =(\color{red}{b}+\color{orange}{(-19)}).(\color{green}{x}+\color{blue}{\frac{15}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{15}{16})} + \color{orange}{(-19)} . \color{green}{(x)} + \color{orange}{(-19)} . \color{blue}{(\frac{15}{16})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{15}{16}b-19x-19.\frac{15}{16}& \text{Uitwerken } \\ & =bx+\frac{15}{16}b-19x-\frac{285}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-7}{20})(x-\frac{19}{3})& =(\color{red}{p}+\color{orange}{\frac{-7}{20}}).(\color{green}{x}+\color{blue}{\frac{-19}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{3})} + \color{orange}{(\frac{-7}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(\frac{-19}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{19}{3}p-\frac{7}{20}x+\frac{7}{20}.\frac{19}{3}& \text{Uitwerken } \\ & =px-\frac{19}{3}p-\frac{7}{20}x+\frac{133}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q+\frac{13}{10})(\frac{-10}{2}+x)& =(\color{red}{q}+\color{orange}{\frac{13}{10}}).(\color{green}{x}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-5)} + \color{orange}{(\frac{13}{10})} . \color{green}{(x)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = qx-5q+\frac{13}{10}x-\frac{13}{10}.5& \text{Uitwerken } \\ & =qx-5q+\frac{13}{10}x-\frac{65}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-5q+\frac{13}{10}x-\frac{13}{2} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q-\frac{14}{16})(\frac{12}{3}+p)& =(\color{red}{q}+\color{orange}{\frac{-7}{8}}).(\color{green}{p}+\color{blue}{4})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(4)} + \color{orange}{(\frac{-7}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = pq+4q-\frac{7}{8}p-\frac{7}{8}.4& \text{Uitwerken } \\ & =pq+4q-\frac{7}{8}p-\frac{28}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+4q-\frac{7}{8}p-\frac{7}{2} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a+\frac{-16}{13})(\frac{5}{14}-a)& =(\color{red}{a}+\color{orange}{\frac{-16}{13}}).(\color{green}{-a}+\color{blue}{\frac{5}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{5}{14})} + \color{orange}{(\frac{-16}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{-16}{13})} . \color{blue}{(\frac{5}{14})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{5}{14}a+\frac{16}{13}a-\frac{16}{13}.\frac{5}{14}& \text{Uitwerken } \\ & =-a^2+(\frac{5}{14}+\frac{16}{13})a-\frac{80}{182} & \text{Neem samen} \\ &=-a^2+\frac{289}{182}a-\frac{80}{182} & \text{Maak de som} \\ &=-a^2+\frac{289}{182}a-\frac{40}{91} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{-12}{10}+q)(\frac{4}{10}-a)& =(\color{red}{q}+\color{orange}{\frac{-6}{5}}).(\color{green}{-a}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{2}{5}q+\frac{6}{5}a-\frac{6}{5}.\frac{2}{5}& \text{Uitwerken } \\ & =-aq+\frac{2}{5}q+\frac{6}{5}a-\frac{12}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-9}{8}+q)(11-p)& =(\color{red}{q}+\color{orange}{\frac{-9}{8}}).(\color{green}{-p}+\color{blue}{11})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(11)} + \color{orange}{(\frac{-9}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = -pq+11q+\frac{9}{8}p-\frac{9}{8}.11& \text{Uitwerken } \\ & =-pq+11q+\frac{9}{8}p-\frac{99}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-3}{2}-b)(\frac{-20}{13}-x)& =(\color{red}{-b}+\color{orange}{\frac{-3}{2}}).(\color{green}{-x}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{20}{13}b+\frac{3}{2}x+\frac{3}{2}.\frac{20}{13}& \text{Uitwerken } \\ & =bx+\frac{20}{13}b+\frac{3}{2}x+\frac{60}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{20}{13}b+\frac{3}{2}x+\frac{30}{13} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x+\frac{8}{10})(\frac{-17}{10}+p)& =(\color{red}{x}+\color{orange}{\frac{4}{5}}).(\color{green}{p}+\color{blue}{\frac{-17}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{10})} + \color{orange}{(\frac{4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-17}{10})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{10}x+\frac{4}{5}p-\frac{4}{5}.\frac{17}{10}& \text{Uitwerken } \\ & =px-\frac{17}{10}x+\frac{4}{5}p-\frac{68}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{17}{10}x+\frac{4}{5}p-\frac{34}{25} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-19}{3}+a)(\frac{4}{11}+q)& =(\color{red}{a}+\color{orange}{\frac{-19}{3}}).(\color{green}{q}+\color{blue}{\frac{4}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{4}{11})} + \color{orange}{(\frac{-19}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{3})} . \color{blue}{(\frac{4}{11})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{4}{11}a-\frac{19}{3}q-\frac{19}{3}.\frac{4}{11}& \text{Uitwerken } \\ & =aq+\frac{4}{11}a-\frac{19}{3}q-\frac{76}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{4}{17}+p)(\frac{-1}{20}+p)& =(\color{red}{p}+\color{orange}{\frac{4}{17}}).(\color{green}{p}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(\frac{4}{17})} . \color{green}{(p)} + \color{orange}{(\frac{4}{17})} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{20}p+\frac{4}{17}p-\frac{4}{17}.\frac{1}{20}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{20})+\frac{4}{17})p-(\frac{-4}{340}) & \text{Neem samen} \\ &=p^2+\frac{63}{340}p-(\frac{-4}{340}) & \text{Maak de som} \\ &=p^2+\frac{63}{340}p+\frac{1}{85} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{17}{12}-a)(\frac{12}{13}+b)& =(\color{red}{-a}+\color{orange}{\frac{17}{12}}).(\color{green}{b}+\color{blue}{\frac{12}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{12}{13})} + \color{orange}{(\frac{17}{12})} . \color{green}{(b)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{12}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{12}{13}a+\frac{17}{12}b+\frac{17}{12}.\frac{12}{13}& \text{Uitwerken } \\ & =-ab-\frac{12}{13}a+\frac{17}{12}b+\frac{204}{156} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{12}{13}a+\frac{17}{12}b+\frac{17}{13} & \text{Vereenvoudig} \\\end{align}\)
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