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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-11}{20})(p-\frac{-14}{17})& =(\color{red}{p}+\color{orange}{\frac{11}{20}}).(\color{green}{p}+\color{blue}{\frac{14}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{14}{17})} + \color{orange}{(\frac{11}{20})} . \color{green}{(p)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{14}{17})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{14}{17}p+\frac{11}{20}p+\frac{11}{20}.\frac{14}{17}& \text{Uitwerken } \\ & =p^2+(\frac{14}{17}+\frac{11}{20})p+\frac{154}{340} & \text{Neem samen} \\ &=p^2+\frac{467}{340}p+\frac{154}{340} & \text{Maak de som} \\ &=p^2+\frac{467}{340}p+\frac{77}{170} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{5}{11}-q)(\frac{1}{3}-b)& =(\color{red}{-q}+\color{orange}{\frac{5}{11}}).(\color{green}{-b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{5}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{3}q-\frac{5}{11}b+\frac{5}{11}.\frac{1}{3}& \text{Uitwerken } \\ & =bq-\frac{1}{3}q-\frac{5}{11}b+\frac{5}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+(-19))(a-\frac{-10}{17})& =(\color{red}{a}+\color{orange}{(-19)}).(\color{green}{a}+\color{blue}{\frac{10}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{10}{17})} + \color{orange}{(-19)} . \color{green}{(a)} + \color{orange}{(-19)} . \color{blue}{(\frac{10}{17})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{10}{17}a-19a-19.\frac{10}{17}& \text{Uitwerken } \\ & =a^2+(\frac{10}{17}+(-19))a-(\frac{-190}{17}) & \text{Neem samen} \\ &=a^2-\frac{313}{17}a-(\frac{-190}{17}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(p+\frac{13}{15})(\frac{9}{5}+q)& =(\color{red}{p}+\color{orange}{\frac{13}{15}}).(\color{green}{q}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{13}{15})} . \color{green}{(q)} + \color{orange}{(\frac{13}{15})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{9}{5}p+\frac{13}{15}q+\frac{13}{15}.\frac{9}{5}& \text{Uitwerken } \\ & =pq+\frac{9}{5}p+\frac{13}{15}q+\frac{117}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{9}{5}p+\frac{13}{15}q+\frac{39}{25} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p+(-13))(p-\frac{4}{6})& =(\color{red}{p}+\color{orange}{(-13)}).(\color{green}{p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(-13)} . \color{green}{(p)} + \color{orange}{(-13)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{2}{3}p-13p+13.\frac{2}{3}& \text{Uitwerken } \\ & =p^2+((\frac{-2}{3})+(-13))p+\frac{26}{3} & \text{Neem samen} \\ &=p^2-\frac{41}{3}p+\frac{26}{3} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{-9}{8}-x)(q+\frac{2}{13})& =(\color{red}{-x}+\color{orange}{\frac{-9}{8}}).(\color{green}{q}+\color{blue}{\frac{2}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{2}{13})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{2}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{2}{13}x-\frac{9}{8}q-\frac{9}{8}.\frac{2}{13}& \text{Uitwerken } \\ & =-qx-\frac{2}{13}x-\frac{9}{8}q-\frac{18}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{2}{13}x-\frac{9}{8}q-\frac{9}{52} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{10}{5}-b)(b-\frac{18}{17})& =(\color{red}{-b}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{18}{17}b+2b-2.\frac{18}{17}& \text{Uitwerken } \\ & =-b^2+(\frac{18}{17}+2)b-\frac{36}{17} & \text{Neem samen} \\ &=-b^2+\frac{52}{17}b-\frac{36}{17} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-16}{4}+q)(\frac{9}{10}+a)& =(\color{red}{q}+\color{orange}{(-4)}).(\color{green}{a}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(-4)} . \color{green}{(a)} + \color{orange}{(-4)} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{10}q-4a-4.\frac{9}{10}& \text{Uitwerken } \\ & =aq+\frac{9}{10}q-4a-\frac{36}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{9}{10}q-4a-\frac{18}{5} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x+\frac{-10}{17})(\frac{13}{11}+q)& =(\color{red}{x}+\color{orange}{\frac{-10}{17}}).(\color{green}{q}+\color{blue}{\frac{13}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{13}{11})} + \color{orange}{(\frac{-10}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{17})} . \color{blue}{(\frac{13}{11})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{13}{11}x-\frac{10}{17}q-\frac{10}{17}.\frac{13}{11}& \text{Uitwerken } \\ & =qx+\frac{13}{11}x-\frac{10}{17}q-\frac{130}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q-\frac{4}{15})(a-\frac{-19}{12})& =(\color{red}{q}+\color{orange}{\frac{-4}{15}}).(\color{green}{a}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{-4}{15})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{15})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{19}{12}q-\frac{4}{15}a-\frac{4}{15}.\frac{19}{12}& \text{Uitwerken } \\ & =aq+\frac{19}{12}q-\frac{4}{15}a-\frac{76}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{19}{12}q-\frac{4}{15}a-\frac{19}{45} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{15}{6}-x)(11-q)& =(\color{red}{-x}+\color{orange}{\frac{5}{2}}).(\color{green}{-q}+\color{blue}{11})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(11)} + \color{orange}{(\frac{5}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = qx-11x-\frac{5}{2}q+\frac{5}{2}.11& \text{Uitwerken } \\ & =qx-11x-\frac{5}{2}q+\frac{55}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a-\frac{16}{3})(8+b)& =(\color{red}{a}+\color{orange}{\frac{-16}{3}}).(\color{green}{b}+\color{blue}{8})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(8)} + \color{orange}{(\frac{-16}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{3})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = ab+8a-\frac{16}{3}b-\frac{16}{3}.8& \text{Uitwerken } \\ & =ab+8a-\frac{16}{3}b-\frac{128}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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