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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{-6}{7})(\frac{13}{8}+x)& =(\color{red}{q}+\color{orange}{\frac{6}{7}}).(\color{green}{x}+\color{blue}{\frac{13}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{13}{8})} + \color{orange}{(\frac{6}{7})} . \color{green}{(x)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{13}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{13}{8}q+\frac{6}{7}x+\frac{6}{7}.\frac{13}{8}& \text{Uitwerken } \\ & =qx+\frac{13}{8}q+\frac{6}{7}x+\frac{78}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{13}{8}q+\frac{6}{7}x+\frac{39}{28} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q+\frac{-16}{2})(p-\frac{9}{8})& =(\color{red}{q}+\color{orange}{(-8)}).(\color{green}{p}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(-8)} . \color{green}{(p)} + \color{orange}{(-8)} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{9}{8}q-8p+8.\frac{9}{8}& \text{Uitwerken } \\ & =pq-\frac{9}{8}q-8p+\frac{72}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{9}{8}q-8p+9 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-19}{20}+x)(\frac{8}{17}-q)& =(\color{red}{x}+\color{orange}{\frac{-19}{20}}).(\color{green}{-q}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(\frac{-19}{20})} . \color{green}{(-q)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{8}{17}x+\frac{19}{20}q-\frac{19}{20}.\frac{8}{17}& \text{Uitwerken } \\ & =-qx+\frac{8}{17}x+\frac{19}{20}q-\frac{152}{340} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{8}{17}x+\frac{19}{20}q-\frac{38}{85} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p+\frac{11}{10})(q-\frac{-3}{12})& =(\color{red}{p}+\color{orange}{\frac{11}{10}}).(\color{green}{q}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{11}{10})} . \color{green}{(q)} + \color{orange}{(\frac{11}{10})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{4}p+\frac{11}{10}q+\frac{11}{10}.\frac{1}{4}& \text{Uitwerken } \\ & =pq+\frac{1}{4}p+\frac{11}{10}q+\frac{11}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{11}{10}-a)(b+\frac{-4}{13})& =(\color{red}{-a}+\color{orange}{\frac{11}{10}}).(\color{green}{b}+\color{blue}{\frac{-4}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-4}{13})} + \color{orange}{(\frac{11}{10})} . \color{green}{(b)} + \color{orange}{(\frac{11}{10})} . \color{blue}{(\frac{-4}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{4}{13}a+\frac{11}{10}b-\frac{11}{10}.\frac{4}{13}& \text{Uitwerken } \\ & =-ab+\frac{4}{13}a+\frac{11}{10}b-\frac{44}{130} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{4}{13}a+\frac{11}{10}b-\frac{22}{65} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-2}{7}-q)(a-\frac{7}{12})& =(\color{red}{-q}+\color{orange}{\frac{-2}{7}}).(\color{green}{a}+\color{blue}{\frac{-7}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-7}{12})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{-7}{12})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{7}{12}q-\frac{2}{7}a+\frac{2}{7}.\frac{7}{12}& \text{Uitwerken } \\ & =-aq+\frac{7}{12}q-\frac{2}{7}a+\frac{14}{84} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{7}{12}q-\frac{2}{7}a+\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{11}{14}+q)(\frac{-16}{14}+p)& =(\color{red}{q}+\color{orange}{\frac{11}{14}}).(\color{green}{p}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{11}{14})} . \color{green}{(p)} + \color{orange}{(\frac{11}{14})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{8}{7}q+\frac{11}{14}p-\frac{11}{14}.\frac{8}{7}& \text{Uitwerken } \\ & =pq-\frac{8}{7}q+\frac{11}{14}p-\frac{88}{98} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{8}{7}q+\frac{11}{14}p-\frac{44}{49} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(q-\frac{20}{14})(a-\frac{5}{4})& =(\color{red}{q}+\color{orange}{\frac{-10}{7}}).(\color{green}{a}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{4}q-\frac{10}{7}a+\frac{10}{7}.\frac{5}{4}& \text{Uitwerken } \\ & =aq-\frac{5}{4}q-\frac{10}{7}a+\frac{50}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{5}{4}q-\frac{10}{7}a+\frac{25}{14} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{17}{6}-b)(\frac{-11}{12}-a)& =(\color{red}{-b}+\color{orange}{\frac{17}{6}}).(\color{green}{-a}+\color{blue}{\frac{-11}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-11}{12})} + \color{orange}{(\frac{17}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{17}{6})} . \color{blue}{(\frac{-11}{12})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{11}{12}b-\frac{17}{6}a-\frac{17}{6}.\frac{11}{12}& \text{Uitwerken } \\ & =ab+\frac{11}{12}b-\frac{17}{6}a-\frac{187}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{11}{17})(b-\frac{-19}{10})& =(\color{red}{a}+\color{orange}{\frac{-11}{17}}).(\color{green}{b}+\color{blue}{\frac{19}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{19}{10})} + \color{orange}{(\frac{-11}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{17})} . \color{blue}{(\frac{19}{10})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{19}{10}a-\frac{11}{17}b-\frac{11}{17}.\frac{19}{10}& \text{Uitwerken } \\ & =ab+\frac{19}{10}a-\frac{11}{17}b-\frac{209}{170} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b+\frac{18}{18})(\frac{2}{2}-b)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bb+1b-1b+1.1& \text{Uitwerken } \\ & =-b^2+(1+(-1))b+(-1) & \text{Neem samen} \\ &=-b^2+0b+(-1) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(b-\frac{8}{9})(\frac{-11}{20}-x)& =(\color{red}{b}+\color{orange}{\frac{-8}{9}}).(\color{green}{-x}+\color{blue}{\frac{-11}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{20})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{-11}{20})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{11}{20}b+\frac{8}{9}x+\frac{8}{9}.\frac{11}{20}& \text{Uitwerken } \\ & =-bx-\frac{11}{20}b+\frac{8}{9}x+\frac{88}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{11}{20}b+\frac{8}{9}x+\frac{22}{45} & \text{Vereenvoudig} \\\end{align}\)
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