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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{19}{18})(1-b)& =(\color{red}{x}+\color{orange}{\frac{19}{18}}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{19}{18})} . \color{green}{(-b)} + \color{orange}{(\frac{19}{18})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bx+1x-\frac{19}{18}b+\frac{19}{18}.1& \text{Uitwerken } \\ & =-bx+1x-\frac{19}{18}b+\frac{19}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{12}{3}+p)(p+\frac{18}{13})& =(\color{red}{p}+\color{orange}{4}).(\color{green}{p}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(4)} . \color{green}{(p)} + \color{orange}{(4)} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{18}{13}p+4p+4.\frac{18}{13}& \text{Uitwerken } \\ & =p^2+(\frac{18}{13}+4)p+\frac{72}{13} & \text{Neem samen} \\ &=p^2+\frac{70}{13}p+\frac{72}{13} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-5}{6}-b)(\frac{-7}{9}+x)& =(\color{red}{-b}+\color{orange}{\frac{-5}{6}}).(\color{green}{x}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{7}{9}b-\frac{5}{6}x+\frac{5}{6}.\frac{7}{9}& \text{Uitwerken } \\ & =-bx+\frac{7}{9}b-\frac{5}{6}x+\frac{35}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{2}{7}-p)(\frac{-12}{6}+a)& =(\color{red}{-p}+\color{orange}{\frac{2}{7}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(-2)} + \color{orange}{(\frac{2}{7})} . \color{green}{(a)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -ap+2p+\frac{2}{7}a-\frac{2}{7}.2& \text{Uitwerken } \\ & =-ap+2p+\frac{2}{7}a-\frac{4}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x+\frac{1}{7})(\frac{-11}{13}+b)& =(\color{red}{x}+\color{orange}{\frac{1}{7}}).(\color{green}{b}+\color{blue}{\frac{-11}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{13})} + \color{orange}{(\frac{1}{7})} . \color{green}{(b)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{-11}{13})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{13}x+\frac{1}{7}b-\frac{1}{7}.\frac{11}{13}& \text{Uitwerken } \\ & =bx-\frac{11}{13}x+\frac{1}{7}b-\frac{11}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-15}{13}-x)(x-\frac{-17}{8})& =(\color{red}{-x}+\color{orange}{\frac{-15}{13}}).(\color{green}{x}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{17}{8}x-\frac{15}{13}x-\frac{15}{13}.\frac{17}{8}& \text{Uitwerken } \\ & =-x^2+((\frac{-17}{8})+(\frac{-15}{13}))x-\frac{255}{104} & \text{Neem samen} \\ &=-x^2-\frac{341}{104}x-\frac{255}{104} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-7}{13}+p)(\frac{-13}{12}+p)& =(\color{red}{p}+\color{orange}{\frac{-7}{13}}).(\color{green}{p}+\color{blue}{\frac{-13}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{12})} + \color{orange}{(\frac{-7}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{13})} . \color{blue}{(\frac{-13}{12})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{13}{12}p-\frac{7}{13}p+\frac{7}{13}.\frac{13}{12}& \text{Uitwerken } \\ & =p^2+((\frac{-13}{12})+(\frac{-7}{13}))p+\frac{91}{156} & \text{Neem samen} \\ &=p^2-\frac{253}{156}p+\frac{91}{156} & \text{Maak de som} \\ &=p^2-\frac{253}{156}p+\frac{7}{12} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{12}{11}+a)(\frac{-5}{20}-a)& =(\color{red}{a}+\color{orange}{\frac{12}{11}}).(\color{green}{-a}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{12}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{12}{11})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{1}{4}a-\frac{12}{11}a-\frac{12}{11}.\frac{1}{4}& \text{Uitwerken } \\ & =-a^2+((\frac{-1}{4})+(\frac{-12}{11}))a-\frac{12}{44} & \text{Neem samen} \\ &=-a^2-\frac{59}{44}a-\frac{12}{44} & \text{Maak de som} \\ &=-a^2-\frac{59}{44}a-\frac{3}{11} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{-17}{10}+b)(\frac{3}{18}-a)& =(\color{red}{b}+\color{orange}{\frac{-17}{10}}).(\color{green}{-a}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-17}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{-17}{10})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{6}b+\frac{17}{10}a-\frac{17}{10}.\frac{1}{6}& \text{Uitwerken } \\ & =-ab+\frac{1}{6}b+\frac{17}{10}a-\frac{17}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-18}{2})(p+\frac{6}{20})& =(\color{red}{q}+\color{orange}{9}).(\color{green}{p}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(9)} . \color{green}{(p)} + \color{orange}{(9)} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{10}q+9p+9.\frac{3}{10}& \text{Uitwerken } \\ & =pq+\frac{3}{10}q+9p+\frac{27}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a+\frac{17}{13})(p+\frac{-20}{3})& =(\color{red}{a}+\color{orange}{\frac{17}{13}}).(\color{green}{p}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(\frac{17}{13})} . \color{green}{(p)} + \color{orange}{(\frac{17}{13})} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{20}{3}a+\frac{17}{13}p-\frac{17}{13}.\frac{20}{3}& \text{Uitwerken } \\ & =ap-\frac{20}{3}a+\frac{17}{13}p-\frac{340}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(12-b)(x+\frac{-9}{17})& =(\color{red}{-b}+\color{orange}{12}).(\color{green}{x}+\color{blue}{\frac{-9}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-9}{17})} + \color{orange}{(12)} . \color{green}{(x)} + \color{orange}{(12)} . \color{blue}{(\frac{-9}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{9}{17}b+12x-12.\frac{9}{17}& \text{Uitwerken } \\ & =-bx+\frac{9}{17}b+12x-\frac{108}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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