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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{3}{11}-q)(\frac{-12}{19}+p)& =(\color{red}{-q}+\color{orange}{\frac{3}{11}}).(\color{green}{p}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(\frac{3}{11})} . \color{green}{(p)} + \color{orange}{(\frac{3}{11})} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{12}{19}q+\frac{3}{11}p-\frac{3}{11}.\frac{12}{19}& \text{Uitwerken } \\ & =-pq+\frac{12}{19}q+\frac{3}{11}p-\frac{36}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-3}{18}+p)(\frac{20}{11}-a)& =(\color{red}{p}+\color{orange}{\frac{-1}{6}}).(\color{green}{-a}+\color{blue}{\frac{20}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{20}{11})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{20}{11})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{20}{11}p+\frac{1}{6}a-\frac{1}{6}.\frac{20}{11}& \text{Uitwerken } \\ & =-ap+\frac{20}{11}p+\frac{1}{6}a-\frac{20}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{20}{11}p+\frac{1}{6}a-\frac{10}{33} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-1}{5}+x)(x-\frac{4}{7})& =(\color{red}{x}+\color{orange}{\frac{-1}{5}}).(\color{green}{x}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{4}{7}x-\frac{1}{5}x+\frac{1}{5}.\frac{4}{7}& \text{Uitwerken } \\ & =x^2+((\frac{-4}{7})+(\frac{-1}{5}))x+\frac{4}{35} & \text{Neem samen} \\ &=x^2-\frac{27}{35}x+\frac{4}{35} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{9}{16}-a)(a-\frac{10}{20})& =(\color{red}{-a}+\color{orange}{\frac{9}{16}}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{9}{16})} . \color{green}{(a)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{1}{2}a+\frac{9}{16}a-\frac{9}{16}.\frac{1}{2}& \text{Uitwerken } \\ & =-a^2+(\frac{1}{2}+\frac{9}{16})a-\frac{9}{32} & \text{Neem samen} \\ &=-a^2+\frac{17}{16}a-\frac{9}{32} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(q+\frac{16}{6})(\frac{18}{2}+q)& =(\color{red}{q}+\color{orange}{\frac{8}{3}}).(\color{green}{q}+\color{blue}{9})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(9)} + \color{orange}{(\frac{8}{3})} . \color{green}{(q)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = qq+9q+\frac{8}{3}q+\frac{8}{3}.9& \text{Uitwerken } \\ & =q^2+(9+\frac{8}{3})q+\frac{72}{3} & \text{Neem samen} \\ &=q^2+\frac{35}{3}q+\frac{72}{3} & \text{Maak de som} \\ &=q^2+\frac{35}{3}q+24 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{20}{17}-p)(x+\frac{-3}{20})& =(\color{red}{-p}+\color{orange}{\frac{20}{17}}).(\color{green}{x}+\color{blue}{\frac{-3}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-3}{20})} + \color{orange}{(\frac{20}{17})} . \color{green}{(x)} + \color{orange}{(\frac{20}{17})} . \color{blue}{(\frac{-3}{20})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{3}{20}p+\frac{20}{17}x-\frac{20}{17}.\frac{3}{20}& \text{Uitwerken } \\ & =-px+\frac{3}{20}p+\frac{20}{17}x-\frac{60}{340} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{3}{20}p+\frac{20}{17}x-\frac{3}{17} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q+\frac{-6}{3})(\frac{-9}{20}-q)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{-q}+\color{blue}{\frac{-9}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{20})} + \color{orange}{(-2)} . \color{green}{(-q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-9}{20})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{9}{20}q+2q+2.\frac{9}{20}& \text{Uitwerken } \\ & =-q^2+((\frac{-9}{20})+2)q+(\frac{-18}{20}) & \text{Neem samen} \\ &=-q^2+\frac{31}{20}q+(\frac{-18}{20}) & \text{Maak de som} \\ &=-q^2+\frac{31}{20}q+(\frac{-9}{10}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(a+\frac{-15}{20})(\frac{-13}{19}-a)& =(\color{red}{a}+\color{orange}{\frac{-3}{4}}).(\color{green}{-a}+\color{blue}{\frac{-13}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{19})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-13}{19})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{13}{19}a+\frac{3}{4}a+\frac{3}{4}.\frac{13}{19}& \text{Uitwerken } \\ & =-a^2+((\frac{-13}{19})+\frac{3}{4})a+(\frac{-39}{76}) & \text{Neem samen} \\ &=-a^2+\frac{5}{76}a+(\frac{-39}{76}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(11-a)(\frac{19}{17}+q)& =(\color{red}{-a}+\color{orange}{11}).(\color{green}{q}+\color{blue}{\frac{19}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{19}{17})} + \color{orange}{(11)} . \color{green}{(q)} + \color{orange}{(11)} . \color{blue}{(\frac{19}{17})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{19}{17}a+11q+11.\frac{19}{17}& \text{Uitwerken } \\ & =-aq-\frac{19}{17}a+11q+\frac{209}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-13}{11})(\frac{-10}{14}+a)& =(\color{red}{p}+\color{orange}{\frac{-13}{11}}).(\color{green}{a}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{-13}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{11})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{5}{7}p-\frac{13}{11}a+\frac{13}{11}.\frac{5}{7}& \text{Uitwerken } \\ & =ap-\frac{5}{7}p-\frac{13}{11}a+\frac{65}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(x-\frac{3}{13})(b+\frac{18}{4})& =(\color{red}{x}+\color{orange}{\frac{-3}{13}}).(\color{green}{b}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-3}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{13})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{9}{2}x-\frac{3}{13}b-\frac{3}{13}.\frac{9}{2}& \text{Uitwerken } \\ & =bx+\frac{9}{2}x-\frac{3}{13}b-\frac{27}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-13}{16})((-7)+b)& =(\color{red}{q}+\color{orange}{\frac{-13}{16}}).(\color{green}{b}+\color{blue}{(-7)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-7)} + \color{orange}{(\frac{-13}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = bq-7q-\frac{13}{16}b+\frac{13}{16}.7& \text{Uitwerken } \\ & =bq-7q-\frac{13}{16}b+\frac{91}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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