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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{6}{11}+q)(\frac{6}{11}-x)& =(\color{red}{q}+\color{orange}{\frac{6}{11}}).(\color{green}{-x}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{6}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{6}{11})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{6}{11}q-\frac{6}{11}x+\frac{6}{11}.\frac{6}{11}& \text{Uitwerken } \\ & =-qx+\frac{6}{11}q-\frac{6}{11}x+\frac{36}{121} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{19}{17}+a)(\frac{-5}{10}+x)& =(\color{red}{a}+\color{orange}{\frac{19}{17}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{19}{17})} . \color{green}{(x)} + \color{orange}{(\frac{19}{17})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{2}a+\frac{19}{17}x-\frac{19}{17}.\frac{1}{2}& \text{Uitwerken } \\ & =ax-\frac{1}{2}a+\frac{19}{17}x-\frac{19}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-6}{19}+x)(x+\frac{-14}{13})& =(\color{red}{x}+\color{orange}{\frac{-6}{19}}).(\color{green}{x}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(\frac{-6}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-6}{19})} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{14}{13}x-\frac{6}{19}x+\frac{6}{19}.\frac{14}{13}& \text{Uitwerken } \\ & =x^2+((\frac{-14}{13})+(\frac{-6}{19}))x+\frac{84}{247} & \text{Neem samen} \\ &=x^2-\frac{344}{247}x+\frac{84}{247} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-6}{13})(\frac{12}{11}-a)& =(\color{red}{a}+\color{orange}{\frac{6}{13}}).(\color{green}{-a}+\color{blue}{\frac{12}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{12}{11})} + \color{orange}{(\frac{6}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{6}{13})} . \color{blue}{(\frac{12}{11})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{12}{11}a-\frac{6}{13}a+\frac{6}{13}.\frac{12}{11}& \text{Uitwerken } \\ & =-a^2+(\frac{12}{11}+(\frac{-6}{13}))a+(\frac{-72}{143}) & \text{Neem samen} \\ &=-a^2+\frac{90}{143}a+(\frac{-72}{143}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(q+\frac{11}{15})(a+\frac{1}{14})& =(\color{red}{q}+\color{orange}{\frac{11}{15}}).(\color{green}{a}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(\frac{11}{15})} . \color{green}{(a)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{14}q+\frac{11}{15}a+\frac{11}{15}.\frac{1}{14}& \text{Uitwerken } \\ & =aq+\frac{1}{14}q+\frac{11}{15}a+\frac{11}{210} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q-\frac{6}{7})(a-\frac{-6}{11})& =(\color{red}{q}+\color{orange}{\frac{-6}{7}}).(\color{green}{a}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{6}{11}q-\frac{6}{7}a-\frac{6}{7}.\frac{6}{11}& \text{Uitwerken } \\ & =aq+\frac{6}{11}q-\frac{6}{7}a-\frac{36}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-11}{9}-b)(\frac{-1}{15}+x)& =(\color{red}{-b}+\color{orange}{\frac{-11}{9}}).(\color{green}{x}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(\frac{-11}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{15}b-\frac{11}{9}x+\frac{11}{9}.\frac{1}{15}& \text{Uitwerken } \\ & =-bx+\frac{1}{15}b-\frac{11}{9}x+\frac{11}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{13}{5})(\frac{-2}{13}-a)& =(\color{red}{p}+\color{orange}{\frac{13}{5}}).(\color{green}{-a}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(\frac{13}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{5})} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{2}{13}p-\frac{13}{5}a-\frac{13}{5}.\frac{2}{13}& \text{Uitwerken } \\ & =-ap-\frac{2}{13}p-\frac{13}{5}a-\frac{26}{65} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{2}{13}p-\frac{13}{5}a-\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{2}{12})(\frac{-9}{12}-a)& =(\color{red}{b}+\color{orange}{\frac{-1}{6}}).(\color{green}{-a}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{3}{4}b+\frac{1}{6}a+\frac{1}{6}.\frac{3}{4}& \text{Uitwerken } \\ & =-ab-\frac{3}{4}b+\frac{1}{6}a+\frac{3}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{3}{4}b+\frac{1}{6}a+\frac{1}{8} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-11}{14}+p)(\frac{-8}{4}-x)& =(\color{red}{p}+\color{orange}{\frac{-11}{14}}).(\color{green}{-x}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-11}{14})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -px-2p+\frac{11}{14}x+\frac{11}{14}.2& \text{Uitwerken } \\ & =-px-2p+\frac{11}{14}x+\frac{22}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-2p+\frac{11}{14}x+\frac{11}{7} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b+\frac{-19}{19})(x+\frac{10}{4})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{2}b-1x-1.\frac{5}{2}& \text{Uitwerken } \\ & =bx+\frac{5}{2}b-1x-\frac{5}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-1}{2})(b-\frac{19}{14})& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{-19}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{14})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-19}{14})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{19}{14}b+\frac{1}{2}b-\frac{1}{2}.\frac{19}{14}& \text{Uitwerken } \\ & =b^2+((\frac{-19}{14})+\frac{1}{2})b-(\frac{-19}{28}) & \text{Neem samen} \\ &=b^2-\frac{12}{14}b-(\frac{-19}{28}) & \text{Maak de som} \\ &=b^2-\frac{6}{7}b+\frac{19}{28} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
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