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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{-16}{14})(x-\frac{10}{17})& =(\color{red}{a}+\color{orange}{\frac{8}{7}}).(\color{green}{x}+\color{blue}{\frac{-10}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{17})} + \color{orange}{(\frac{8}{7})} . \color{green}{(x)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-10}{17})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{10}{17}a+\frac{8}{7}x-\frac{8}{7}.\frac{10}{17}& \text{Uitwerken } \\ & =ax-\frac{10}{17}a+\frac{8}{7}x-\frac{80}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{15}{20}+x)(x+\frac{-20}{9})& =(\color{red}{x}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{\frac{-20}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-20}{9})} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-20}{9})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{20}{9}x+\frac{3}{4}x-\frac{3}{4}.\frac{20}{9}& \text{Uitwerken } \\ & =x^2+((\frac{-20}{9})+\frac{3}{4})x-(\frac{-60}{36}) & \text{Neem samen} \\ &=x^2-\frac{53}{36}x-(\frac{-60}{36}) & \text{Maak de som} \\ &=x^2-\frac{53}{36}x+\frac{5}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(\frac{1}{3}-p)(\frac{-2}{3}+a)& =(\color{red}{-p}+\color{orange}{\frac{1}{3}}).(\color{green}{a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{2}{3}p+\frac{1}{3}a-\frac{1}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =-ap+\frac{2}{3}p+\frac{1}{3}a-\frac{2}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-13}{14}-b)(\frac{1}{16}-p)& =(\color{red}{-b}+\color{orange}{\frac{-13}{14}}).(\color{green}{-p}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(\frac{-13}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{16}b+\frac{13}{14}p-\frac{13}{14}.\frac{1}{16}& \text{Uitwerken } \\ & =bp-\frac{1}{16}b+\frac{13}{14}p-\frac{13}{224} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{5}{15}-q)(p+\frac{-17}{6})& =(\color{red}{-q}+\color{orange}{\frac{1}{3}}).(\color{green}{p}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(\frac{1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{17}{6}q+\frac{1}{3}p-\frac{1}{3}.\frac{17}{6}& \text{Uitwerken } \\ & =-pq+\frac{17}{6}q+\frac{1}{3}p-\frac{17}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-11}{13})(p+\frac{14}{9})& =(\color{red}{a}+\color{orange}{\frac{11}{13}}).(\color{green}{p}+\color{blue}{\frac{14}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{14}{9})} + \color{orange}{(\frac{11}{13})} . \color{green}{(p)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(\frac{14}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{14}{9}a+\frac{11}{13}p+\frac{11}{13}.\frac{14}{9}& \text{Uitwerken } \\ & =ap+\frac{14}{9}a+\frac{11}{13}p+\frac{154}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{3}{13})(a+\frac{-13}{4})& =(\color{red}{b}+\color{orange}{\frac{-3}{13}}).(\color{green}{a}+\color{blue}{\frac{-13}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{4})} + \color{orange}{(\frac{-3}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{13})} . \color{blue}{(\frac{-13}{4})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{4}b-\frac{3}{13}a+\frac{3}{13}.\frac{13}{4}& \text{Uitwerken } \\ & =ab-\frac{13}{4}b-\frac{3}{13}a+\frac{39}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{13}{4}b-\frac{3}{13}a+\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-10}{15}+b)(\frac{-9}{15}+q)& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{q}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{5}b-\frac{2}{3}q+\frac{2}{3}.\frac{3}{5}& \text{Uitwerken } \\ & =bq-\frac{3}{5}b-\frac{2}{3}q+\frac{6}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{3}{5}b-\frac{2}{3}q+\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p+\frac{7}{8})(p-\frac{10}{13})& =(\color{red}{p}+\color{orange}{\frac{7}{8}}).(\color{green}{p}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{7}{8})} . \color{green}{(p)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{10}{13}p+\frac{7}{8}p-\frac{7}{8}.\frac{10}{13}& \text{Uitwerken } \\ & =p^2+((\frac{-10}{13})+\frac{7}{8})p-(\frac{-70}{104}) & \text{Neem samen} \\ &=p^2+\frac{11}{104}p-(\frac{-70}{104}) & \text{Maak de som} \\ &=p^2+\frac{11}{104}p+\frac{35}{52} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(a-\frac{20}{7})(\frac{-13}{10}-p)& =(\color{red}{a}+\color{orange}{\frac{-20}{7}}).(\color{green}{-p}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(\frac{-20}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-20}{7})} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{13}{10}a+\frac{20}{7}p+\frac{20}{7}.\frac{13}{10}& \text{Uitwerken } \\ & =-ap-\frac{13}{10}a+\frac{20}{7}p+\frac{260}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{13}{10}a+\frac{20}{7}p+\frac{26}{7} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(p-\frac{-1}{6})(\frac{-6}{3}-p)& =(\color{red}{p}+\color{orange}{\frac{1}{6}}).(\color{green}{-p}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{1}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -pp-2p-\frac{1}{6}p-\frac{1}{6}.2& \text{Uitwerken } \\ & =-p^2+((-2)+(\frac{-1}{6}))p-\frac{2}{6} & \text{Neem samen} \\ &=-p^2-\frac{13}{6}p-\frac{2}{6} & \text{Maak de som} \\ &=-p^2-\frac{13}{6}p-\frac{1}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-11}{12})(q+\frac{18}{3})& =(\color{red}{q}+\color{orange}{\frac{-11}{12}}).(\color{green}{q}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(6)} + \color{orange}{(\frac{-11}{12})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{12})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = qq+6q-\frac{11}{12}q-\frac{11}{12}.6& \text{Uitwerken } \\ & =q^2+(6+(\frac{-11}{12}))q-(\frac{-66}{12}) & \text{Neem samen} \\ &=q^2+\frac{61}{12}q-(\frac{-66}{12}) & \text{Maak de som} \\ &=q^2+\frac{61}{12}q+\frac{11}{2} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
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