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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-19}{19})(\frac{-20}{11}+a)& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-20}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{11})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-20}{11})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{20}{11}a-1a+1.\frac{20}{11}& \text{Uitwerken } \\ & =a^2+((\frac{-20}{11})+(-1))a+\frac{20}{11} & \text{Neem samen} \\ &=a^2-\frac{31}{11}a+\frac{20}{11} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(p-\frac{-10}{13})(a-\frac{18}{19})& =(\color{red}{p}+\color{orange}{\frac{10}{13}}).(\color{green}{a}+\color{blue}{\frac{-18}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-18}{19})} + \color{orange}{(\frac{10}{13})} . \color{green}{(a)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{-18}{19})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{18}{19}p+\frac{10}{13}a-\frac{10}{13}.\frac{18}{19}& \text{Uitwerken } \\ & =ap-\frac{18}{19}p+\frac{10}{13}a-\frac{180}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{-7}{6})(\frac{11}{18}-a)& =(\color{red}{a}+\color{orange}{\frac{-7}{6}}).(\color{green}{-a}+\color{blue}{\frac{11}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{11}{18})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{11}{18})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{11}{18}a+\frac{7}{6}a-\frac{7}{6}.\frac{11}{18}& \text{Uitwerken } \\ & =-a^2+(\frac{11}{18}+\frac{7}{6})a-\frac{77}{108} & \text{Neem samen} \\ &=-a^2+\frac{32}{18}a-\frac{77}{108} & \text{Maak de som} \\ &=-a^2+\frac{16}{9}a-\frac{77}{108} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-1}{2})(\frac{8}{10}+x)& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{4}{5}x+\frac{1}{2}x+\frac{1}{2}.\frac{4}{5}& \text{Uitwerken } \\ & =x^2+(\frac{4}{5}+\frac{1}{2})x+\frac{4}{10} & \text{Neem samen} \\ &=x^2+\frac{13}{10}x+\frac{4}{10} & \text{Maak de som} \\ &=x^2+\frac{13}{10}x+\frac{2}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(x-\frac{15}{20})(b-\frac{-9}{2})& =(\color{red}{x}+\color{orange}{\frac{-3}{4}}).(\color{green}{b}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{9}{2}x-\frac{3}{4}b-\frac{3}{4}.\frac{9}{2}& \text{Uitwerken } \\ & =bx+\frac{9}{2}x-\frac{3}{4}b-\frac{27}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{3}{4}+q)(a+\frac{-2}{14})& =(\color{red}{q}+\color{orange}{\frac{3}{4}}).(\color{green}{a}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{3}{4})} . \color{green}{(a)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{7}q+\frac{3}{4}a-\frac{3}{4}.\frac{1}{7}& \text{Uitwerken } \\ & =aq-\frac{1}{7}q+\frac{3}{4}a-\frac{3}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x+\frac{15}{15})(a-\frac{-8}{12})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{3}x+1a+1.\frac{2}{3}& \text{Uitwerken } \\ & =ax+\frac{2}{3}x+1a+\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x+\frac{-14}{16})(b+\frac{-3}{20})& =(\color{red}{x}+\color{orange}{\frac{-7}{8}}).(\color{green}{b}+\color{blue}{\frac{-3}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{20})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{-3}{20})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{20}x-\frac{7}{8}b+\frac{7}{8}.\frac{3}{20}& \text{Uitwerken } \\ & =bx-\frac{3}{20}x-\frac{7}{8}b+\frac{21}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-14}{9}+b)(\frac{-2}{20}-p)& =(\color{red}{b}+\color{orange}{\frac{-14}{9}}).(\color{green}{-p}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-14}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{10}b+\frac{14}{9}p+\frac{14}{9}.\frac{1}{10}& \text{Uitwerken } \\ & =-bp-\frac{1}{10}b+\frac{14}{9}p+\frac{14}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{1}{10}b+\frac{14}{9}p+\frac{7}{45} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b+\frac{-20}{13})(\frac{16}{17}-p)& =(\color{red}{b}+\color{orange}{\frac{-20}{13}}).(\color{green}{-p}+\color{blue}{\frac{16}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{16}{17})} + \color{orange}{(\frac{-20}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{-20}{13})} . \color{blue}{(\frac{16}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{16}{17}b+\frac{20}{13}p-\frac{20}{13}.\frac{16}{17}& \text{Uitwerken } \\ & =-bp+\frac{16}{17}b+\frac{20}{13}p-\frac{320}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-11}{11}-b)(q-\frac{-2}{16})& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{8}b-1q-1.\frac{1}{8}& \text{Uitwerken } \\ & =-bq-\frac{1}{8}b-1q-\frac{1}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{19}{20})(a-\frac{12}{19})& =(\color{red}{a}+\color{orange}{\frac{19}{20}}).(\color{green}{a}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(\frac{19}{20})} . \color{green}{(a)} + \color{orange}{(\frac{19}{20})} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{12}{19}a+\frac{19}{20}a-\frac{19}{20}.\frac{12}{19}& \text{Uitwerken } \\ & =a^2+((\frac{-12}{19})+\frac{19}{20})a-(\frac{-228}{380}) & \text{Neem samen} \\ &=a^2+\frac{121}{380}a-(\frac{-228}{380}) & \text{Maak de som} \\ &=a^2+\frac{121}{380}a+\frac{3}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
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