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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{17}{6}+a)(b-\frac{-7}{9})& =(\color{red}{a}+\color{orange}{\frac{17}{6}}).(\color{green}{b}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{17}{6})} . \color{green}{(b)} + \color{orange}{(\frac{17}{6})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{7}{9}a+\frac{17}{6}b+\frac{17}{6}.\frac{7}{9}& \text{Uitwerken } \\ & =ab+\frac{7}{9}a+\frac{17}{6}b+\frac{119}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-13}{4})(\frac{6}{20}-q)& =(\color{red}{p}+\color{orange}{\frac{-13}{4}}).(\color{green}{-q}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{-13}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{3}{10}p+\frac{13}{4}q-\frac{13}{4}.\frac{3}{10}& \text{Uitwerken } \\ & =-pq+\frac{3}{10}p+\frac{13}{4}q-\frac{39}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p-\frac{-17}{7})(x-\frac{11}{11})& =(\color{red}{p}+\color{orange}{\frac{17}{7}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{17}{7})} . \color{green}{(x)} + \color{orange}{(\frac{17}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1p+\frac{17}{7}x-\frac{17}{7}.1& \text{Uitwerken } \\ & =px-1p+\frac{17}{7}x-\frac{17}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{2}{13})(\frac{16}{17}+x)& =(\color{red}{b}+\color{orange}{\frac{-2}{13}}).(\color{green}{x}+\color{blue}{\frac{16}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{16}{17})} + \color{orange}{(\frac{-2}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(\frac{16}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{16}{17}b-\frac{2}{13}x-\frac{2}{13}.\frac{16}{17}& \text{Uitwerken } \\ & =bx+\frac{16}{17}b-\frac{2}{13}x-\frac{32}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-7}{20}-p)(\frac{17}{9}-q)& =(\color{red}{-p}+\color{orange}{\frac{-7}{20}}).(\color{green}{-q}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(\frac{-7}{20})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{9}p+\frac{7}{20}q-\frac{7}{20}.\frac{17}{9}& \text{Uitwerken } \\ & =pq-\frac{17}{9}p+\frac{7}{20}q-\frac{119}{180} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-9}{3})(p-\frac{-5}{3})& =(\color{red}{p}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{5}{3}p-3p-3.\frac{5}{3}& \text{Uitwerken } \\ & =p^2+(\frac{5}{3}+(-3))p-(\frac{-15}{3}) & \text{Neem samen} \\ &=p^2-\frac{4}{3}p-(\frac{-15}{3}) & \text{Maak de som} \\ &=p^2-\frac{4}{3}p+5 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(x-\frac{6}{3})(x-\frac{-20}{13})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{20}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{20}{13})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{20}{13})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{20}{13}x-2x-2.\frac{20}{13}& \text{Uitwerken } \\ & =x^2+(\frac{20}{13}+(-2))x-(\frac{-40}{13}) & \text{Neem samen} \\ &=x^2-\frac{6}{13}x-(\frac{-40}{13}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(p+\frac{-9}{19})(p+\frac{-12}{20})& =(\color{red}{p}+\color{orange}{\frac{-9}{19}}).(\color{green}{p}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-9}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{19})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{3}{5}p-\frac{9}{19}p+\frac{9}{19}.\frac{3}{5}& \text{Uitwerken } \\ & =p^2+((\frac{-3}{5})+(\frac{-9}{19}))p+\frac{27}{95} & \text{Neem samen} \\ &=p^2-\frac{102}{95}p+\frac{27}{95} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-18}{7}-a)(\frac{11}{10}-q)& =(\color{red}{-a}+\color{orange}{\frac{-18}{7}}).(\color{green}{-q}+\color{blue}{\frac{11}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{10})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{11}{10})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{11}{10}a+\frac{18}{7}q-\frac{18}{7}.\frac{11}{10}& \text{Uitwerken } \\ & =aq-\frac{11}{10}a+\frac{18}{7}q-\frac{198}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{11}{10}a+\frac{18}{7}q-\frac{99}{35} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q+\frac{16}{6})(p+\frac{15}{12})& =(\color{red}{q}+\color{orange}{\frac{8}{3}}).(\color{green}{p}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{8}{3})} . \color{green}{(p)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{4}q+\frac{8}{3}p+\frac{8}{3}.\frac{5}{4}& \text{Uitwerken } \\ & =pq+\frac{5}{4}q+\frac{8}{3}p+\frac{40}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{5}{4}q+\frac{8}{3}p+\frac{10}{3} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q+\frac{-10}{20})(x-\frac{-2}{16})& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{8}q-\frac{1}{2}x-\frac{1}{2}.\frac{1}{8}& \text{Uitwerken } \\ & =qx+\frac{1}{8}q-\frac{1}{2}x-\frac{1}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{19}{8}-q)(\frac{-15}{13}-a)& =(\color{red}{-q}+\color{orange}{\frac{19}{8}}).(\color{green}{-a}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(\frac{19}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{15}{13}q-\frac{19}{8}a-\frac{19}{8}.\frac{15}{13}& \text{Uitwerken } \\ & =aq+\frac{15}{13}q-\frac{19}{8}a-\frac{285}{104} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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