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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{11}{15}-p)(\frac{3}{6}-p)& =(\color{red}{-p}+\color{orange}{\frac{11}{15}}).(\color{green}{-p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{11}{15})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{2}p-\frac{11}{15}p+\frac{11}{15}.\frac{1}{2}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{2})+(\frac{-11}{15}))p+\frac{11}{30} & \text{Neem samen} \\ &=p^2-\frac{37}{30}p+\frac{11}{30} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(b-\frac{-4}{20})(a-\frac{17}{17})& =(\color{red}{b}+\color{orange}{\frac{1}{5}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab-1b+\frac{1}{5}a-\frac{1}{5}.1& \text{Uitwerken } \\ & =ab-1b+\frac{1}{5}a-\frac{1}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+(-11))(a+\frac{-9}{8})& =(\color{red}{x}+\color{orange}{(-11)}).(\color{green}{a}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(-11)} . \color{green}{(a)} + \color{orange}{(-11)} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{9}{8}x-11a+11.\frac{9}{8}& \text{Uitwerken } \\ & =ax-\frac{9}{8}x-11a+\frac{99}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{12}{8}+b)(x-\frac{-9}{5})& =(\color{red}{b}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{9}{5}b+\frac{3}{2}x+\frac{3}{2}.\frac{9}{5}& \text{Uitwerken } \\ & =bx+\frac{9}{5}b+\frac{3}{2}x+\frac{27}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{5}{17}+b)(\frac{1}{4}+p)& =(\color{red}{b}+\color{orange}{\frac{5}{17}}).(\color{green}{p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{5}{17})} . \color{green}{(p)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{4}b+\frac{5}{17}p+\frac{5}{17}.\frac{1}{4}& \text{Uitwerken } \\ & =bp+\frac{1}{4}b+\frac{5}{17}p+\frac{5}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-1}{12}+p)(\frac{-13}{19}+q)& =(\color{red}{p}+\color{orange}{\frac{-1}{12}}).(\color{green}{q}+\color{blue}{\frac{-13}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{19})} + \color{orange}{(\frac{-1}{12})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{12})} . \color{blue}{(\frac{-13}{19})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{13}{19}p-\frac{1}{12}q+\frac{1}{12}.\frac{13}{19}& \text{Uitwerken } \\ & =pq-\frac{13}{19}p-\frac{1}{12}q+\frac{13}{228} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{16}+b)(b+\frac{-5}{13})& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{13})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{5}{13}b+\frac{1}{2}b-\frac{1}{2}.\frac{5}{13}& \text{Uitwerken } \\ & =b^2+((\frac{-5}{13})+\frac{1}{2})b-(\frac{-5}{26}) & \text{Neem samen} \\ &=b^2+\frac{3}{26}b-(\frac{-5}{26}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(b-\frac{-2}{2})(q-\frac{4}{10})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{2}{5}b+1q-1.\frac{2}{5}& \text{Uitwerken } \\ & =bq-\frac{2}{5}b+1q-\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-4}{6}+a)(a-\frac{-19}{4})& =(\color{red}{a}+\color{orange}{\frac{-2}{3}}).(\color{green}{a}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{19}{4}a-\frac{2}{3}a-\frac{2}{3}.\frac{19}{4}& \text{Uitwerken } \\ & =a^2+(\frac{19}{4}+(\frac{-2}{3}))a-(\frac{-38}{12}) & \text{Neem samen} \\ &=a^2+\frac{49}{12}a-(\frac{-38}{12}) & \text{Maak de som} \\ &=a^2+\frac{49}{12}a+\frac{19}{6} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-13}{12})(\frac{-16}{11}-a)& =(\color{red}{b}+\color{orange}{\frac{13}{12}}).(\color{green}{-a}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(\frac{13}{12})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{16}{11}b-\frac{13}{12}a-\frac{13}{12}.\frac{16}{11}& \text{Uitwerken } \\ & =-ab-\frac{16}{11}b-\frac{13}{12}a-\frac{208}{132} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{16}{11}b-\frac{13}{12}a-\frac{52}{33} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a-\frac{8}{20})(\frac{15}{18}-x)& =(\color{red}{a}+\color{orange}{\frac{-2}{5}}).(\color{green}{-x}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{5}{6}a+\frac{2}{5}x-\frac{2}{5}.\frac{5}{6}& \text{Uitwerken } \\ & =-ax+\frac{5}{6}a+\frac{2}{5}x-\frac{10}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{5}{6}a+\frac{2}{5}x-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{15}{17}+b)(\frac{-10}{14}+a)& =(\color{red}{b}+\color{orange}{\frac{15}{17}}).(\color{green}{a}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{15}{17})} . \color{green}{(a)} + \color{orange}{(\frac{15}{17})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{7}b+\frac{15}{17}a-\frac{15}{17}.\frac{5}{7}& \text{Uitwerken } \\ & =ab-\frac{5}{7}b+\frac{15}{17}a-\frac{75}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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