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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{10}{12})(\frac{-19}{8}+q)& =(\color{red}{a}+\color{orange}{\frac{-5}{6}}).(\color{green}{q}+\color{blue}{\frac{-19}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{8})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-19}{8})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{19}{8}a-\frac{5}{6}q+\frac{5}{6}.\frac{19}{8}& \text{Uitwerken } \\ & =aq-\frac{19}{8}a-\frac{5}{6}q+\frac{95}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-18}{6}+q)(p+\frac{13}{4})& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{13}{4}q-3p-3.\frac{13}{4}& \text{Uitwerken } \\ & =pq+\frac{13}{4}q-3p-\frac{39}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(q-\frac{20}{5})(\frac{-11}{14}-b)& =(\color{red}{q}+\color{orange}{(-4)}).(\color{green}{-b}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(-4)} . \color{green}{(-b)} + \color{orange}{(-4)} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{11}{14}q+4b+4.\frac{11}{14}& \text{Uitwerken } \\ & =-bq-\frac{11}{14}q+4b+\frac{44}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{11}{14}q+4b+\frac{22}{7} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-4}{10}+a)(\frac{-9}{20}-p)& =(\color{red}{a}+\color{orange}{\frac{-2}{5}}).(\color{green}{-p}+\color{blue}{\frac{-9}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{20})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-9}{20})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{9}{20}a+\frac{2}{5}p+\frac{2}{5}.\frac{9}{20}& \text{Uitwerken } \\ & =-ap-\frac{9}{20}a+\frac{2}{5}p+\frac{18}{100} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{9}{20}a+\frac{2}{5}p+\frac{9}{50} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-10}{18}+x)(\frac{1}{3}-a)& =(\color{red}{x}+\color{orange}{\frac{-5}{9}}).(\color{green}{-a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{3}x+\frac{5}{9}a-\frac{5}{9}.\frac{1}{3}& \text{Uitwerken } \\ & =-ax+\frac{1}{3}x+\frac{5}{9}a-\frac{5}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-4}{13}-q)(p+\frac{1}{19})& =(\color{red}{-q}+\color{orange}{\frac{-4}{13}}).(\color{green}{p}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{19}q-\frac{4}{13}p-\frac{4}{13}.\frac{1}{19}& \text{Uitwerken } \\ & =-pq-\frac{1}{19}q-\frac{4}{13}p-\frac{4}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x+\frac{-15}{20})(p+\frac{-12}{19})& =(\color{red}{x}+\color{orange}{\frac{-3}{4}}).(\color{green}{p}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{12}{19}x-\frac{3}{4}p+\frac{3}{4}.\frac{12}{19}& \text{Uitwerken } \\ & =px-\frac{12}{19}x-\frac{3}{4}p+\frac{36}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{12}{19}x-\frac{3}{4}p+\frac{9}{19} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x-\frac{20}{15})(\frac{1}{16}+p)& =(\color{red}{x}+\color{orange}{\frac{-4}{3}}).(\color{green}{p}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{16}x-\frac{4}{3}p-\frac{4}{3}.\frac{1}{16}& \text{Uitwerken } \\ & =px+\frac{1}{16}x-\frac{4}{3}p-\frac{4}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{1}{16}x-\frac{4}{3}p-\frac{1}{12} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p-\frac{7}{15})(b-\frac{-12}{17})& =(\color{red}{p}+\color{orange}{\frac{-7}{15}}).(\color{green}{b}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{-7}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{12}{17}p-\frac{7}{15}b-\frac{7}{15}.\frac{12}{17}& \text{Uitwerken } \\ & =bp+\frac{12}{17}p-\frac{7}{15}b-\frac{84}{255} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{12}{17}p-\frac{7}{15}b-\frac{28}{85} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p+\frac{11}{3})(b-\frac{18}{6})& =(\color{red}{p}+\color{orange}{\frac{11}{3}}).(\color{green}{b}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-3)} + \color{orange}{(\frac{11}{3})} . \color{green}{(b)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bp-3p+\frac{11}{3}b-\frac{11}{3}.3& \text{Uitwerken } \\ & =bp-3p+\frac{11}{3}b-\frac{33}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-3p+\frac{11}{3}b-11 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{7}{17}+q)(\frac{-6}{18}+x)& =(\color{red}{q}+\color{orange}{\frac{7}{17}}).(\color{green}{x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{7}{17})} . \color{green}{(x)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{3}q+\frac{7}{17}x-\frac{7}{17}.\frac{1}{3}& \text{Uitwerken } \\ & =qx-\frac{1}{3}q+\frac{7}{17}x-\frac{7}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{20}{10})(\frac{5}{20}+a)& =(\color{red}{a}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{4}a+2a+2.\frac{1}{4}& \text{Uitwerken } \\ & =a^2+(\frac{1}{4}+2)a+\frac{2}{4} & \text{Neem samen} \\ &=a^2+\frac{9}{4}a+\frac{2}{4} & \text{Maak de som} \\ &=a^2+\frac{9}{4}a+\frac{1}{2} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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