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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-17}{3}+b)(\frac{14}{18}+x)& =(\color{red}{b}+\color{orange}{\frac{-17}{3}}).(\color{green}{x}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{9}b-\frac{17}{3}x-\frac{17}{3}.\frac{7}{9}& \text{Uitwerken } \\ & =bx+\frac{7}{9}b-\frac{17}{3}x-\frac{119}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-9}{17})(\frac{-16}{19}+x)& =(\color{red}{a}+\color{orange}{\frac{9}{17}}).(\color{green}{x}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{9}{17})} . \color{green}{(x)} + \color{orange}{(\frac{9}{17})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{16}{19}a+\frac{9}{17}x-\frac{9}{17}.\frac{16}{19}& \text{Uitwerken } \\ & =ax-\frac{16}{19}a+\frac{9}{17}x-\frac{144}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-18}{19}+b)(x-\frac{4}{14})& =(\color{red}{b}+\color{orange}{\frac{-18}{19}}).(\color{green}{x}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{-18}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{2}{7}b-\frac{18}{19}x+\frac{18}{19}.\frac{2}{7}& \text{Uitwerken } \\ & =bx-\frac{2}{7}b-\frac{18}{19}x+\frac{36}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{16}{9})(\frac{11}{19}+b)& =(\color{red}{q}+\color{orange}{\frac{16}{9}}).(\color{green}{b}+\color{blue}{\frac{11}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{11}{19})} + \color{orange}{(\frac{16}{9})} . \color{green}{(b)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(\frac{11}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{11}{19}q+\frac{16}{9}b+\frac{16}{9}.\frac{11}{19}& \text{Uitwerken } \\ & =bq+\frac{11}{19}q+\frac{16}{9}b+\frac{176}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-16}{17}-b)(\frac{16}{4}-q)& =(\color{red}{-b}+\color{orange}{\frac{-16}{17}}).(\color{green}{-q}+\color{blue}{4})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(4)} + \color{orange}{(\frac{-16}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{-16}{17})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = bq-4b+\frac{16}{17}q-\frac{16}{17}.4& \text{Uitwerken } \\ & =bq-4b+\frac{16}{17}q-\frac{64}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-10)(x+\frac{-2}{20})& =(\color{red}{p}+\color{orange}{(-10)}).(\color{green}{x}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(-10)} . \color{green}{(x)} + \color{orange}{(-10)} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{10}p-10x+10.\frac{1}{10}& \text{Uitwerken } \\ & =px-\frac{1}{10}p-10x+\frac{10}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{1}{10}p-10x+1 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{17}{7}-x)(\frac{-9}{16}-x)& =(\color{red}{-x}+\color{orange}{\frac{17}{7}}).(\color{green}{-x}+\color{blue}{\frac{-9}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(\frac{-9}{16})} + \color{orange}{(\frac{17}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{7})} . \color{blue}{(\frac{-9}{16})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{9}{16}x-\frac{17}{7}x-\frac{17}{7}.\frac{9}{16}& \text{Uitwerken } \\ & =x^2+(\frac{9}{16}+(\frac{-17}{7}))x-(\frac{-153}{112}) & \text{Neem samen} \\ &=x^2-\frac{209}{112}x-(\frac{-153}{112}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-16}{4}+a)(a+\frac{9}{4})& =(\color{red}{a}+\color{orange}{(-4)}).(\color{green}{a}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(-4)} . \color{green}{(a)} + \color{orange}{(-4)} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{9}{4}a-4a-4.\frac{9}{4}& \text{Uitwerken } \\ & =a^2+(\frac{9}{4}+(-4))a-(\frac{-36}{4}) & \text{Neem samen} \\ &=a^2-\frac{7}{4}a-(\frac{-36}{4}) & \text{Maak de som} \\ &=a^2-\frac{7}{4}a+9 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(\frac{6}{10}+b)(a+\frac{19}{3})& =(\color{red}{b}+\color{orange}{\frac{3}{5}}).(\color{green}{a}+\color{blue}{\frac{19}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{19}{3})} + \color{orange}{(\frac{3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{19}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{19}{3}b+\frac{3}{5}a+\frac{3}{5}.\frac{19}{3}& \text{Uitwerken } \\ & =ab+\frac{19}{3}b+\frac{3}{5}a+\frac{57}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{19}{3}b+\frac{3}{5}a+\frac{19}{5} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{11}{2}+a)(13-a)& =(\color{red}{a}+\color{orange}{\frac{11}{2}}).(\color{green}{-a}+\color{blue}{13})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(13)} + \color{orange}{(\frac{11}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{11}{2})} . \color{blue}{(13)}& \text{Boogjes en uitschrijven} \\ & = -aa+13a-\frac{11}{2}a+\frac{11}{2}.13& \text{Uitwerken } \\ & =-a^2+(13+(\frac{-11}{2}))a+(\frac{-143}{2}) & \text{Neem samen} \\ &=-a^2+\frac{15}{2}a+(\frac{-143}{2}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(x-(-3))(\frac{17}{10}+a)& =(\color{red}{x}+\color{orange}{3}).(\color{green}{a}+\color{blue}{\frac{17}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{17}{10})} + \color{orange}{(3)} . \color{green}{(a)} + \color{orange}{(3)} . \color{blue}{(\frac{17}{10})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{10}x+3a+3.\frac{17}{10}& \text{Uitwerken } \\ & =ax+\frac{17}{10}x+3a+\frac{51}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{17}{20}+q)(\frac{18}{20}+p)& =(\color{red}{q}+\color{orange}{\frac{17}{20}}).(\color{green}{p}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{17}{20})} . \color{green}{(p)} + \color{orange}{(\frac{17}{20})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{9}{10}q+\frac{17}{20}p+\frac{17}{20}.\frac{9}{10}& \text{Uitwerken } \\ & =pq+\frac{9}{10}q+\frac{17}{20}p+\frac{153}{200} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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