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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-20}{14}+p)(\frac{18}{9}+q)& =(\color{red}{p}+\color{orange}{\frac{-10}{7}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{-10}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = pq+2p-\frac{10}{7}q-\frac{10}{7}.2& \text{Uitwerken } \\ & =pq+2p-\frac{10}{7}q-\frac{20}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(b-\frac{6}{18})(p-\frac{-7}{10})& =(\color{red}{b}+\color{orange}{\frac{-1}{3}}).(\color{green}{p}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{10}b-\frac{1}{3}p-\frac{1}{3}.\frac{7}{10}& \text{Uitwerken } \\ & =bp+\frac{7}{10}b-\frac{1}{3}p-\frac{7}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-10}{7}-p)(\frac{17}{18}+p)& =(\color{red}{-p}+\color{orange}{\frac{-10}{7}}).(\color{green}{p}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{17}{18}p-\frac{10}{7}p-\frac{10}{7}.\frac{17}{18}& \text{Uitwerken } \\ & =-p^2+((\frac{-17}{18})+(\frac{-10}{7}))p-\frac{170}{126} & \text{Neem samen} \\ &=-p^2-\frac{299}{126}p-\frac{170}{126} & \text{Maak de som} \\ &=-p^2-\frac{299}{126}p-\frac{85}{63} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(b-10)(b-\frac{-11}{18})& =(\color{red}{b}+\color{orange}{(-10)}).(\color{green}{b}+\color{blue}{\frac{11}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{11}{18})} + \color{orange}{(-10)} . \color{green}{(b)} + \color{orange}{(-10)} . \color{blue}{(\frac{11}{18})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{11}{18}b-10b-10.\frac{11}{18}& \text{Uitwerken } \\ & =b^2+(\frac{11}{18}+(-10))b-(\frac{-110}{18}) & \text{Neem samen} \\ &=b^2-\frac{169}{18}b-(\frac{-110}{18}) & \text{Maak de som} \\ &=b^2-\frac{169}{18}b+\frac{55}{9} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(q-\frac{6}{2})(b+\frac{17}{5})& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{17}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{17}{5})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{17}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{5}q-3b-3.\frac{17}{5}& \text{Uitwerken } \\ & =bq+\frac{17}{5}q-3b-\frac{51}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-12}{17}+a)(\frac{2}{6}+a)& =(\color{red}{a}+\color{orange}{\frac{-12}{17}}).(\color{green}{a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-12}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-12}{17})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{3}a-\frac{12}{17}a-\frac{12}{17}.\frac{1}{3}& \text{Uitwerken } \\ & =a^2+(\frac{1}{3}+(\frac{-12}{17}))a-(\frac{-12}{51}) & \text{Neem samen} \\ &=a^2-\frac{19}{51}a-(\frac{-12}{51}) & \text{Maak de som} \\ &=a^2-\frac{19}{51}a+\frac{4}{17} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(\frac{6}{17}-p)(\frac{-7}{6}-x)& =(\color{red}{-p}+\color{orange}{\frac{6}{17}}).(\color{green}{-x}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(\frac{6}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{6}{17})} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{7}{6}p-\frac{6}{17}x-\frac{6}{17}.\frac{7}{6}& \text{Uitwerken } \\ & =px+\frac{7}{6}p-\frac{6}{17}x-\frac{42}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{7}{6}p-\frac{6}{17}x-\frac{7}{17} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-14}{16}+a)(\frac{-16}{16}-b)& =(\color{red}{a}+\color{orange}{\frac{-7}{8}}).(\color{green}{-b}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-7}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ab-1a+\frac{7}{8}b+\frac{7}{8}.1& \text{Uitwerken } \\ & =-ab-1a+\frac{7}{8}b+\frac{7}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-(-18))(x-\frac{17}{7})& =(\color{red}{b}+\color{orange}{18}).(\color{green}{x}+\color{blue}{\frac{-17}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{7})} + \color{orange}{(18)} . \color{green}{(x)} + \color{orange}{(18)} . \color{blue}{(\frac{-17}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{17}{7}b+18x-18.\frac{17}{7}& \text{Uitwerken } \\ & =bx-\frac{17}{7}b+18x-\frac{306}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a-\frac{13}{18})(\frac{5}{6}-p)& =(\color{red}{a}+\color{orange}{\frac{-13}{18}}).(\color{green}{-p}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-13}{18})} . \color{green}{(-p)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{5}{6}a+\frac{13}{18}p-\frac{13}{18}.\frac{5}{6}& \text{Uitwerken } \\ & =-ap+\frac{5}{6}a+\frac{13}{18}p-\frac{65}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-16}{5}-q)(\frac{-5}{7}-b)& =(\color{red}{-q}+\color{orange}{\frac{-16}{5}}).(\color{green}{-b}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{-16}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-16}{5})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{7}q+\frac{16}{5}b+\frac{16}{5}.\frac{5}{7}& \text{Uitwerken } \\ & =bq+\frac{5}{7}q+\frac{16}{5}b+\frac{80}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{5}{7}q+\frac{16}{5}b+\frac{16}{7} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(x+\frac{2}{11})(\frac{9}{4}+a)& =(\color{red}{x}+\color{orange}{\frac{2}{11}}).(\color{green}{a}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{2}{11})} . \color{green}{(a)} + \color{orange}{(\frac{2}{11})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{4}x+\frac{2}{11}a+\frac{2}{11}.\frac{9}{4}& \text{Uitwerken } \\ & =ax+\frac{9}{4}x+\frac{2}{11}a+\frac{18}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{9}{4}x+\frac{2}{11}a+\frac{9}{22} & \text{Vereenvoudig} \\\end{align}\)
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