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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-15}{10})(x-\frac{-17}{14})& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{x}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{14}b-\frac{3}{2}x-\frac{3}{2}.\frac{17}{14}& \text{Uitwerken } \\ & =bx+\frac{17}{14}b-\frac{3}{2}x-\frac{51}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{19}{8}-a)(\frac{-14}{6}-b)& =(\color{red}{-a}+\color{orange}{\frac{19}{8}}).(\color{green}{-b}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{19}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{7}{3}a-\frac{19}{8}b-\frac{19}{8}.\frac{7}{3}& \text{Uitwerken } \\ & =ab+\frac{7}{3}a-\frac{19}{8}b-\frac{133}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-10}{9}-q)(p+\frac{-9}{7})& =(\color{red}{-q}+\color{orange}{\frac{-10}{9}}).(\color{green}{p}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{9}{7}q-\frac{10}{9}p+\frac{10}{9}.\frac{9}{7}& \text{Uitwerken } \\ & =-pq+\frac{9}{7}q-\frac{10}{9}p+\frac{90}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{9}{7}q-\frac{10}{9}p+\frac{10}{7} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{13}{12}+p)(p-\frac{-11}{16})& =(\color{red}{p}+\color{orange}{\frac{13}{12}}).(\color{green}{p}+\color{blue}{\frac{11}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{11}{16})} + \color{orange}{(\frac{13}{12})} . \color{green}{(p)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(\frac{11}{16})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{11}{16}p+\frac{13}{12}p+\frac{13}{12}.\frac{11}{16}& \text{Uitwerken } \\ & =p^2+(\frac{11}{16}+\frac{13}{12})p+\frac{143}{192} & \text{Neem samen} \\ &=p^2+\frac{85}{48}p+\frac{143}{192} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-13}{7}-x)(\frac{-19}{7}+b)& =(\color{red}{-x}+\color{orange}{\frac{-13}{7}}).(\color{green}{b}+\color{blue}{\frac{-19}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-19}{7})} + \color{orange}{(\frac{-13}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{7})} . \color{blue}{(\frac{-19}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{19}{7}x-\frac{13}{7}b+\frac{13}{7}.\frac{19}{7}& \text{Uitwerken } \\ & =-bx+\frac{19}{7}x-\frac{13}{7}b+\frac{247}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{-5}{6})(\frac{-3}{4}-b)& =(\color{red}{b}+\color{orange}{\frac{-5}{6}}).(\color{green}{-b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{3}{4}b+\frac{5}{6}b+\frac{5}{6}.\frac{3}{4}& \text{Uitwerken } \\ & =-b^2+((\frac{-3}{4})+\frac{5}{6})b+(\frac{-15}{24}) & \text{Neem samen} \\ &=-b^2+\frac{1}{12}b+(\frac{-15}{24}) & \text{Maak de som} \\ &=-b^2+\frac{1}{12}b+(\frac{-5}{8}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-8}{9})(\frac{3}{14}-x)& =(\color{red}{b}+\color{orange}{\frac{8}{9}}).(\color{green}{-x}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(\frac{8}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{3}{14}b-\frac{8}{9}x+\frac{8}{9}.\frac{3}{14}& \text{Uitwerken } \\ & =-bx+\frac{3}{14}b-\frac{8}{9}x+\frac{24}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{3}{14}b-\frac{8}{9}x+\frac{4}{21} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b+\frac{9}{19})(\frac{20}{16}+a)& =(\color{red}{b}+\color{orange}{\frac{9}{19}}).(\color{green}{a}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{9}{19})} . \color{green}{(a)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{4}b+\frac{9}{19}a+\frac{9}{19}.\frac{5}{4}& \text{Uitwerken } \\ & =ab+\frac{5}{4}b+\frac{9}{19}a+\frac{45}{76} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-1}{17}+x)(a+\frac{-10}{10})& =(\color{red}{x}+\color{orange}{\frac{-1}{17}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1x-\frac{1}{17}a+\frac{1}{17}.1& \text{Uitwerken } \\ & =ax-1x-\frac{1}{17}a+\frac{1}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{11}{10})(a+\frac{-6}{3})& =(\color{red}{p}+\color{orange}{\frac{11}{10}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{11}{10})} . \color{green}{(a)} + \color{orange}{(\frac{11}{10})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ap-2p+\frac{11}{10}a-\frac{11}{10}.2& \text{Uitwerken } \\ & =ap-2p+\frac{11}{10}a-\frac{22}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-2p+\frac{11}{10}a-\frac{11}{5} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(b+\frac{17}{7})(\frac{2}{18}-a)& =(\color{red}{b}+\color{orange}{\frac{17}{7}}).(\color{green}{-a}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{17}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{17}{7})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{9}b-\frac{17}{7}a+\frac{17}{7}.\frac{1}{9}& \text{Uitwerken } \\ & =-ab+\frac{1}{9}b-\frac{17}{7}a+\frac{17}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-12}{7}-q)(b+\frac{-5}{10})& =(\color{red}{-q}+\color{orange}{\frac{-12}{7}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-12}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-12}{7})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{2}q-\frac{12}{7}b+\frac{12}{7}.\frac{1}{2}& \text{Uitwerken } \\ & =-bq+\frac{1}{2}q-\frac{12}{7}b+\frac{12}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{1}{2}q-\frac{12}{7}b+\frac{6}{7} & \text{Vereenvoudig} \\\end{align}\)
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