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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{-17}{12})(\frac{5}{16}+p)& =(\color{red}{b}+\color{orange}{\frac{-17}{12}}).(\color{green}{p}+\color{blue}{\frac{5}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{5}{16})} + \color{orange}{(\frac{-17}{12})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{12})} . \color{blue}{(\frac{5}{16})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{16}b-\frac{17}{12}p-\frac{17}{12}.\frac{5}{16}& \text{Uitwerken } \\ & =bp+\frac{5}{16}b-\frac{17}{12}p-\frac{85}{192} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{10}{17}-p)(\frac{15}{4}+p)& =(\color{red}{-p}+\color{orange}{\frac{10}{17}}).(\color{green}{p}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{10}{17})} . \color{green}{(p)} + \color{orange}{(\frac{10}{17})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{15}{4}p+\frac{10}{17}p+\frac{10}{17}.\frac{15}{4}& \text{Uitwerken } \\ & =-p^2+((\frac{-15}{4})+\frac{10}{17})p+(\frac{-150}{68}) & \text{Neem samen} \\ &=-p^2-\frac{215}{68}p+(\frac{-150}{68}) & \text{Maak de som} \\ &=-p^2-\frac{215}{68}p+(\frac{-75}{34}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(4+b)(p+\frac{-19}{11})& =(\color{red}{b}+\color{orange}{4}).(\color{green}{p}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(4)} . \color{green}{(p)} + \color{orange}{(4)} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{11}b+4p-4.\frac{19}{11}& \text{Uitwerken } \\ & =bp-\frac{19}{11}b+4p-\frac{76}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{14}{11}+x)(\frac{11}{20}+b)& =(\color{red}{x}+\color{orange}{\frac{14}{11}}).(\color{green}{b}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{14}{11})} . \color{green}{(b)} + \color{orange}{(\frac{14}{11})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{20}x+\frac{14}{11}b+\frac{14}{11}.\frac{11}{20}& \text{Uitwerken } \\ & =bx+\frac{11}{20}x+\frac{14}{11}b+\frac{154}{220} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{11}{20}x+\frac{14}{11}b+\frac{7}{10} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(b-\frac{-4}{4})(x-\frac{-11}{12})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{11}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{11}{12})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{11}{12})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{12}b+1x+1.\frac{11}{12}& \text{Uitwerken } \\ & =bx+\frac{11}{12}b+1x+\frac{11}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-13}{10})(\frac{-14}{15}-x)& =(\color{red}{a}+\color{orange}{\frac{-13}{10}}).(\color{green}{-x}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(\frac{-13}{10})} . \color{green}{(-x)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{14}{15}a+\frac{13}{10}x+\frac{13}{10}.\frac{14}{15}& \text{Uitwerken } \\ & =-ax-\frac{14}{15}a+\frac{13}{10}x+\frac{182}{150} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{14}{15}a+\frac{13}{10}x+\frac{91}{75} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-6}{7}-b)(\frac{16}{14}-b)& =(\color{red}{-b}+\color{orange}{\frac{-6}{7}}).(\color{green}{-b}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{8}{7}b+\frac{6}{7}b-\frac{6}{7}.\frac{8}{7}& \text{Uitwerken } \\ & =b^2+((\frac{-8}{7})+\frac{6}{7})b-(\frac{-48}{49}) & \text{Neem samen} \\ &=b^2-\frac{2}{7}b-(\frac{-48}{49}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(p+\frac{-1}{13})(a+\frac{7}{15})& =(\color{red}{p}+\color{orange}{\frac{-1}{13}}).(\color{green}{a}+\color{blue}{\frac{7}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{7}{15})} + \color{orange}{(\frac{-1}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{13})} . \color{blue}{(\frac{7}{15})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{7}{15}p-\frac{1}{13}a-\frac{1}{13}.\frac{7}{15}& \text{Uitwerken } \\ & =ap+\frac{7}{15}p-\frac{1}{13}a-\frac{7}{195} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-1}{2}-a)(q+\frac{-9}{18})& =(\color{red}{-a}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{2}a-\frac{1}{2}q+\frac{1}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =-aq+\frac{1}{2}a-\frac{1}{2}q+\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p-\frac{7}{13})(\frac{4}{3}+p)& =(\color{red}{p}+\color{orange}{\frac{-7}{13}}).(\color{green}{p}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-7}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{13})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{4}{3}p-\frac{7}{13}p-\frac{7}{13}.\frac{4}{3}& \text{Uitwerken } \\ & =p^2+(\frac{4}{3}+(\frac{-7}{13}))p-(\frac{-28}{39}) & \text{Neem samen} \\ &=p^2+\frac{31}{39}p-(\frac{-28}{39}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{3}{18}-b)(x-\frac{17}{14})& =(\color{red}{-b}+\color{orange}{\frac{1}{6}}).(\color{green}{x}+\color{blue}{\frac{-17}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-17}{14})} + \color{orange}{(\frac{1}{6})} . \color{green}{(x)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-17}{14})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{17}{14}b+\frac{1}{6}x-\frac{1}{6}.\frac{17}{14}& \text{Uitwerken } \\ & =-bx+\frac{17}{14}b+\frac{1}{6}x-\frac{17}{84} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-13}{18})(\frac{-15}{14}-p)& =(\color{red}{q}+\color{orange}{\frac{-13}{18}}).(\color{green}{-p}+\color{blue}{\frac{-15}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{14})} + \color{orange}{(\frac{-13}{18})} . \color{green}{(-p)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(\frac{-15}{14})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{15}{14}q+\frac{13}{18}p+\frac{13}{18}.\frac{15}{14}& \text{Uitwerken } \\ & =-pq-\frac{15}{14}q+\frac{13}{18}p+\frac{195}{252} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{15}{14}q+\frac{13}{18}p+\frac{65}{84} & \text{Vereenvoudig} \\\end{align}\)
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