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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{-12}{17})(\frac{-2}{19}+x)& =(\color{red}{b}+\color{orange}{\frac{12}{17}}).(\color{green}{x}+\color{blue}{\frac{-2}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{19})} + \color{orange}{(\frac{12}{17})} . \color{green}{(x)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{-2}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{2}{19}b+\frac{12}{17}x-\frac{12}{17}.\frac{2}{19}& \text{Uitwerken } \\ & =bx-\frac{2}{19}b+\frac{12}{17}x-\frac{24}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{9}+b)(p-\frac{-19}{11})& =(\color{red}{b}+\color{orange}{\frac{8}{9}}).(\color{green}{p}+\color{blue}{\frac{19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{19}{11})} + \color{orange}{(\frac{8}{9})} . \color{green}{(p)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{19}{11})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{11}b+\frac{8}{9}p+\frac{8}{9}.\frac{19}{11}& \text{Uitwerken } \\ & =bp+\frac{19}{11}b+\frac{8}{9}p+\frac{152}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p+\frac{3}{8})(q+\frac{-12}{6})& =(\color{red}{p}+\color{orange}{\frac{3}{8}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{3}{8})} . \color{green}{(q)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pq-2p+\frac{3}{8}q-\frac{3}{8}.2& \text{Uitwerken } \\ & =pq-2p+\frac{3}{8}q-\frac{6}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-2p+\frac{3}{8}q-\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-2}{4}+x)(\frac{-11}{8}+x)& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{11}{8}x-\frac{1}{2}x+\frac{1}{2}.\frac{11}{8}& \text{Uitwerken } \\ & =x^2+((\frac{-11}{8})+(\frac{-1}{2}))x+\frac{11}{16} & \text{Neem samen} \\ &=x^2-\frac{15}{8}x+\frac{11}{16} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(b-\frac{-14}{10})(p-\frac{-17}{18})& =(\color{red}{b}+\color{orange}{\frac{7}{5}}).(\color{green}{p}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{7}{5})} . \color{green}{(p)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{17}{18}b+\frac{7}{5}p+\frac{7}{5}.\frac{17}{18}& \text{Uitwerken } \\ & =bp+\frac{17}{18}b+\frac{7}{5}p+\frac{119}{90} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-13}{4}+b)(\frac{3}{20}+b)& =(\color{red}{b}+\color{orange}{\frac{-13}{4}}).(\color{green}{b}+\color{blue}{\frac{3}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{3}{20})} + \color{orange}{(\frac{-13}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(\frac{3}{20})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{3}{20}b-\frac{13}{4}b-\frac{13}{4}.\frac{3}{20}& \text{Uitwerken } \\ & =b^2+(\frac{3}{20}+(\frac{-13}{4}))b-(\frac{-39}{80}) & \text{Neem samen} \\ &=b^2-\frac{62}{20}b-(\frac{-39}{80}) & \text{Maak de som} \\ &=b^2-\frac{31}{10}b+\frac{39}{80} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(a-(-16))(b-\frac{-19}{12})& =(\color{red}{a}+\color{orange}{16}).(\color{green}{b}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(16)} . \color{green}{(b)} + \color{orange}{(16)} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{19}{12}a+16b+16.\frac{19}{12}& \text{Uitwerken } \\ & =ab+\frac{19}{12}a+16b+\frac{304}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{19}{12}a+16b+\frac{76}{3} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{14}{6}+x)(a-\frac{-7}{2})& =(\color{red}{x}+\color{orange}{\frac{7}{3}}).(\color{green}{a}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{7}{3})} . \color{green}{(a)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{2}x+\frac{7}{3}a+\frac{7}{3}.\frac{7}{2}& \text{Uitwerken } \\ & =ax+\frac{7}{2}x+\frac{7}{3}a+\frac{49}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{6}{12}-q)(\frac{-18}{5}+p)& =(\color{red}{-q}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{-18}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-18}{5})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-18}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{18}{5}q+\frac{1}{2}p-\frac{1}{2}.\frac{18}{5}& \text{Uitwerken } \\ & =-pq+\frac{18}{5}q+\frac{1}{2}p-\frac{18}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{18}{5}q+\frac{1}{2}p-\frac{9}{5} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b+\frac{5}{3})(p+\frac{7}{16})& =(\color{red}{b}+\color{orange}{\frac{5}{3}}).(\color{green}{p}+\color{blue}{\frac{7}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{7}{16})} + \color{orange}{(\frac{5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{7}{16})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{16}b+\frac{5}{3}p+\frac{5}{3}.\frac{7}{16}& \text{Uitwerken } \\ & =bp+\frac{7}{16}b+\frac{5}{3}p+\frac{35}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q-\frac{-8}{9})(x-\frac{-17}{18})& =(\color{red}{q}+\color{orange}{\frac{8}{9}}).(\color{green}{x}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(\frac{8}{9})} . \color{green}{(x)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{17}{18}q+\frac{8}{9}x+\frac{8}{9}.\frac{17}{18}& \text{Uitwerken } \\ & =qx+\frac{17}{18}q+\frac{8}{9}x+\frac{136}{162} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{17}{18}q+\frac{8}{9}x+\frac{68}{81} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p+10)(q+\frac{-7}{19})& =(\color{red}{p}+\color{orange}{10}).(\color{green}{q}+\color{blue}{\frac{-7}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{19})} + \color{orange}{(10)} . \color{green}{(q)} + \color{orange}{(10)} . \color{blue}{(\frac{-7}{19})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{7}{19}p+10q-10.\frac{7}{19}& \text{Uitwerken } \\ & =pq-\frac{7}{19}p+10q-\frac{70}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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