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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{-13}{4})(x-\frac{4}{4})& =(\color{red}{a}+\color{orange}{\frac{13}{4}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{13}{4})} . \color{green}{(x)} + \color{orange}{(\frac{13}{4})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1a+\frac{13}{4}x-\frac{13}{4}.1& \text{Uitwerken } \\ & =ax-1a+\frac{13}{4}x-\frac{13}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x-\frac{19}{2})(a+\frac{-1}{2})& =(\color{red}{x}+\color{orange}{\frac{-19}{2}}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-19}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{2}x-\frac{19}{2}a+\frac{19}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =ax-\frac{1}{2}x-\frac{19}{2}a+\frac{19}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x-\frac{-6}{8})(\frac{20}{18}+p)& =(\color{red}{x}+\color{orange}{\frac{3}{4}}).(\color{green}{p}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{10}{9}x+\frac{3}{4}p+\frac{3}{4}.\frac{10}{9}& \text{Uitwerken } \\ & =px+\frac{10}{9}x+\frac{3}{4}p+\frac{30}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{10}{9}x+\frac{3}{4}p+\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-3}{8}+x)(\frac{5}{12}+x)& =(\color{red}{x}+\color{orange}{\frac{-3}{8}}).(\color{green}{x}+\color{blue}{\frac{5}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{5}{12})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{5}{12})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{5}{12}x-\frac{3}{8}x-\frac{3}{8}.\frac{5}{12}& \text{Uitwerken } \\ & =x^2+(\frac{5}{12}+(\frac{-3}{8}))x-(\frac{-15}{96}) & \text{Neem samen} \\ &=x^2+\frac{1}{24}x-(\frac{-15}{96}) & \text{Maak de som} \\ &=x^2+\frac{1}{24}x+\frac{5}{32} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(\frac{18}{16}+b)(\frac{-12}{18}-x)& =(\color{red}{b}+\color{orange}{\frac{9}{8}}).(\color{green}{-x}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{9}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{2}{3}b-\frac{9}{8}x-\frac{9}{8}.\frac{2}{3}& \text{Uitwerken } \\ & =-bx-\frac{2}{3}b-\frac{9}{8}x-\frac{18}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{2}{3}b-\frac{9}{8}x-\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{19}{19}-b)(x+\frac{17}{10})& =(\color{red}{-b}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{17}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{17}{10})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{17}{10})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{17}{10}b+1x+1.\frac{17}{10}& \text{Uitwerken } \\ & =-bx-\frac{17}{10}b+1x+\frac{17}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{5}+a)(a+\frac{3}{15})& =(\color{red}{a}+\color{orange}{\frac{8}{5}}).(\color{green}{a}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{8}{5})} . \color{green}{(a)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{5}a+\frac{8}{5}a+\frac{8}{5}.\frac{1}{5}& \text{Uitwerken } \\ & =a^2+(\frac{1}{5}+\frac{8}{5})a+\frac{8}{25} & \text{Neem samen} \\ &=a^2+\frac{9}{5}a+\frac{8}{25} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(a+\frac{-15}{11})(a+\frac{3}{14})& =(\color{red}{a}+\color{orange}{\frac{-15}{11}}).(\color{green}{a}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{3}{14}a-\frac{15}{11}a-\frac{15}{11}.\frac{3}{14}& \text{Uitwerken } \\ & =a^2+(\frac{3}{14}+(\frac{-15}{11}))a-(\frac{-45}{154}) & \text{Neem samen} \\ &=a^2-\frac{177}{154}a-(\frac{-45}{154}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(p-\frac{18}{16})(a-\frac{12}{3})& =(\color{red}{p}+\color{orange}{\frac{-9}{8}}).(\color{green}{a}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-4)} + \color{orange}{(\frac{-9}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = ap-4p-\frac{9}{8}a+\frac{9}{8}.4& \text{Uitwerken } \\ & =ap-4p-\frac{9}{8}a+\frac{36}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-4p-\frac{9}{8}a+\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(x-\frac{-20}{4})(b-\frac{-11}{3})& =(\color{red}{x}+\color{orange}{5}).(\color{green}{b}+\color{blue}{\frac{11}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{11}{3})} + \color{orange}{(5)} . \color{green}{(b)} + \color{orange}{(5)} . \color{blue}{(\frac{11}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{3}x+5b+5.\frac{11}{3}& \text{Uitwerken } \\ & =bx+\frac{11}{3}x+5b+\frac{55}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-18}{15}-a)(\frac{16}{16}-a)& =(\color{red}{-a}+\color{orange}{\frac{-6}{5}}).(\color{green}{-a}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(1)} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = aa-1a+\frac{6}{5}a-\frac{6}{5}.1& \text{Uitwerken } \\ & =a^2+((-1)+\frac{6}{5})a-(\frac{-6}{5}) & \text{Neem samen} \\ &=a^2+\frac{1}{5}a-(\frac{-6}{5}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{-10}{2}-b)(\frac{-4}{11}-b)& =(\color{red}{-b}+\color{orange}{(-5)}).(\color{green}{-b}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(-5)} . \color{green}{(-b)} + \color{orange}{(-5)} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{4}{11}b+5b+5.\frac{4}{11}& \text{Uitwerken } \\ & =b^2+(\frac{4}{11}+5)b+\frac{20}{11} & \text{Neem samen} \\ &=b^2+\frac{59}{11}b+\frac{20}{11} & \text{Maak de som} \\\end{align}\)
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