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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{7}{4})(\frac{-20}{5}+a)& =(\color{red}{a}+\color{orange}{\frac{7}{4}}).(\color{green}{a}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-4)} + \color{orange}{(\frac{7}{4})} . \color{green}{(a)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = aa-4a+\frac{7}{4}a-\frac{7}{4}.4& \text{Uitwerken } \\ & =a^2+((-4)+\frac{7}{4})a-(\frac{-28}{4}) & \text{Neem samen} \\ &=a^2-\frac{9}{4}a-(\frac{-28}{4}) & \text{Maak de som} \\ &=a^2-\frac{9}{4}a+7 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(a+\frac{5}{11})(20-q)& =(\color{red}{a}+\color{orange}{\frac{5}{11}}).(\color{green}{-q}+\color{blue}{20})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(20)} + \color{orange}{(\frac{5}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(20)}& \text{Boogjes en uitschrijven} \\ & = -aq+20a-\frac{5}{11}q+\frac{5}{11}.20& \text{Uitwerken } \\ & =-aq+20a-\frac{5}{11}q+\frac{100}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-3}{8}-x)(a-\frac{-3}{19})& =(\color{red}{-x}+\color{orange}{\frac{-3}{8}}).(\color{green}{a}+\color{blue}{\frac{3}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{19})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{3}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{3}{19}x-\frac{3}{8}a-\frac{3}{8}.\frac{3}{19}& \text{Uitwerken } \\ & =-ax-\frac{3}{19}x-\frac{3}{8}a-\frac{9}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p-\frac{17}{12})(p+20)& =(\color{red}{p}+\color{orange}{\frac{-17}{12}}).(\color{green}{p}+\color{blue}{20})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(20)} + \color{orange}{(\frac{-17}{12})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{12})} . \color{blue}{(20)}& \text{Boogjes en uitschrijven} \\ & = pp+20p-\frac{17}{12}p-\frac{17}{12}.20& \text{Uitwerken } \\ & =p^2+(20+(\frac{-17}{12}))p-(\frac{-340}{12}) & \text{Neem samen} \\ &=p^2+\frac{223}{12}p-(\frac{-340}{12}) & \text{Maak de som} \\ &=p^2+\frac{223}{12}p+\frac{85}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(a+\frac{4}{16})(\frac{-2}{9}+p)& =(\color{red}{a}+\color{orange}{\frac{1}{4}}).(\color{green}{p}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{9}a+\frac{1}{4}p-\frac{1}{4}.\frac{2}{9}& \text{Uitwerken } \\ & =ap-\frac{2}{9}a+\frac{1}{4}p-\frac{2}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{2}{9}a+\frac{1}{4}p-\frac{1}{18} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(q-\frac{-18}{8})(\frac{-20}{6}-a)& =(\color{red}{q}+\color{orange}{\frac{9}{4}}).(\color{green}{-a}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(\frac{9}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{10}{3}q-\frac{9}{4}a-\frac{9}{4}.\frac{10}{3}& \text{Uitwerken } \\ & =-aq-\frac{10}{3}q-\frac{9}{4}a-\frac{90}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{10}{3}q-\frac{9}{4}a-\frac{15}{2} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x+\frac{-9}{13})(b+\frac{-4}{12})& =(\color{red}{x}+\color{orange}{\frac{-9}{13}}).(\color{green}{b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{3}x-\frac{9}{13}b+\frac{9}{13}.\frac{1}{3}& \text{Uitwerken } \\ & =bx-\frac{1}{3}x-\frac{9}{13}b+\frac{9}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{1}{3}x-\frac{9}{13}b+\frac{3}{13} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(q+\frac{8}{8})(a+\frac{3}{2})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{2}q+1a+1.\frac{3}{2}& \text{Uitwerken } \\ & =aq+\frac{3}{2}q+1a+\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-7}{3}-a)(\frac{19}{15}+p)& =(\color{red}{-a}+\color{orange}{\frac{-7}{3}}).(\color{green}{p}+\color{blue}{\frac{19}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{19}{15})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{19}{15})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{19}{15}a-\frac{7}{3}p-\frac{7}{3}.\frac{19}{15}& \text{Uitwerken } \\ & =-ap-\frac{19}{15}a-\frac{7}{3}p-\frac{133}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{18}{16}+p)(b-\frac{-2}{9})& =(\color{red}{p}+\color{orange}{\frac{9}{8}}).(\color{green}{b}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{9}{8})} . \color{green}{(b)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{9}p+\frac{9}{8}b+\frac{9}{8}.\frac{2}{9}& \text{Uitwerken } \\ & =bp+\frac{2}{9}p+\frac{9}{8}b+\frac{18}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{2}{9}p+\frac{9}{8}b+\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{4}{5}-p)(\frac{9}{19}+x)& =(\color{red}{-p}+\color{orange}{\frac{4}{5}}).(\color{green}{x}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(\frac{4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{9}{19}p+\frac{4}{5}x+\frac{4}{5}.\frac{9}{19}& \text{Uitwerken } \\ & =-px-\frac{9}{19}p+\frac{4}{5}x+\frac{36}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{19}{4})(x+\frac{-17}{16})& =(\color{red}{p}+\color{orange}{\frac{-19}{4}}).(\color{green}{x}+\color{blue}{\frac{-17}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{16})} + \color{orange}{(\frac{-19}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{4})} . \color{blue}{(\frac{-17}{16})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{16}p-\frac{19}{4}x+\frac{19}{4}.\frac{17}{16}& \text{Uitwerken } \\ & =px-\frac{17}{16}p-\frac{19}{4}x+\frac{323}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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