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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-2}{4}+a)(a+\frac{-20}{2})& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{(-10)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-10)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = aa-10a-\frac{1}{2}a+\frac{1}{2}.10& \text{Uitwerken } \\ & =a^2+((-10)+(\frac{-1}{2}))a+\frac{10}{2} & \text{Neem samen} \\ &=a^2-\frac{21}{2}a+\frac{10}{2} & \text{Maak de som} \\ &=a^2-\frac{21}{2}a+5 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{-3}{10}+p)(p+\frac{9}{14})& =(\color{red}{p}+\color{orange}{\frac{-3}{10}}).(\color{green}{p}+\color{blue}{\frac{9}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{9}{14})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{9}{14})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{9}{14}p-\frac{3}{10}p-\frac{3}{10}.\frac{9}{14}& \text{Uitwerken } \\ & =p^2+(\frac{9}{14}+(\frac{-3}{10}))p-(\frac{-27}{140}) & \text{Neem samen} \\ &=p^2+\frac{24}{70}p-(\frac{-27}{140}) & \text{Maak de som} \\ &=p^2+\frac{12}{35}p+\frac{27}{140} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(\frac{-11}{14}+x)(x+\frac{14}{7})& =(\color{red}{x}+\color{orange}{\frac{-11}{14}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{-11}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = xx+2x-\frac{11}{14}x-\frac{11}{14}.2& \text{Uitwerken } \\ & =x^2+(2+(\frac{-11}{14}))x-(\frac{-22}{14}) & \text{Neem samen} \\ &=x^2+\frac{17}{14}x-(\frac{-22}{14}) & \text{Maak de som} \\ &=x^2+\frac{17}{14}x+\frac{11}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  4. \(\begin{align}(q-\frac{5}{9})(q+\frac{14}{20})& =(\color{red}{q}+\color{orange}{\frac{-5}{9}}).(\color{green}{q}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{7}{10}q-\frac{5}{9}q-\frac{5}{9}.\frac{7}{10}& \text{Uitwerken } \\ & =q^2+(\frac{7}{10}+(\frac{-5}{9}))q-(\frac{-35}{90}) & \text{Neem samen} \\ &=q^2+\frac{13}{90}q-(\frac{-35}{90}) & \text{Maak de som} \\ &=q^2+\frac{13}{90}q+\frac{7}{18} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(\frac{10}{13}+b)(q+\frac{18}{5})& =(\color{red}{b}+\color{orange}{\frac{10}{13}}).(\color{green}{q}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{10}{13})} . \color{green}{(q)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{18}{5}b+\frac{10}{13}q+\frac{10}{13}.\frac{18}{5}& \text{Uitwerken } \\ & =bq+\frac{18}{5}b+\frac{10}{13}q+\frac{180}{65} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{18}{5}b+\frac{10}{13}q+\frac{36}{13} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{12}{16}-b)(q+\frac{14}{8})& =(\color{red}{-b}+\color{orange}{\frac{3}{4}}).(\color{green}{q}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{7}{4}b+\frac{3}{4}q+\frac{3}{4}.\frac{7}{4}& \text{Uitwerken } \\ & =-bq-\frac{7}{4}b+\frac{3}{4}q+\frac{21}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-2}{9}+p)(p-\frac{-3}{15})& =(\color{red}{p}+\color{orange}{\frac{-2}{9}}).(\color{green}{p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{5}p-\frac{2}{9}p-\frac{2}{9}.\frac{1}{5}& \text{Uitwerken } \\ & =p^2+(\frac{1}{5}+(\frac{-2}{9}))p-(\frac{-2}{45}) & \text{Neem samen} \\ &=p^2-\frac{1}{45}p-(\frac{-2}{45}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(a-\frac{18}{4})(x-\frac{-18}{2})& =(\color{red}{a}+\color{orange}{\frac{-9}{2}}).(\color{green}{x}+\color{blue}{9})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(9)} + \color{orange}{(\frac{-9}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = ax+9a-\frac{9}{2}x-\frac{9}{2}.9& \text{Uitwerken } \\ & =ax+9a-\frac{9}{2}x-\frac{81}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-3}{8})(\frac{-2}{9}-p)& =(\color{red}{b}+\color{orange}{\frac{3}{8}}).(\color{green}{-p}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{3}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{2}{9}b-\frac{3}{8}p-\frac{3}{8}.\frac{2}{9}& \text{Uitwerken } \\ & =-bp-\frac{2}{9}b-\frac{3}{8}p-\frac{6}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{2}{9}b-\frac{3}{8}p-\frac{1}{12} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q-\frac{10}{8})(\frac{-11}{15}+q)& =(\color{red}{q}+\color{orange}{\frac{-5}{4}}).(\color{green}{q}+\color{blue}{\frac{-11}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{15})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-11}{15})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{11}{15}q-\frac{5}{4}q+\frac{5}{4}.\frac{11}{15}& \text{Uitwerken } \\ & =q^2+((\frac{-11}{15})+(\frac{-5}{4}))q+\frac{55}{60} & \text{Neem samen} \\ &=q^2-\frac{119}{60}q+\frac{55}{60} & \text{Maak de som} \\ &=q^2-\frac{119}{60}q+\frac{11}{12} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(p+\frac{-7}{9})(x-\frac{5}{11})& =(\color{red}{p}+\color{orange}{\frac{-7}{9}}).(\color{green}{x}+\color{blue}{\frac{-5}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{11})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{-5}{11})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{5}{11}p-\frac{7}{9}x+\frac{7}{9}.\frac{5}{11}& \text{Uitwerken } \\ & =px-\frac{5}{11}p-\frac{7}{9}x+\frac{35}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{16}{15})(\frac{-1}{16}+b)& =(\color{red}{x}+\color{orange}{\frac{16}{15}}).(\color{green}{b}+\color{blue}{\frac{-1}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{16})} + \color{orange}{(\frac{16}{15})} . \color{green}{(b)} + \color{orange}{(\frac{16}{15})} . \color{blue}{(\frac{-1}{16})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{16}x+\frac{16}{15}b-\frac{16}{15}.\frac{1}{16}& \text{Uitwerken } \\ & =bx-\frac{1}{16}x+\frac{16}{15}b-\frac{16}{240} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{1}{16}x+\frac{16}{15}b-\frac{1}{15} & \text{Vereenvoudig} \\\end{align}\)
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