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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{16}{7})(a-\frac{18}{4})& =(\color{red}{a}+\color{orange}{\frac{-16}{7}}).(\color{green}{a}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{-16}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{7})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{9}{2}a-\frac{16}{7}a+\frac{16}{7}.\frac{9}{2}& \text{Uitwerken } \\ & =a^2+((\frac{-9}{2})+(\frac{-16}{7}))a+\frac{144}{14} & \text{Neem samen} \\ &=a^2-\frac{95}{14}a+\frac{144}{14} & \text{Maak de som} \\ &=a^2-\frac{95}{14}a+\frac{72}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(q+\frac{8}{12})(p-\frac{16}{9})& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{16}{9}q+\frac{2}{3}p-\frac{2}{3}.\frac{16}{9}& \text{Uitwerken } \\ & =pq-\frac{16}{9}q+\frac{2}{3}p-\frac{32}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b+\frac{-17}{19})(\frac{14}{7}-a)& =(\color{red}{b}+\color{orange}{\frac{-17}{19}}).(\color{green}{-a}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(\frac{-17}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -ab+2b+\frac{17}{19}a-\frac{17}{19}.2& \text{Uitwerken } \\ & =-ab+2b+\frac{17}{19}a-\frac{34}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{-6}{5})(\frac{-1}{10}-x)& =(\color{red}{q}+\color{orange}{\frac{-6}{5}}).(\color{green}{-x}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{1}{10}q+\frac{6}{5}x+\frac{6}{5}.\frac{1}{10}& \text{Uitwerken } \\ & =-qx-\frac{1}{10}q+\frac{6}{5}x+\frac{6}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{1}{10}q+\frac{6}{5}x+\frac{3}{25} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a+\frac{-14}{7})(\frac{17}{19}+b)& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{17}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{17}{19})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{17}{19})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{19}a-2b-2.\frac{17}{19}& \text{Uitwerken } \\ & =ab+\frac{17}{19}a-2b-\frac{34}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{-5}{20})(\frac{-13}{15}-q)& =(\color{red}{b}+\color{orange}{\frac{-1}{4}}).(\color{green}{-q}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{13}{15}b+\frac{1}{4}q+\frac{1}{4}.\frac{13}{15}& \text{Uitwerken } \\ & =-bq-\frac{13}{15}b+\frac{1}{4}q+\frac{13}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{4}{4}+a)(\frac{6}{5}+a)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{6}{5}a+1a+1.\frac{6}{5}& \text{Uitwerken } \\ & =a^2+(\frac{6}{5}+1)a+\frac{6}{5} & \text{Neem samen} \\ &=a^2+\frac{11}{5}a+\frac{6}{5} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-19}{15}+x)(b+\frac{-1}{2})& =(\color{red}{x}+\color{orange}{\frac{-19}{15}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-19}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{15})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{2}x-\frac{19}{15}b+\frac{19}{15}.\frac{1}{2}& \text{Uitwerken } \\ & =bx-\frac{1}{2}x-\frac{19}{15}b+\frac{19}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x+\frac{3}{12})(x+\frac{-12}{15})& =(\color{red}{x}+\color{orange}{\frac{1}{4}}).(\color{green}{x}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{4}{5}x+\frac{1}{4}x-\frac{1}{4}.\frac{4}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-4}{5})+\frac{1}{4})x-(\frac{-4}{20}) & \text{Neem samen} \\ &=x^2-\frac{11}{20}x-(\frac{-4}{20}) & \text{Maak de som} \\ &=x^2-\frac{11}{20}x+\frac{1}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(p+\frac{-9}{18})(\frac{15}{4}-q)& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{-q}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{15}{4}p+\frac{1}{2}q-\frac{1}{2}.\frac{15}{4}& \text{Uitwerken } \\ & =-pq+\frac{15}{4}p+\frac{1}{2}q-\frac{15}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-11}{19})(\frac{13}{9}+q)& =(\color{red}{a}+\color{orange}{\frac{11}{19}}).(\color{green}{q}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{11}{19})} . \color{green}{(q)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{13}{9}a+\frac{11}{19}q+\frac{11}{19}.\frac{13}{9}& \text{Uitwerken } \\ & =aq+\frac{13}{9}a+\frac{11}{19}q+\frac{143}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-18}{3}-a)(p+\frac{-13}{16})& =(\color{red}{-a}+\color{orange}{(-6)}).(\color{green}{p}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(-6)} . \color{green}{(p)} + \color{orange}{(-6)} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{13}{16}a-6p+6.\frac{13}{16}& \text{Uitwerken } \\ & =-ap+\frac{13}{16}a-6p+\frac{78}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{13}{16}a-6p+\frac{39}{8} & \text{Vereenvoudig} \\\end{align}\)
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