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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{3}{7})(\frac{-9}{10}-x)& =(\color{red}{p}+\color{orange}{\frac{3}{7}}).(\color{green}{-x}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{3}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{9}{10}p-\frac{3}{7}x-\frac{3}{7}.\frac{9}{10}& \text{Uitwerken } \\ & =-px-\frac{9}{10}p-\frac{3}{7}x-\frac{27}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q-15)(\frac{15}{18}-x)& =(\color{red}{q}+\color{orange}{(-15)}).(\color{green}{-x}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(-15)} . \color{green}{(-x)} + \color{orange}{(-15)} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{5}{6}q+15x-15.\frac{5}{6}& \text{Uitwerken } \\ & =-qx+\frac{5}{6}q+15x-\frac{75}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{5}{6}q+15x-\frac{25}{2} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(q+\frac{-12}{19})(\frac{-3}{11}+b)& =(\color{red}{q}+\color{orange}{\frac{-12}{19}}).(\color{green}{b}+\color{blue}{\frac{-3}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{11})} + \color{orange}{(\frac{-12}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-12}{19})} . \color{blue}{(\frac{-3}{11})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{11}q-\frac{12}{19}b+\frac{12}{19}.\frac{3}{11}& \text{Uitwerken } \\ & =bq-\frac{3}{11}q-\frac{12}{19}b+\frac{36}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+4)(q-\frac{3}{9})& =(\color{red}{q}+\color{orange}{4}).(\color{green}{q}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(4)} . \color{green}{(q)} + \color{orange}{(4)} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{1}{3}q+4q-4.\frac{1}{3}& \text{Uitwerken } \\ & =q^2+((\frac{-1}{3})+4)q-(\frac{-4}{3}) & \text{Neem samen} \\ &=q^2+\frac{11}{3}q-(\frac{-4}{3}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-20}{14}-b)(\frac{1}{16}-q)& =(\color{red}{-b}+\color{orange}{\frac{-10}{7}}).(\color{green}{-q}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{16}b+\frac{10}{7}q-\frac{10}{7}.\frac{1}{16}& \text{Uitwerken } \\ & =bq-\frac{1}{16}b+\frac{10}{7}q-\frac{10}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{1}{16}b+\frac{10}{7}q-\frac{5}{56} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(p-\frac{7}{17})(\frac{-13}{3}-q)& =(\color{red}{p}+\color{orange}{\frac{-7}{17}}).(\color{green}{-q}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(\frac{-7}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{13}{3}p+\frac{7}{17}q+\frac{7}{17}.\frac{13}{3}& \text{Uitwerken } \\ & =-pq-\frac{13}{3}p+\frac{7}{17}q+\frac{91}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x-\frac{-4}{15})(\frac{4}{20}-p)& =(\color{red}{x}+\color{orange}{\frac{4}{15}}).(\color{green}{-p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{4}{15})} . \color{green}{(-p)} + \color{orange}{(\frac{4}{15})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{1}{5}x-\frac{4}{15}p+\frac{4}{15}.\frac{1}{5}& \text{Uitwerken } \\ & =-px+\frac{1}{5}x-\frac{4}{15}p+\frac{4}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{-11}{13})(b-\frac{10}{13})& =(\color{red}{q}+\color{orange}{\frac{-11}{13}}).(\color{green}{b}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{10}{13}q-\frac{11}{13}b+\frac{11}{13}.\frac{10}{13}& \text{Uitwerken } \\ & =bq-\frac{10}{13}q-\frac{11}{13}b+\frac{110}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{2}{3}-q)(\frac{-18}{2}+p)& =(\color{red}{-q}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{(-9)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(-9)} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = -pq+9q+\frac{2}{3}p-\frac{2}{3}.9& \text{Uitwerken } \\ & =-pq+9q+\frac{2}{3}p-\frac{18}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+9q+\frac{2}{3}p-6 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-7}{17}-p)(\frac{15}{17}-q)& =(\color{red}{-p}+\color{orange}{\frac{-7}{17}}).(\color{green}{-q}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(\frac{-7}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{15}{17}p+\frac{7}{17}q-\frac{7}{17}.\frac{15}{17}& \text{Uitwerken } \\ & =pq-\frac{15}{17}p+\frac{7}{17}q-\frac{105}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{19}{8}+b)(\frac{-19}{2}-a)& =(\color{red}{b}+\color{orange}{\frac{19}{8}}).(\color{green}{-a}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(\frac{19}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{19}{2}b-\frac{19}{8}a-\frac{19}{8}.\frac{19}{2}& \text{Uitwerken } \\ & =-ab-\frac{19}{2}b-\frac{19}{8}a-\frac{361}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p+\frac{-14}{6})(a+\frac{7}{9})& =(\color{red}{p}+\color{orange}{\frac{-7}{3}}).(\color{green}{a}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{7}{9}p-\frac{7}{3}a-\frac{7}{3}.\frac{7}{9}& \text{Uitwerken } \\ & =ap+\frac{7}{9}p-\frac{7}{3}a-\frac{49}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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