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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{4}{11}+b)(b-\frac{12}{5})& =(\color{red}{b}+\color{orange}{\frac{4}{11}}).(\color{green}{b}+\color{blue}{\frac{-12}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-12}{5})} + \color{orange}{(\frac{4}{11})} . \color{green}{(b)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(\frac{-12}{5})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{12}{5}b+\frac{4}{11}b-\frac{4}{11}.\frac{12}{5}& \text{Uitwerken } \\ & =b^2+((\frac{-12}{5})+\frac{4}{11})b-(\frac{-48}{55}) & \text{Neem samen} \\ &=b^2-\frac{112}{55}b-(\frac{-48}{55}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{11}{18}-a)(x+\frac{6}{8})& =(\color{red}{-a}+\color{orange}{\frac{11}{18}}).(\color{green}{x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{11}{18})} . \color{green}{(x)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{3}{4}a+\frac{11}{18}x+\frac{11}{18}.\frac{3}{4}& \text{Uitwerken } \\ & =-ax-\frac{3}{4}a+\frac{11}{18}x+\frac{33}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{3}{4}a+\frac{11}{18}x+\frac{11}{24} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-3}{6})(b+\frac{20}{6})& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{10}{3}x-\frac{1}{2}b-\frac{1}{2}.\frac{10}{3}& \text{Uitwerken } \\ & =bx+\frac{10}{3}x-\frac{1}{2}b-\frac{10}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{10}{3}x-\frac{1}{2}b-\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-19}{6}+x)(\frac{15}{20}-a)& =(\color{red}{x}+\color{orange}{\frac{-19}{6}}).(\color{green}{-a}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-19}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{6})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{3}{4}x+\frac{19}{6}a-\frac{19}{6}.\frac{3}{4}& \text{Uitwerken } \\ & =-ax+\frac{3}{4}x+\frac{19}{6}a-\frac{57}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{3}{4}x+\frac{19}{6}a-\frac{19}{8} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(x+\frac{-10}{10})(p-\frac{14}{20})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{7}{10}x-1p+1.\frac{7}{10}& \text{Uitwerken } \\ & =px-\frac{7}{10}x-1p+\frac{7}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(5-b)(\frac{-14}{12}-a)& =(\color{red}{-b}+\color{orange}{5}).(\color{green}{-a}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(5)} . \color{green}{(-a)} + \color{orange}{(5)} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{7}{6}b-5a-5.\frac{7}{6}& \text{Uitwerken } \\ & =ab+\frac{7}{6}b-5a-\frac{35}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-17}{14}+a)(a-\frac{-3}{7})& =(\color{red}{a}+\color{orange}{\frac{-17}{14}}).(\color{green}{a}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{-17}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{14})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{3}{7}a-\frac{17}{14}a-\frac{17}{14}.\frac{3}{7}& \text{Uitwerken } \\ & =a^2+(\frac{3}{7}+(\frac{-17}{14}))a-(\frac{-51}{98}) & \text{Neem samen} \\ &=a^2-\frac{11}{14}a-(\frac{-51}{98}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-14}{18}+p)(a+\frac{5}{7})& =(\color{red}{p}+\color{orange}{\frac{-7}{9}}).(\color{green}{a}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{5}{7}p-\frac{7}{9}a-\frac{7}{9}.\frac{5}{7}& \text{Uitwerken } \\ & =ap+\frac{5}{7}p-\frac{7}{9}a-\frac{35}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{5}{7}p-\frac{7}{9}a-\frac{5}{9} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p+\frac{-14}{19})(q+\frac{16}{10})& =(\color{red}{p}+\color{orange}{\frac{-14}{19}}).(\color{green}{q}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{8}{5}p-\frac{14}{19}q-\frac{14}{19}.\frac{8}{5}& \text{Uitwerken } \\ & =pq+\frac{8}{5}p-\frac{14}{19}q-\frac{112}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-3}{13}+x)(\frac{14}{3}+p)& =(\color{red}{x}+\color{orange}{\frac{-3}{13}}).(\color{green}{p}+\color{blue}{\frac{14}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{14}{3})} + \color{orange}{(\frac{-3}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{13})} . \color{blue}{(\frac{14}{3})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{14}{3}x-\frac{3}{13}p-\frac{3}{13}.\frac{14}{3}& \text{Uitwerken } \\ & =px+\frac{14}{3}x-\frac{3}{13}p-\frac{42}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{14}{3}x-\frac{3}{13}p-\frac{14}{13} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-12}{13}-q)(\frac{-2}{15}-b)& =(\color{red}{-q}+\color{orange}{\frac{-12}{13}}).(\color{green}{-b}+\color{blue}{\frac{-2}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{-2}{15})} + \color{orange}{(\frac{-12}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-12}{13})} . \color{blue}{(\frac{-2}{15})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{2}{15}q+\frac{12}{13}b+\frac{12}{13}.\frac{2}{15}& \text{Uitwerken } \\ & =bq+\frac{2}{15}q+\frac{12}{13}b+\frac{24}{195} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{2}{15}q+\frac{12}{13}b+\frac{8}{65} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{12}{3}+q)(\frac{-15}{4}+p)& =(\color{red}{q}+\color{orange}{4}).(\color{green}{p}+\color{blue}{\frac{-15}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{4})} + \color{orange}{(4)} . \color{green}{(p)} + \color{orange}{(4)} . \color{blue}{(\frac{-15}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{15}{4}q+4p-4.\frac{15}{4}& \text{Uitwerken } \\ & =pq-\frac{15}{4}q+4p-\frac{60}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{15}{4}q+4p-15 & \text{Vereenvoudig} \\\end{align}\)
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