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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{2}{20})(\frac{6}{2}+p)& =(\color{red}{p}+\color{orange}{\frac{1}{10}}).(\color{green}{p}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(\frac{1}{10})} . \color{green}{(p)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = pp+3p+\frac{1}{10}p+\frac{1}{10}.3& \text{Uitwerken } \\ & =p^2+(3+\frac{1}{10})p+\frac{3}{10} & \text{Neem samen} \\ &=p^2+\frac{31}{10}p+\frac{3}{10} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{18}{6}-b)(\frac{20}{4}+b)& =(\color{red}{-b}+\color{orange}{3}).(\color{green}{b}+\color{blue}{5})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(5)} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -bb-5b+3b+3.5& \text{Uitwerken } \\ & =-b^2+((-5)+3)b+(-15) & \text{Neem samen} \\ &=-b^2-2b+(-15) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(b-\frac{18}{16})(x+\frac{9}{19})& =(\color{red}{b}+\color{orange}{\frac{-9}{8}}).(\color{green}{x}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{9}{19}b-\frac{9}{8}x-\frac{9}{8}.\frac{9}{19}& \text{Uitwerken } \\ & =bx+\frac{9}{19}b-\frac{9}{8}x-\frac{81}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-7}{12}-q)(\frac{-17}{7}+x)& =(\color{red}{-q}+\color{orange}{\frac{-7}{12}}).(\color{green}{x}+\color{blue}{\frac{-17}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-17}{7})} + \color{orange}{(\frac{-7}{12})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{12})} . \color{blue}{(\frac{-17}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{17}{7}q-\frac{7}{12}x+\frac{7}{12}.\frac{17}{7}& \text{Uitwerken } \\ & =-qx+\frac{17}{7}q-\frac{7}{12}x+\frac{119}{84} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{17}{7}q-\frac{7}{12}x+\frac{17}{12} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-7}{15}+q)(\frac{6}{13}-b)& =(\color{red}{q}+\color{orange}{\frac{-7}{15}}).(\color{green}{-b}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{-7}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{6}{13}q+\frac{7}{15}b-\frac{7}{15}.\frac{6}{13}& \text{Uitwerken } \\ & =-bq+\frac{6}{13}q+\frac{7}{15}b-\frac{42}{195} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{6}{13}q+\frac{7}{15}b-\frac{14}{65} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{3}{15}-a)(\frac{-17}{6}+x)& =(\color{red}{-a}+\color{orange}{\frac{1}{5}}).(\color{green}{x}+\color{blue}{\frac{-17}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-17}{6})} + \color{orange}{(\frac{1}{5})} . \color{green}{(x)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-17}{6})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{17}{6}a+\frac{1}{5}x-\frac{1}{5}.\frac{17}{6}& \text{Uitwerken } \\ & =-ax+\frac{17}{6}a+\frac{1}{5}x-\frac{17}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-5}{6}+x)(\frac{15}{2}+a)& =(\color{red}{x}+\color{orange}{\frac{-5}{6}}).(\color{green}{a}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{15}{2}x-\frac{5}{6}a-\frac{5}{6}.\frac{15}{2}& \text{Uitwerken } \\ & =ax+\frac{15}{2}x-\frac{5}{6}a-\frac{75}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{15}{2}x-\frac{5}{6}a-\frac{25}{4} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b-\frac{14}{11})(q+\frac{19}{20})& =(\color{red}{b}+\color{orange}{\frac{-14}{11}}).(\color{green}{q}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(\frac{-14}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{19}{20}b-\frac{14}{11}q-\frac{14}{11}.\frac{19}{20}& \text{Uitwerken } \\ & =bq+\frac{19}{20}b-\frac{14}{11}q-\frac{266}{220} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{19}{20}b-\frac{14}{11}q-\frac{133}{110} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-19}{13}-p)(\frac{-5}{9}-p)& =(\color{red}{-p}+\color{orange}{\frac{-19}{13}}).(\color{green}{-p}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{-19}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{-19}{13})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{5}{9}p+\frac{19}{13}p+\frac{19}{13}.\frac{5}{9}& \text{Uitwerken } \\ & =p^2+(\frac{5}{9}+\frac{19}{13})p+\frac{95}{117} & \text{Neem samen} \\ &=p^2+\frac{236}{117}p+\frac{95}{117} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{10}{10}-a)(\frac{-13}{18}-q)& =(\color{red}{-a}+\color{orange}{1}).(\color{green}{-q}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(1)} . \color{green}{(-q)} + \color{orange}{(1)} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{13}{18}a-1q-1.\frac{13}{18}& \text{Uitwerken } \\ & =aq+\frac{13}{18}a-1q-\frac{13}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{5}{6}+x)(b+\frac{3}{10})& =(\color{red}{x}+\color{orange}{\frac{5}{6}}).(\color{green}{b}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{5}{6})} . \color{green}{(b)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{10}x+\frac{5}{6}b+\frac{5}{6}.\frac{3}{10}& \text{Uitwerken } \\ & =bx+\frac{3}{10}x+\frac{5}{6}b+\frac{15}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{3}{10}x+\frac{5}{6}b+\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(q-\frac{-1}{14})(b-\frac{18}{7})& =(\color{red}{q}+\color{orange}{\frac{1}{14}}).(\color{green}{b}+\color{blue}{\frac{-18}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-18}{7})} + \color{orange}{(\frac{1}{14})} . \color{green}{(b)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(\frac{-18}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{18}{7}q+\frac{1}{14}b-\frac{1}{14}.\frac{18}{7}& \text{Uitwerken } \\ & =bq-\frac{18}{7}q+\frac{1}{14}b-\frac{18}{98} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{18}{7}q+\frac{1}{14}b-\frac{9}{49} & \text{Vereenvoudig} \\\end{align}\)
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