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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x+\frac{3}{11})(\frac{-12}{19}+q)& =(\color{red}{x}+\color{orange}{\frac{3}{11}}).(\color{green}{q}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(\frac{3}{11})} . \color{green}{(q)} + \color{orange}{(\frac{3}{11})} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{12}{19}x+\frac{3}{11}q-\frac{3}{11}.\frac{12}{19}& \text{Uitwerken } \\ & =qx-\frac{12}{19}x+\frac{3}{11}q-\frac{36}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{3}{16}-p)(p-\frac{17}{9})& =(\color{red}{-p}+\color{orange}{\frac{3}{16}}).(\color{green}{p}+\color{blue}{\frac{-17}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-17}{9})} + \color{orange}{(\frac{3}{16})} . \color{green}{(p)} + \color{orange}{(\frac{3}{16})} . \color{blue}{(\frac{-17}{9})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{17}{9}p+\frac{3}{16}p-\frac{3}{16}.\frac{17}{9}& \text{Uitwerken } \\ & =-p^2+(\frac{17}{9}+\frac{3}{16})p-\frac{51}{144} & \text{Neem samen} \\ &=-p^2+\frac{299}{144}p-\frac{51}{144} & \text{Maak de som} \\ &=-p^2+\frac{299}{144}p-\frac{17}{48} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{14}{11}+b)(\frac{-12}{16}-p)& =(\color{red}{b}+\color{orange}{\frac{14}{11}}).(\color{green}{-p}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{14}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{14}{11})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{3}{4}b-\frac{14}{11}p-\frac{14}{11}.\frac{3}{4}& \text{Uitwerken } \\ & =-bp-\frac{3}{4}b-\frac{14}{11}p-\frac{42}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{3}{4}b-\frac{14}{11}p-\frac{21}{22} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p-\frac{13}{5})(q-\frac{-8}{10})& =(\color{red}{p}+\color{orange}{\frac{-13}{5}}).(\color{green}{q}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-13}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{5})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{5}p-\frac{13}{5}q-\frac{13}{5}.\frac{4}{5}& \text{Uitwerken } \\ & =pq+\frac{4}{5}p-\frac{13}{5}q-\frac{52}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{8}{7}-a)(12-p)& =(\color{red}{-a}+\color{orange}{\frac{8}{7}}).(\color{green}{-p}+\color{blue}{12})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(12)} + \color{orange}{(\frac{8}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = ap-12a-\frac{8}{7}p+\frac{8}{7}.12& \text{Uitwerken } \\ & =ap-12a-\frac{8}{7}p+\frac{96}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-1}{17}-x)(18-q)& =(\color{red}{-x}+\color{orange}{\frac{-1}{17}}).(\color{green}{-q}+\color{blue}{18})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(18)} + \color{orange}{(\frac{-1}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(18)}& \text{Boogjes en uitschrijven} \\ & = qx-18x+\frac{1}{17}q-\frac{1}{17}.18& \text{Uitwerken } \\ & =qx-18x+\frac{1}{17}q-\frac{18}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{2}{8}-a)(a+\frac{16}{7})& =(\color{red}{-a}+\color{orange}{\frac{1}{4}}).(\color{green}{a}+\color{blue}{\frac{16}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{16}{7})} + \color{orange}{(\frac{1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{16}{7})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{16}{7}a+\frac{1}{4}a+\frac{1}{4}.\frac{16}{7}& \text{Uitwerken } \\ & =-a^2+((\frac{-16}{7})+\frac{1}{4})a+(\frac{-16}{28}) & \text{Neem samen} \\ &=-a^2-\frac{57}{28}a+(\frac{-16}{28}) & \text{Maak de som} \\ &=-a^2-\frac{57}{28}a+(\frac{-4}{7}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(\frac{2}{4}+b)(x+\frac{-10}{9})& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{10}{9}b+\frac{1}{2}x-\frac{1}{2}.\frac{10}{9}& \text{Uitwerken } \\ & =bx-\frac{10}{9}b+\frac{1}{2}x-\frac{10}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{10}{9}b+\frac{1}{2}x-\frac{5}{9} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(a-\frac{-10}{4})(q+\frac{2}{19})& =(\color{red}{a}+\color{orange}{\frac{5}{2}}).(\color{green}{q}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(\frac{5}{2})} . \color{green}{(q)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{2}{19}a+\frac{5}{2}q+\frac{5}{2}.\frac{2}{19}& \text{Uitwerken } \\ & =aq+\frac{2}{19}a+\frac{5}{2}q+\frac{10}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{2}{19}a+\frac{5}{2}q+\frac{5}{19} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{13}{19}+p)(\frac{19}{14}+b)& =(\color{red}{p}+\color{orange}{\frac{13}{19}}).(\color{green}{b}+\color{blue}{\frac{19}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{19}{14})} + \color{orange}{(\frac{13}{19})} . \color{green}{(b)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{19}{14})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{14}p+\frac{13}{19}b+\frac{13}{19}.\frac{19}{14}& \text{Uitwerken } \\ & =bp+\frac{19}{14}p+\frac{13}{19}b+\frac{247}{266} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{19}{14}p+\frac{13}{19}b+\frac{13}{14} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-13}{8}-q)(b+\frac{2}{2})& =(\color{red}{-q}+\color{orange}{\frac{-13}{8}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(1)} + \color{orange}{(\frac{-13}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{8})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bq-1q-\frac{13}{8}b-\frac{13}{8}.1& \text{Uitwerken } \\ & =-bq-1q-\frac{13}{8}b-\frac{13}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}((-4)-b)(\frac{-19}{2}+p)& =(\color{red}{-b}+\color{orange}{(-4)}).(\color{green}{p}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(-4)} . \color{green}{(p)} + \color{orange}{(-4)} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{19}{2}b-4p+4.\frac{19}{2}& \text{Uitwerken } \\ & =-bp+\frac{19}{2}b-4p+\frac{76}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{19}{2}b-4p+38 & \text{Vereenvoudig} \\\end{align}\)
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