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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{1}{3})(q-\frac{15}{12})& =(\color{red}{p}+\color{orange}{\frac{-1}{3}}).(\color{green}{q}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{4}p-\frac{1}{3}q+\frac{1}{3}.\frac{5}{4}& \text{Uitwerken } \\ & =pq-\frac{5}{4}p-\frac{1}{3}q+\frac{5}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p+\frac{9}{3})(x+\frac{16}{5})& =(\color{red}{p}+\color{orange}{3}).(\color{green}{x}+\color{blue}{\frac{16}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{16}{5})} + \color{orange}{(3)} . \color{green}{(x)} + \color{orange}{(3)} . \color{blue}{(\frac{16}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{16}{5}p+3x+3.\frac{16}{5}& \text{Uitwerken } \\ & =px+\frac{16}{5}p+3x+\frac{48}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{17}{18}-p)(b+\frac{-14}{19})& =(\color{red}{-p}+\color{orange}{\frac{17}{18}}).(\color{green}{b}+\color{blue}{\frac{-14}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-14}{19})} + \color{orange}{(\frac{17}{18})} . \color{green}{(b)} + \color{orange}{(\frac{17}{18})} . \color{blue}{(\frac{-14}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{14}{19}p+\frac{17}{18}b-\frac{17}{18}.\frac{14}{19}& \text{Uitwerken } \\ & =-bp+\frac{14}{19}p+\frac{17}{18}b-\frac{238}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{14}{19}p+\frac{17}{18}b-\frac{119}{171} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{17}{9}-a)(\frac{-19}{4}+q)& =(\color{red}{-a}+\color{orange}{\frac{17}{9}}).(\color{green}{q}+\color{blue}{\frac{-19}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{4})} + \color{orange}{(\frac{17}{9})} . \color{green}{(q)} + \color{orange}{(\frac{17}{9})} . \color{blue}{(\frac{-19}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{19}{4}a+\frac{17}{9}q-\frac{17}{9}.\frac{19}{4}& \text{Uitwerken } \\ & =-aq+\frac{19}{4}a+\frac{17}{9}q-\frac{323}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{4}{12}-p)(q-\frac{10}{4})& =(\color{red}{-p}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{2}p+\frac{1}{3}q-\frac{1}{3}.\frac{5}{2}& \text{Uitwerken } \\ & =-pq+\frac{5}{2}p+\frac{1}{3}q-\frac{5}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{9}{3})(\frac{11}{3}-p)& =(\color{red}{b}+\color{orange}{3}).(\color{green}{-p}+\color{blue}{\frac{11}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{11}{3})} + \color{orange}{(3)} . \color{green}{(-p)} + \color{orange}{(3)} . \color{blue}{(\frac{11}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{11}{3}b-3p+3.\frac{11}{3}& \text{Uitwerken } \\ & =-bp+\frac{11}{3}b-3p+\frac{33}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{11}{3}b-3p+11 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a+18)(p-\frac{-14}{3})& =(\color{red}{a}+\color{orange}{18}).(\color{green}{p}+\color{blue}{\frac{14}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{14}{3})} + \color{orange}{(18)} . \color{green}{(p)} + \color{orange}{(18)} . \color{blue}{(\frac{14}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{14}{3}a+18p+18.\frac{14}{3}& \text{Uitwerken } \\ & =ap+\frac{14}{3}a+18p+\frac{252}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{14}{3}a+18p+84 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-15}{18})(\frac{-2}{9}-b)& =(\color{red}{x}+\color{orange}{\frac{5}{6}}).(\color{green}{-b}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{5}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{2}{9}x-\frac{5}{6}b-\frac{5}{6}.\frac{2}{9}& \text{Uitwerken } \\ & =-bx-\frac{2}{9}x-\frac{5}{6}b-\frac{10}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{2}{9}x-\frac{5}{6}b-\frac{5}{27} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p-\frac{12}{11})(a+\frac{15}{10})& =(\color{red}{p}+\color{orange}{\frac{-12}{11}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-12}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-12}{11})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{2}p-\frac{12}{11}a-\frac{12}{11}.\frac{3}{2}& \text{Uitwerken } \\ & =ap+\frac{3}{2}p-\frac{12}{11}a-\frac{36}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{3}{2}p-\frac{12}{11}a-\frac{18}{11} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-5}{11}+p)(\frac{-18}{11}-p)& =(\color{red}{p}+\color{orange}{\frac{-5}{11}}).(\color{green}{-p}+\color{blue}{\frac{-18}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-18}{11})} + \color{orange}{(\frac{-5}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(\frac{-18}{11})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{18}{11}p+\frac{5}{11}p+\frac{5}{11}.\frac{18}{11}& \text{Uitwerken } \\ & =-p^2+((\frac{-18}{11})+\frac{5}{11})p+(\frac{-90}{121}) & \text{Neem samen} \\ &=-p^2-\frac{13}{11}p+(\frac{-90}{121}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(\frac{-20}{9}+p)(\frac{-14}{8}+q)& =(\color{red}{p}+\color{orange}{\frac{-20}{9}}).(\color{green}{q}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{-20}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-20}{9})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{7}{4}p-\frac{20}{9}q+\frac{20}{9}.\frac{7}{4}& \text{Uitwerken } \\ & =pq-\frac{7}{4}p-\frac{20}{9}q+\frac{140}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{7}{4}p-\frac{20}{9}q+\frac{35}{9} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(x+\frac{-15}{4})(\frac{-13}{16}+a)& =(\color{red}{x}+\color{orange}{\frac{-15}{4}}).(\color{green}{a}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{13}{16}x-\frac{15}{4}a+\frac{15}{4}.\frac{13}{16}& \text{Uitwerken } \\ & =ax-\frac{13}{16}x-\frac{15}{4}a+\frac{195}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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