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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{3}{3}+p)(b+\frac{14}{19})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{14}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{14}{19})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{14}{19})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{14}{19}p+1b+1.\frac{14}{19}& \text{Uitwerken } \\ & =bp+\frac{14}{19}p+1b+\frac{14}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{18}{3}-b)(b+\frac{-19}{15})& =(\color{red}{-b}+\color{orange}{6}).(\color{green}{b}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(6)} . \color{green}{(b)} + \color{orange}{(6)} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{19}{15}b+6b-6.\frac{19}{15}& \text{Uitwerken } \\ & =-b^2+(\frac{19}{15}+6)b-\frac{114}{15} & \text{Neem samen} \\ &=-b^2+\frac{109}{15}b-\frac{114}{15} & \text{Maak de som} \\ &=-b^2+\frac{109}{15}b-\frac{38}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{-8}{11}-x)(\frac{18}{2}+p)& =(\color{red}{-x}+\color{orange}{\frac{-8}{11}}).(\color{green}{p}+\color{blue}{9})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(9)} + \color{orange}{(\frac{-8}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{11})} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = -px-9x-\frac{8}{11}p-\frac{8}{11}.9& \text{Uitwerken } \\ & =-px-9x-\frac{8}{11}p-\frac{72}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{7}{2}+q)(q-\frac{11}{6})& =(\color{red}{q}+\color{orange}{\frac{7}{2}}).(\color{green}{q}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{7}{2})} . \color{green}{(q)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{11}{6}q+\frac{7}{2}q-\frac{7}{2}.\frac{11}{6}& \text{Uitwerken } \\ & =q^2+((\frac{-11}{6})+\frac{7}{2})q-(\frac{-77}{12}) & \text{Neem samen} \\ &=q^2+\frac{10}{6}q-(\frac{-77}{12}) & \text{Maak de som} \\ &=q^2+\frac{5}{3}q+\frac{77}{12} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  5. \(\begin{align}(\frac{-1}{2}-a)(\frac{-13}{12}-p)& =(\color{red}{-a}+\color{orange}{\frac{-1}{2}}).(\color{green}{-p}+\color{blue}{\frac{-13}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{12})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-13}{12})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{12}a+\frac{1}{2}p+\frac{1}{2}.\frac{13}{12}& \text{Uitwerken } \\ & =ap+\frac{13}{12}a+\frac{1}{2}p+\frac{13}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{17}{17})(\frac{6}{10}-a)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{-a}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(1)} . \color{green}{(-a)} + \color{orange}{(1)} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{3}{5}b-1a+1.\frac{3}{5}& \text{Uitwerken } \\ & =-ab+\frac{3}{5}b-1a+\frac{3}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-14}{14}-a)(\frac{4}{6}-x)& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{-x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(-1)} . \color{green}{(-x)} + \color{orange}{(-1)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{2}{3}a+1x-1.\frac{2}{3}& \text{Uitwerken } \\ & =ax-\frac{2}{3}a+1x-\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p+\frac{20}{18})(\frac{4}{16}+x)& =(\color{red}{p}+\color{orange}{\frac{10}{9}}).(\color{green}{x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{10}{9})} . \color{green}{(x)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{4}p+\frac{10}{9}x+\frac{10}{9}.\frac{1}{4}& \text{Uitwerken } \\ & =px+\frac{1}{4}p+\frac{10}{9}x+\frac{10}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{1}{4}p+\frac{10}{9}x+\frac{5}{18} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{11}{5}-b)(p+\frac{1}{12})& =(\color{red}{-b}+\color{orange}{\frac{11}{5}}).(\color{green}{p}+\color{blue}{\frac{1}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{12})} + \color{orange}{(\frac{11}{5})} . \color{green}{(p)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(\frac{1}{12})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{12}b+\frac{11}{5}p+\frac{11}{5}.\frac{1}{12}& \text{Uitwerken } \\ & =-bp-\frac{1}{12}b+\frac{11}{5}p+\frac{11}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(3-q)(\frac{-10}{13}+q)& =(\color{red}{-q}+\color{orange}{3}).(\color{green}{q}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(3)} . \color{green}{(q)} + \color{orange}{(3)} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{10}{13}q+3q-3.\frac{10}{13}& \text{Uitwerken } \\ & =-q^2+(\frac{10}{13}+3)q-\frac{30}{13} & \text{Neem samen} \\ &=-q^2+\frac{49}{13}q-\frac{30}{13} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(b+\frac{2}{5})(b+\frac{-16}{15})& =(\color{red}{b}+\color{orange}{\frac{2}{5}}).(\color{green}{b}+\color{blue}{\frac{-16}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{15})} + \color{orange}{(\frac{2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-16}{15})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{16}{15}b+\frac{2}{5}b-\frac{2}{5}.\frac{16}{15}& \text{Uitwerken } \\ & =b^2+((\frac{-16}{15})+\frac{2}{5})b-(\frac{-32}{75}) & \text{Neem samen} \\ &=b^2-\frac{10}{15}b-(\frac{-32}{75}) & \text{Maak de som} \\ &=b^2-\frac{2}{3}b+\frac{32}{75} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{4}{11}-a)(\frac{19}{12}-p)& =(\color{red}{-a}+\color{orange}{\frac{4}{11}}).(\color{green}{-p}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{4}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{12}a-\frac{4}{11}p+\frac{4}{11}.\frac{19}{12}& \text{Uitwerken } \\ & =ap-\frac{19}{12}a-\frac{4}{11}p+\frac{76}{132} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{19}{12}a-\frac{4}{11}p+\frac{19}{33} & \text{Vereenvoudig} \\\end{align}\)
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