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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{7}{7}-p)(a+\frac{14}{13})& =(\color{red}{-p}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{14}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{14}{13})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{14}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{14}{13}p+1a+1.\frac{14}{13}& \text{Uitwerken } \\ & =-ap-\frac{14}{13}p+1a+\frac{14}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a+\frac{15}{9})(q+\frac{-20}{6})& =(\color{red}{a}+\color{orange}{\frac{5}{3}}).(\color{green}{q}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(\frac{5}{3})} . \color{green}{(q)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{10}{3}a+\frac{5}{3}q-\frac{5}{3}.\frac{10}{3}& \text{Uitwerken } \\ & =aq-\frac{10}{3}a+\frac{5}{3}q-\frac{50}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{18}{8})(b-\frac{16}{7})& =(\color{red}{a}+\color{orange}{\frac{9}{4}}).(\color{green}{b}+\color{blue}{\frac{-16}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{7})} + \color{orange}{(\frac{9}{4})} . \color{green}{(b)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{-16}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{16}{7}a+\frac{9}{4}b-\frac{9}{4}.\frac{16}{7}& \text{Uitwerken } \\ & =ab-\frac{16}{7}a+\frac{9}{4}b-\frac{144}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{16}{7}a+\frac{9}{4}b-\frac{36}{7} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-5}{17})(\frac{-19}{19}+a)& =(\color{red}{x}+\color{orange}{\frac{5}{17}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{5}{17})} . \color{green}{(a)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1x+\frac{5}{17}a-\frac{5}{17}.1& \text{Uitwerken } \\ & =ax-1x+\frac{5}{17}a-\frac{5}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-15}{2}+a)(q+\frac{-3}{9})& =(\color{red}{a}+\color{orange}{\frac{-15}{2}}).(\color{green}{q}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-15}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{3}a-\frac{15}{2}q+\frac{15}{2}.\frac{1}{3}& \text{Uitwerken } \\ & =aq-\frac{1}{3}a-\frac{15}{2}q+\frac{15}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{1}{3}a-\frac{15}{2}q+\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-13}{11}-q)(\frac{-17}{15}+a)& =(\color{red}{-q}+\color{orange}{\frac{-13}{11}}).(\color{green}{a}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{-13}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{11})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{17}{15}q-\frac{13}{11}a+\frac{13}{11}.\frac{17}{15}& \text{Uitwerken } \\ & =-aq+\frac{17}{15}q-\frac{13}{11}a+\frac{221}{165} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{17}{20}-x)(\frac{-9}{5}-a)& =(\color{red}{-x}+\color{orange}{\frac{17}{20}}).(\color{green}{-a}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{17}{20})} . \color{green}{(-a)} + \color{orange}{(\frac{17}{20})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{5}x-\frac{17}{20}a-\frac{17}{20}.\frac{9}{5}& \text{Uitwerken } \\ & =ax+\frac{9}{5}x-\frac{17}{20}a-\frac{153}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{12}{15}-b)(\frac{20}{19}+p)& =(\color{red}{-b}+\color{orange}{\frac{4}{5}}).(\color{green}{p}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{20}{19}b+\frac{4}{5}p+\frac{4}{5}.\frac{20}{19}& \text{Uitwerken } \\ & =-bp-\frac{20}{19}b+\frac{4}{5}p+\frac{80}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{20}{19}b+\frac{4}{5}p+\frac{16}{19} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p-\frac{-1}{11})(p-\frac{17}{14})& =(\color{red}{p}+\color{orange}{\frac{1}{11}}).(\color{green}{p}+\color{blue}{\frac{-17}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{14})} + \color{orange}{(\frac{1}{11})} . \color{green}{(p)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(\frac{-17}{14})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{17}{14}p+\frac{1}{11}p-\frac{1}{11}.\frac{17}{14}& \text{Uitwerken } \\ & =p^2+((\frac{-17}{14})+\frac{1}{11})p-(\frac{-17}{154}) & \text{Neem samen} \\ &=p^2-\frac{173}{154}p-(\frac{-17}{154}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(a-\frac{-18}{16})(\frac{-13}{4}+b)& =(\color{red}{a}+\color{orange}{\frac{9}{8}}).(\color{green}{b}+\color{blue}{\frac{-13}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{4})} + \color{orange}{(\frac{9}{8})} . \color{green}{(b)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{-13}{4})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{4}a+\frac{9}{8}b-\frac{9}{8}.\frac{13}{4}& \text{Uitwerken } \\ & =ab-\frac{13}{4}a+\frac{9}{8}b-\frac{117}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q-\frac{-17}{10})(p-\frac{-1}{12})& =(\color{red}{q}+\color{orange}{\frac{17}{10}}).(\color{green}{p}+\color{blue}{\frac{1}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{12})} + \color{orange}{(\frac{17}{10})} . \color{green}{(p)} + \color{orange}{(\frac{17}{10})} . \color{blue}{(\frac{1}{12})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{12}q+\frac{17}{10}p+\frac{17}{10}.\frac{1}{12}& \text{Uitwerken } \\ & =pq+\frac{1}{12}q+\frac{17}{10}p+\frac{17}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-17}{15}-p)(\frac{10}{8}+q)& =(\color{red}{-p}+\color{orange}{\frac{-17}{15}}).(\color{green}{q}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-17}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{15})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{5}{4}p-\frac{17}{15}q-\frac{17}{15}.\frac{5}{4}& \text{Uitwerken } \\ & =-pq-\frac{5}{4}p-\frac{17}{15}q-\frac{85}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{5}{4}p-\frac{17}{15}q-\frac{17}{12} & \text{Vereenvoudig} \\\end{align}\)
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