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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{-12}{10})(\frac{18}{6}-a)& =(\color{red}{x}+\color{orange}{\frac{6}{5}}).(\color{green}{-a}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(3)} + \color{orange}{(\frac{6}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -ax+3x-\frac{6}{5}a+\frac{6}{5}.3& \text{Uitwerken } \\ & =-ax+3x-\frac{6}{5}a+\frac{18}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{4}{10}-b)(x-\frac{19}{9})& =(\color{red}{-b}+\color{orange}{\frac{2}{5}}).(\color{green}{x}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{2}{5})} . \color{green}{(x)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{19}{9}b+\frac{2}{5}x-\frac{2}{5}.\frac{19}{9}& \text{Uitwerken } \\ & =-bx+\frac{19}{9}b+\frac{2}{5}x-\frac{38}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-20}{18}-q)(p+\frac{1}{7})& =(\color{red}{-q}+\color{orange}{\frac{-10}{9}}).(\color{green}{p}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{7}q-\frac{10}{9}p-\frac{10}{9}.\frac{1}{7}& \text{Uitwerken } \\ & =-pq-\frac{1}{7}q-\frac{10}{9}p-\frac{10}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x+\frac{12}{18})(\frac{-12}{3}+q)& =(\color{red}{x}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-4)} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = qx-4x+\frac{2}{3}q-\frac{2}{3}.4& \text{Uitwerken } \\ & =qx-4x+\frac{2}{3}q-\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{7}{20}-b)(\frac{19}{17}-b)& =(\color{red}{-b}+\color{orange}{\frac{7}{20}}).(\color{green}{-b}+\color{blue}{\frac{19}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{17})} + \color{orange}{(\frac{7}{20})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{20})} . \color{blue}{(\frac{19}{17})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{19}{17}b-\frac{7}{20}b+\frac{7}{20}.\frac{19}{17}& \text{Uitwerken } \\ & =b^2+((\frac{-19}{17})+(\frac{-7}{20}))b+\frac{133}{340} & \text{Neem samen} \\ &=b^2-\frac{499}{340}b+\frac{133}{340} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{-18}{11}+q)(a-\frac{-10}{4})& =(\color{red}{q}+\color{orange}{\frac{-18}{11}}).(\color{green}{a}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-18}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-18}{11})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{2}q-\frac{18}{11}a-\frac{18}{11}.\frac{5}{2}& \text{Uitwerken } \\ & =aq+\frac{5}{2}q-\frac{18}{11}a-\frac{90}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{5}{2}q-\frac{18}{11}a-\frac{45}{11} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p-\frac{11}{16})(p-\frac{-6}{5})& =(\color{red}{p}+\color{orange}{\frac{-11}{16}}).(\color{green}{p}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{6}{5}p-\frac{11}{16}p-\frac{11}{16}.\frac{6}{5}& \text{Uitwerken } \\ & =p^2+(\frac{6}{5}+(\frac{-11}{16}))p-(\frac{-66}{80}) & \text{Neem samen} \\ &=p^2+\frac{41}{80}p-(\frac{-66}{80}) & \text{Maak de som} \\ &=p^2+\frac{41}{80}p+\frac{33}{40} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  8. \(\begin{align}(p+\frac{4}{8})(\frac{6}{15}+a)& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{2}{5}p+\frac{1}{2}a+\frac{1}{2}.\frac{2}{5}& \text{Uitwerken } \\ & =ap+\frac{2}{5}p+\frac{1}{2}a+\frac{2}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{2}{5}p+\frac{1}{2}a+\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{5}{12}+x)(\frac{-18}{20}-b)& =(\color{red}{x}+\color{orange}{\frac{5}{12}}).(\color{green}{-b}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{5}{12})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{12})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{9}{10}x-\frac{5}{12}b-\frac{5}{12}.\frac{9}{10}& \text{Uitwerken } \\ & =-bx-\frac{9}{10}x-\frac{5}{12}b-\frac{45}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{9}{10}x-\frac{5}{12}b-\frac{3}{8} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-10}{10}-b)(a-\frac{14}{10})& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{7}{5}b-1a+1.\frac{7}{5}& \text{Uitwerken } \\ & =-ab+\frac{7}{5}b-1a+\frac{7}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-8}{17}-x)(b+\frac{-7}{16})& =(\color{red}{-x}+\color{orange}{\frac{-8}{17}}).(\color{green}{b}+\color{blue}{\frac{-7}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{16})} + \color{orange}{(\frac{-8}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{17})} . \color{blue}{(\frac{-7}{16})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{7}{16}x-\frac{8}{17}b+\frac{8}{17}.\frac{7}{16}& \text{Uitwerken } \\ & =-bx+\frac{7}{16}x-\frac{8}{17}b+\frac{56}{272} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{7}{16}x-\frac{8}{17}b+\frac{7}{34} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{12}{18}-p)(a-\frac{-5}{19})& =(\color{red}{-p}+\color{orange}{\frac{2}{3}}).(\color{green}{a}+\color{blue}{\frac{5}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{19})} + \color{orange}{(\frac{2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{5}{19})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{5}{19}p+\frac{2}{3}a+\frac{2}{3}.\frac{5}{19}& \text{Uitwerken } \\ & =-ap-\frac{5}{19}p+\frac{2}{3}a+\frac{10}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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