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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{7}{20})(b-\frac{11}{12})& =(\color{red}{x}+\color{orange}{\frac{-7}{20}}).(\color{green}{b}+\color{blue}{\frac{-11}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{12})} + \color{orange}{(\frac{-7}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(\frac{-11}{12})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{12}x-\frac{7}{20}b+\frac{7}{20}.\frac{11}{12}& \text{Uitwerken } \\ & =bx-\frac{11}{12}x-\frac{7}{20}b+\frac{77}{240} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-5}{14}-q)(\frac{13}{20}-q)& =(\color{red}{-q}+\color{orange}{\frac{-5}{14}}).(\color{green}{-q}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{13}{20}q+\frac{5}{14}q-\frac{5}{14}.\frac{13}{20}& \text{Uitwerken } \\ & =q^2+((\frac{-13}{20})+\frac{5}{14})q-(\frac{-65}{280}) & \text{Neem samen} \\ &=q^2-\frac{41}{140}q-(\frac{-65}{280}) & \text{Maak de som} \\ &=q^2-\frac{41}{140}q+\frac{13}{56} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(b+\frac{13}{19})(\frac{5}{9}+b)& =(\color{red}{b}+\color{orange}{\frac{13}{19}}).(\color{green}{b}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{13}{19})} . \color{green}{(b)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{9}b+\frac{13}{19}b+\frac{13}{19}.\frac{5}{9}& \text{Uitwerken } \\ & =b^2+(\frac{5}{9}+\frac{13}{19})b+\frac{65}{171} & \text{Neem samen} \\ &=b^2+\frac{212}{171}b+\frac{65}{171} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{7}{8}+q)(a+\frac{-6}{9})& =(\color{red}{q}+\color{orange}{\frac{7}{8}}).(\color{green}{a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{7}{8})} . \color{green}{(a)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{2}{3}q+\frac{7}{8}a-\frac{7}{8}.\frac{2}{3}& \text{Uitwerken } \\ & =aq-\frac{2}{3}q+\frac{7}{8}a-\frac{14}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{2}{3}q+\frac{7}{8}a-\frac{7}{12} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-10}{9}+x)(b+\frac{12}{12})& =(\color{red}{x}+\color{orange}{\frac{-10}{9}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-10}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx+1x-\frac{10}{9}b-\frac{10}{9}.1& \text{Uitwerken } \\ & =bx+1x-\frac{10}{9}b-\frac{10}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-12}{9}-p)(\frac{-12}{16}-b)& =(\color{red}{-p}+\color{orange}{\frac{-4}{3}}).(\color{green}{-b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{4}p+\frac{4}{3}b+\frac{4}{3}.\frac{3}{4}& \text{Uitwerken } \\ & =bp+\frac{3}{4}p+\frac{4}{3}b+\frac{12}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{3}{4}p+\frac{4}{3}b+1 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-10}{18}-p)(\frac{8}{16}+a)& =(\color{red}{-p}+\color{orange}{\frac{-5}{9}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{2}p-\frac{5}{9}a-\frac{5}{9}.\frac{1}{2}& \text{Uitwerken } \\ & =-ap-\frac{1}{2}p-\frac{5}{9}a-\frac{5}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-8}{18})(a-\frac{-12}{7})& =(\color{red}{x}+\color{orange}{\frac{4}{9}}).(\color{green}{a}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(\frac{4}{9})} . \color{green}{(a)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{12}{7}x+\frac{4}{9}a+\frac{4}{9}.\frac{12}{7}& \text{Uitwerken } \\ & =ax+\frac{12}{7}x+\frac{4}{9}a+\frac{48}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{12}{7}x+\frac{4}{9}a+\frac{16}{21} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{11}{16}-b)(b+\frac{-4}{20})& =(\color{red}{-b}+\color{orange}{\frac{11}{16}}).(\color{green}{b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{11}{16})} . \color{green}{(b)} + \color{orange}{(\frac{11}{16})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{1}{5}b+\frac{11}{16}b-\frac{11}{16}.\frac{1}{5}& \text{Uitwerken } \\ & =-b^2+(\frac{1}{5}+\frac{11}{16})b-\frac{11}{80} & \text{Neem samen} \\ &=-b^2+\frac{71}{80}b-\frac{11}{80} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{8}{17}+q)(\frac{-1}{2}-p)& =(\color{red}{q}+\color{orange}{\frac{8}{17}}).(\color{green}{-p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{8}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{8}{17})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{2}q-\frac{8}{17}p-\frac{8}{17}.\frac{1}{2}& \text{Uitwerken } \\ & =-pq-\frac{1}{2}q-\frac{8}{17}p-\frac{8}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{1}{2}q-\frac{8}{17}p-\frac{4}{17} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-14}{4}-b)(\frac{-1}{10}+q)& =(\color{red}{-b}+\color{orange}{\frac{-7}{2}}).(\color{green}{q}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{10}b-\frac{7}{2}q+\frac{7}{2}.\frac{1}{10}& \text{Uitwerken } \\ & =-bq+\frac{1}{10}b-\frac{7}{2}q+\frac{7}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-12}{6})(\frac{-13}{14}+q)& =(\color{red}{b}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{-13}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{14})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{-13}{14})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{13}{14}b+2q-2.\frac{13}{14}& \text{Uitwerken } \\ & =bq-\frac{13}{14}b+2q-\frac{26}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{13}{14}b+2q-\frac{13}{7} & \text{Vereenvoudig} \\\end{align}\)
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