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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-18)(x+\frac{-3}{18})& =(\color{red}{a}+\color{orange}{(-18)}).(\color{green}{x}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(-18)} . \color{green}{(x)} + \color{orange}{(-18)} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{6}a-18x+18.\frac{1}{6}& \text{Uitwerken } \\ & =ax-\frac{1}{6}a-18x+\frac{18}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{1}{6}a-18x+3 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-11}{18})(\frac{16}{7}+b)& =(\color{red}{b}+\color{orange}{\frac{-11}{18}}).(\color{green}{b}+\color{blue}{\frac{16}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{16}{7})} + \color{orange}{(\frac{-11}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{18})} . \color{blue}{(\frac{16}{7})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{16}{7}b-\frac{11}{18}b-\frac{11}{18}.\frac{16}{7}& \text{Uitwerken } \\ & =b^2+(\frac{16}{7}+(\frac{-11}{18}))b-(\frac{-176}{126}) & \text{Neem samen} \\ &=b^2+\frac{211}{126}b-(\frac{-176}{126}) & \text{Maak de som} \\ &=b^2+\frac{211}{126}b+\frac{88}{63} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(b+\frac{-10}{2})(b-\frac{9}{6})& =(\color{red}{b}+\color{orange}{(-5)}).(\color{green}{b}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(-5)} . \color{green}{(b)} + \color{orange}{(-5)} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{3}{2}b-5b+5.\frac{3}{2}& \text{Uitwerken } \\ & =b^2+((\frac{-3}{2})+(-5))b+\frac{15}{2} & \text{Neem samen} \\ &=b^2-\frac{13}{2}b+\frac{15}{2} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-6}{8})(p+\frac{18}{18})& =(\color{red}{x}+\color{orange}{\frac{3}{4}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = px+1x+\frac{3}{4}p+\frac{3}{4}.1& \text{Uitwerken } \\ & =px+1x+\frac{3}{4}p+\frac{3}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-3}{16}-p)(x-\frac{19}{3})& =(\color{red}{-p}+\color{orange}{\frac{-3}{16}}).(\color{green}{x}+\color{blue}{\frac{-19}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-19}{3})} + \color{orange}{(\frac{-3}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{16})} . \color{blue}{(\frac{-19}{3})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{19}{3}p-\frac{3}{16}x+\frac{3}{16}.\frac{19}{3}& \text{Uitwerken } \\ & =-px+\frac{19}{3}p-\frac{3}{16}x+\frac{57}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{19}{3}p-\frac{3}{16}x+\frac{19}{16} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a-17)(\frac{7}{14}-q)& =(\color{red}{a}+\color{orange}{(-17)}).(\color{green}{-q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(-17)} . \color{green}{(-q)} + \color{orange}{(-17)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{2}a+17q-17.\frac{1}{2}& \text{Uitwerken } \\ & =-aq+\frac{1}{2}a+17q-\frac{17}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{11}{19}+a)(a+\frac{-17}{5})& =(\color{red}{a}+\color{orange}{\frac{11}{19}}).(\color{green}{a}+\color{blue}{\frac{-17}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{5})} + \color{orange}{(\frac{11}{19})} . \color{green}{(a)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(\frac{-17}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{17}{5}a+\frac{11}{19}a-\frac{11}{19}.\frac{17}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-17}{5})+\frac{11}{19})a-(\frac{-187}{95}) & \text{Neem samen} \\ &=a^2-\frac{268}{95}a-(\frac{-187}{95}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(x-\frac{19}{6})(\frac{20}{12}-a)& =(\color{red}{x}+\color{orange}{\frac{-19}{6}}).(\color{green}{-a}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-19}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{6})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{5}{3}x+\frac{19}{6}a-\frac{19}{6}.\frac{5}{3}& \text{Uitwerken } \\ & =-ax+\frac{5}{3}x+\frac{19}{6}a-\frac{95}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{19}{8}+a)(20-p)& =(\color{red}{a}+\color{orange}{\frac{19}{8}}).(\color{green}{-p}+\color{blue}{20})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(20)} + \color{orange}{(\frac{19}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(20)}& \text{Boogjes en uitschrijven} \\ & = -ap+20a-\frac{19}{8}p+\frac{19}{8}.20& \text{Uitwerken } \\ & =-ap+20a-\frac{19}{8}p+\frac{380}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+20a-\frac{19}{8}p+\frac{95}{2} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-8}{18})(p-\frac{13}{3})& =(\color{red}{q}+\color{orange}{\frac{-4}{9}}).(\color{green}{p}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{13}{3}q-\frac{4}{9}p+\frac{4}{9}.\frac{13}{3}& \text{Uitwerken } \\ & =pq-\frac{13}{3}q-\frac{4}{9}p+\frac{52}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{13}{10}-p)(\frac{9}{15}+x)& =(\color{red}{-p}+\color{orange}{\frac{13}{10}}).(\color{green}{x}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{13}{10})} . \color{green}{(x)} + \color{orange}{(\frac{13}{10})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{3}{5}p+\frac{13}{10}x+\frac{13}{10}.\frac{3}{5}& \text{Uitwerken } \\ & =-px-\frac{3}{5}p+\frac{13}{10}x+\frac{39}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a-\frac{-20}{2})(\frac{10}{18}-b)& =(\color{red}{a}+\color{orange}{10}).(\color{green}{-b}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(10)} . \color{green}{(-b)} + \color{orange}{(10)} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{5}{9}a-10b+10.\frac{5}{9}& \text{Uitwerken } \\ & =-ab+\frac{5}{9}a-10b+\frac{50}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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