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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{19}{7})(x-\frac{19}{20})& =(\color{red}{b}+\color{orange}{\frac{-19}{7}}).(\color{green}{x}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(\frac{-19}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{7})} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{20}b-\frac{19}{7}x+\frac{19}{7}.\frac{19}{20}& \text{Uitwerken } \\ & =bx-\frac{19}{20}b-\frac{19}{7}x+\frac{361}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-5}{16}-b)(x-\frac{-8}{8})& =(\color{red}{-b}+\color{orange}{\frac{-5}{16}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(1)} + \color{orange}{(\frac{-5}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{16})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bx-1b-\frac{5}{16}x-\frac{5}{16}.1& \text{Uitwerken } \\ & =-bx-1b-\frac{5}{16}x-\frac{5}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p-\frac{8}{6})(a+\frac{13}{11})& =(\color{red}{p}+\color{orange}{\frac{-4}{3}}).(\color{green}{a}+\color{blue}{\frac{13}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{13}{11})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{13}{11})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{11}p-\frac{4}{3}a-\frac{4}{3}.\frac{13}{11}& \text{Uitwerken } \\ & =ap+\frac{13}{11}p-\frac{4}{3}a-\frac{52}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{8}{7}-x)(\frac{-16}{13}+p)& =(\color{red}{-x}+\color{orange}{\frac{8}{7}}).(\color{green}{p}+\color{blue}{\frac{-16}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-16}{13})} + \color{orange}{(\frac{8}{7})} . \color{green}{(p)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-16}{13})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{16}{13}x+\frac{8}{7}p-\frac{8}{7}.\frac{16}{13}& \text{Uitwerken } \\ & =-px+\frac{16}{13}x+\frac{8}{7}p-\frac{128}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b+\frac{8}{19})(b-\frac{-5}{6})& =(\color{red}{b}+\color{orange}{\frac{8}{19}}).(\color{green}{b}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{8}{19})} . \color{green}{(b)} + \color{orange}{(\frac{8}{19})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{5}{6}b+\frac{8}{19}b+\frac{8}{19}.\frac{5}{6}& \text{Uitwerken } \\ & =b^2+(\frac{5}{6}+\frac{8}{19})b+\frac{40}{114} & \text{Neem samen} \\ &=b^2+\frac{143}{114}b+\frac{40}{114} & \text{Maak de som} \\ &=b^2+\frac{143}{114}b+\frac{20}{57} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{-1}{17}+q)((-18)-a)& =(\color{red}{q}+\color{orange}{\frac{-1}{17}}).(\color{green}{-a}+\color{blue}{(-18)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(-18)} + \color{orange}{(\frac{-1}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(-18)}& \text{Boogjes en uitschrijven} \\ & = -aq-18q+\frac{1}{17}a+\frac{1}{17}.18& \text{Uitwerken } \\ & =-aq-18q+\frac{1}{17}a+\frac{18}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-\frac{16}{17})(\frac{-20}{12}-p)& =(\color{red}{q}+\color{orange}{\frac{-16}{17}}).(\color{green}{-p}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-16}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-16}{17})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{5}{3}q+\frac{16}{17}p+\frac{16}{17}.\frac{5}{3}& \text{Uitwerken } \\ & =-pq-\frac{5}{3}q+\frac{16}{17}p+\frac{80}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-1}{15}-b)(a+\frac{-12}{20})& =(\color{red}{-b}+\color{orange}{\frac{-1}{15}}).(\color{green}{a}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{3}{5}b-\frac{1}{15}a+\frac{1}{15}.\frac{3}{5}& \text{Uitwerken } \\ & =-ab+\frac{3}{5}b-\frac{1}{15}a+\frac{3}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{3}{5}b-\frac{1}{15}a+\frac{1}{25} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-5}{4}-b)(x-\frac{15}{15})& =(\color{red}{-b}+\color{orange}{\frac{-5}{4}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bx+1b-\frac{5}{4}x+\frac{5}{4}.1& \text{Uitwerken } \\ & =-bx+1b-\frac{5}{4}x+\frac{5}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q+\frac{-2}{5})(\frac{19}{14}+q)& =(\color{red}{q}+\color{orange}{\frac{-2}{5}}).(\color{green}{q}+\color{blue}{\frac{19}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{19}{14})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{19}{14})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{19}{14}q-\frac{2}{5}q-\frac{2}{5}.\frac{19}{14}& \text{Uitwerken } \\ & =q^2+(\frac{19}{14}+(\frac{-2}{5}))q-(\frac{-38}{70}) & \text{Neem samen} \\ &=q^2+\frac{67}{70}q-(\frac{-38}{70}) & \text{Maak de som} \\ &=q^2+\frac{67}{70}q+\frac{19}{35} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}((-14)-p)((-10)+x)& =(\color{red}{-p}+\color{orange}{(-14)}).(\color{green}{x}+\color{blue}{(-10)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(-10)} + \color{orange}{(-14)} . \color{green}{(x)} + \color{orange}{(-14)} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -px+10p-14x+14.10& \text{Uitwerken } \\ & =-px+10p-14x+140 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q+\frac{3}{19})(q+\frac{-17}{11})& =(\color{red}{q}+\color{orange}{\frac{3}{19}}).(\color{green}{q}+\color{blue}{\frac{-17}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{11})} + \color{orange}{(\frac{3}{19})} . \color{green}{(q)} + \color{orange}{(\frac{3}{19})} . \color{blue}{(\frac{-17}{11})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{17}{11}q+\frac{3}{19}q-\frac{3}{19}.\frac{17}{11}& \text{Uitwerken } \\ & =q^2+((\frac{-17}{11})+\frac{3}{19})q-(\frac{-51}{209}) & \text{Neem samen} \\ &=q^2-\frac{290}{209}q-(\frac{-51}{209}) & \text{Maak de som} \\\end{align}\)
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