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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{18}{6}-a)(q+\frac{-6}{4})& =(\color{red}{-a}+\color{orange}{3}).(\color{green}{q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(3)} . \color{green}{(q)} + \color{orange}{(3)} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{3}{2}a+3q-3.\frac{3}{2}& \text{Uitwerken } \\ & =-aq+\frac{3}{2}a+3q-\frac{9}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{20}{14}+x)(q-\frac{-3}{18})& =(\color{red}{x}+\color{orange}{\frac{10}{7}}).(\color{green}{q}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{10}{7})} . \color{green}{(q)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{6}x+\frac{10}{7}q+\frac{10}{7}.\frac{1}{6}& \text{Uitwerken } \\ & =qx+\frac{1}{6}x+\frac{10}{7}q+\frac{10}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{1}{6}x+\frac{10}{7}q+\frac{5}{21} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{16}{13}+a)(x+\frac{-2}{18})& =(\color{red}{a}+\color{orange}{\frac{16}{13}}).(\color{green}{x}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{16}{13})} . \color{green}{(x)} + \color{orange}{(\frac{16}{13})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{9}a+\frac{16}{13}x-\frac{16}{13}.\frac{1}{9}& \text{Uitwerken } \\ & =ax-\frac{1}{9}a+\frac{16}{13}x-\frac{16}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{16}{3}-q)(b-\frac{-12}{8})& =(\color{red}{-q}+\color{orange}{\frac{16}{3}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{16}{3})} . \color{green}{(b)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{3}{2}q+\frac{16}{3}b+\frac{16}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =-bq-\frac{3}{2}q+\frac{16}{3}b+\frac{48}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{3}{2}q+\frac{16}{3}b+8 & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-12}{16}+b)(x+\frac{-1}{13})& =(\color{red}{b}+\color{orange}{\frac{-3}{4}}).(\color{green}{x}+\color{blue}{\frac{-1}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{13})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-1}{13})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{13}b-\frac{3}{4}x+\frac{3}{4}.\frac{1}{13}& \text{Uitwerken } \\ & =bx-\frac{1}{13}b-\frac{3}{4}x+\frac{3}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-17}{4}+q)(\frac{3}{15}+x)& =(\color{red}{q}+\color{orange}{\frac{-17}{4}}).(\color{green}{x}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-17}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{4})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{5}q-\frac{17}{4}x-\frac{17}{4}.\frac{1}{5}& \text{Uitwerken } \\ & =qx+\frac{1}{5}q-\frac{17}{4}x-\frac{17}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-2}{14}-q)(\frac{19}{7}-a)& =(\color{red}{-q}+\color{orange}{\frac{-1}{7}}).(\color{green}{-a}+\color{blue}{\frac{19}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{19}{7})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{19}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{19}{7}q+\frac{1}{7}a-\frac{1}{7}.\frac{19}{7}& \text{Uitwerken } \\ & =aq-\frac{19}{7}q+\frac{1}{7}a-\frac{19}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{11}{15}-a)(\frac{-10}{4}-b)& =(\color{red}{-a}+\color{orange}{\frac{11}{15}}).(\color{green}{-b}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{11}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{2}a-\frac{11}{15}b-\frac{11}{15}.\frac{5}{2}& \text{Uitwerken } \\ & =ab+\frac{5}{2}a-\frac{11}{15}b-\frac{55}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{5}{2}a-\frac{11}{15}b-\frac{11}{6} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{5}{3}-b)(b-\frac{14}{6})& =(\color{red}{-b}+\color{orange}{\frac{5}{3}}).(\color{green}{b}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{5}{3})} . \color{green}{(b)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{7}{3}b+\frac{5}{3}b-\frac{5}{3}.\frac{7}{3}& \text{Uitwerken } \\ & =-b^2+(\frac{7}{3}+\frac{5}{3})b-\frac{35}{9} & \text{Neem samen} \\ &=-b^2+\frac{12}{3}b-\frac{35}{9} & \text{Maak de som} \\ &=-b^2+4b-\frac{35}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{10}{19}-p)(p-\frac{20}{15})& =(\color{red}{-p}+\color{orange}{\frac{10}{19}}).(\color{green}{p}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{10}{19})} . \color{green}{(p)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{4}{3}p+\frac{10}{19}p-\frac{10}{19}.\frac{4}{3}& \text{Uitwerken } \\ & =-p^2+(\frac{4}{3}+\frac{10}{19})p-\frac{40}{57} & \text{Neem samen} \\ &=-p^2+\frac{106}{57}p-\frac{40}{57} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(a-\frac{15}{16})(\frac{16}{17}+q)& =(\color{red}{a}+\color{orange}{\frac{-15}{16}}).(\color{green}{q}+\color{blue}{\frac{16}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{16}{17})} + \color{orange}{(\frac{-15}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(\frac{16}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{16}{17}a-\frac{15}{16}q-\frac{15}{16}.\frac{16}{17}& \text{Uitwerken } \\ & =aq+\frac{16}{17}a-\frac{15}{16}q-\frac{240}{272} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{16}{17}a-\frac{15}{16}q-\frac{15}{17} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(b-\frac{-19}{5})((-7)+b)& =(\color{red}{b}+\color{orange}{\frac{19}{5}}).(\color{green}{b}+\color{blue}{(-7)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(-7)} + \color{orange}{(\frac{19}{5})} . \color{green}{(b)} + \color{orange}{(\frac{19}{5})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = bb-7b+\frac{19}{5}b-\frac{19}{5}.7& \text{Uitwerken } \\ & =b^2+((-7)+\frac{19}{5})b-(\frac{-133}{5}) & \text{Neem samen} \\ &=b^2-\frac{16}{5}b-(\frac{-133}{5}) & \text{Maak de som} \\\end{align}\)
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