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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{11}{5}-q)(\frac{-14}{7}+x)& =(\color{red}{-q}+\color{orange}{\frac{11}{5}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(-2)} + \color{orange}{(\frac{11}{5})} . \color{green}{(x)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -qx+2q+\frac{11}{5}x-\frac{11}{5}.2& \text{Uitwerken } \\ & =-qx+2q+\frac{11}{5}x-\frac{22}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{17}{14}-p)(\frac{-13}{13}-q)& =(\color{red}{-p}+\color{orange}{\frac{17}{14}}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(-1)} + \color{orange}{(\frac{17}{14})} . \color{green}{(-q)} + \color{orange}{(\frac{17}{14})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq+1p-\frac{17}{14}q-\frac{17}{14}.1& \text{Uitwerken } \\ & =pq+1p-\frac{17}{14}q-\frac{17}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{10}{8}-x)(\frac{4}{6}+a)& =(\color{red}{-x}+\color{orange}{\frac{5}{4}}).(\color{green}{a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{5}{4})} . \color{green}{(a)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{2}{3}x+\frac{5}{4}a+\frac{5}{4}.\frac{2}{3}& \text{Uitwerken } \\ & =-ax-\frac{2}{3}x+\frac{5}{4}a+\frac{10}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{2}{3}x+\frac{5}{4}a+\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-19}{5}+x)(\frac{-18}{17}-b)& =(\color{red}{x}+\color{orange}{\frac{-19}{5}}).(\color{green}{-b}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{-19}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{5})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{18}{17}x+\frac{19}{5}b+\frac{19}{5}.\frac{18}{17}& \text{Uitwerken } \\ & =-bx-\frac{18}{17}x+\frac{19}{5}b+\frac{342}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{15}{19}-a)(\frac{3}{17}+b)& =(\color{red}{-a}+\color{orange}{\frac{15}{19}}).(\color{green}{b}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{15}{19})} . \color{green}{(b)} + \color{orange}{(\frac{15}{19})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{3}{17}a+\frac{15}{19}b+\frac{15}{19}.\frac{3}{17}& \text{Uitwerken } \\ & =-ab-\frac{3}{17}a+\frac{15}{19}b+\frac{45}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b-\frac{2}{4})(a-\frac{-4}{11})& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{4}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{4}{11})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{4}{11})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{4}{11}b-\frac{1}{2}a-\frac{1}{2}.\frac{4}{11}& \text{Uitwerken } \\ & =ab+\frac{4}{11}b-\frac{1}{2}a-\frac{4}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{4}{11}b-\frac{1}{2}a-\frac{2}{11} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{7}+b)(\frac{-11}{17}+p)& =(\color{red}{b}+\color{orange}{\frac{8}{7}}).(\color{green}{p}+\color{blue}{\frac{-11}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{17})} + \color{orange}{(\frac{8}{7})} . \color{green}{(p)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-11}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{11}{17}b+\frac{8}{7}p-\frac{8}{7}.\frac{11}{17}& \text{Uitwerken } \\ & =bp-\frac{11}{17}b+\frac{8}{7}p-\frac{88}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{18}{16}-a)(\frac{-2}{19}-p)& =(\color{red}{-a}+\color{orange}{\frac{9}{8}}).(\color{green}{-p}+\color{blue}{\frac{-2}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{-2}{19})} + \color{orange}{(\frac{9}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{-2}{19})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{2}{19}a-\frac{9}{8}p-\frac{9}{8}.\frac{2}{19}& \text{Uitwerken } \\ & =ap+\frac{2}{19}a-\frac{9}{8}p-\frac{18}{152} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{2}{19}a-\frac{9}{8}p-\frac{9}{76} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b+\frac{14}{15})(\frac{16}{6}-q)& =(\color{red}{b}+\color{orange}{\frac{14}{15}}).(\color{green}{-q}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(\frac{14}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{14}{15})} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{8}{3}b-\frac{14}{15}q+\frac{14}{15}.\frac{8}{3}& \text{Uitwerken } \\ & =-bq+\frac{8}{3}b-\frac{14}{15}q+\frac{112}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x-\frac{-15}{5})(\frac{7}{18}-x)& =(\color{red}{x}+\color{orange}{3}).(\color{green}{-x}+\color{blue}{\frac{7}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{7}{18})} + \color{orange}{(3)} . \color{green}{(-x)} + \color{orange}{(3)} . \color{blue}{(\frac{7}{18})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{7}{18}x-3x+3.\frac{7}{18}& \text{Uitwerken } \\ & =-x^2+(\frac{7}{18}+(-3))x+(\frac{-21}{18}) & \text{Neem samen} \\ &=-x^2-\frac{47}{18}x+(\frac{-21}{18}) & \text{Maak de som} \\ &=-x^2-\frac{47}{18}x+(\frac{-7}{6}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{-12}{5}-a)(a+\frac{10}{6})& =(\color{red}{-a}+\color{orange}{\frac{-12}{5}}).(\color{green}{a}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-12}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-12}{5})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{5}{3}a-\frac{12}{5}a-\frac{12}{5}.\frac{5}{3}& \text{Uitwerken } \\ & =-a^2+((\frac{-5}{3})+(\frac{-12}{5}))a-\frac{60}{15} & \text{Neem samen} \\ &=-a^2-\frac{61}{15}a-\frac{60}{15} & \text{Maak de som} \\ &=-a^2-\frac{61}{15}a-4 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{-7}{4}-q)(\frac{8}{16}-x)& =(\color{red}{-q}+\color{orange}{\frac{-7}{4}}).(\color{green}{-x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{2}q+\frac{7}{4}x-\frac{7}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =qx-\frac{1}{2}q+\frac{7}{4}x-\frac{7}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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