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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{17}{6})(\frac{-7}{15}+b)& =(\color{red}{b}+\color{orange}{\frac{-17}{6}}).(\color{green}{b}+\color{blue}{\frac{-7}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{15})} + \color{orange}{(\frac{-17}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{6})} . \color{blue}{(\frac{-7}{15})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{7}{15}b-\frac{17}{6}b+\frac{17}{6}.\frac{7}{15}& \text{Uitwerken } \\ & =b^2+((\frac{-7}{15})+(\frac{-17}{6}))b+\frac{119}{90} & \text{Neem samen} \\ &=b^2-\frac{99}{30}b+\frac{119}{90} & \text{Maak de som} \\ &=b^2-\frac{33}{10}b+\frac{119}{90} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-20}{9})(\frac{19}{18}-a)& =(\color{red}{p}+\color{orange}{\frac{-20}{9}}).(\color{green}{-a}+\color{blue}{\frac{19}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{19}{18})} + \color{orange}{(\frac{-20}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-20}{9})} . \color{blue}{(\frac{19}{18})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{19}{18}p+\frac{20}{9}a-\frac{20}{9}.\frac{19}{18}& \text{Uitwerken } \\ & =-ap+\frac{19}{18}p+\frac{20}{9}a-\frac{380}{162} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{19}{18}p+\frac{20}{9}a-\frac{190}{81} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{12}{14}-x)((-3)+x)& =(\color{red}{-x}+\color{orange}{\frac{6}{7}}).(\color{green}{x}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(-3)} + \color{orange}{(\frac{6}{7})} . \color{green}{(x)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -xx+3x+\frac{6}{7}x-\frac{6}{7}.3& \text{Uitwerken } \\ & =-x^2+(3+\frac{6}{7})x-\frac{18}{7} & \text{Neem samen} \\ &=-x^2+\frac{27}{7}x-\frac{18}{7} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(\frac{-16}{2}+p)(\frac{16}{14}+q)& =(\color{red}{p}+\color{orange}{(-8)}).(\color{green}{q}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(-8)} . \color{green}{(q)} + \color{orange}{(-8)} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{8}{7}p-8q-8.\frac{8}{7}& \text{Uitwerken } \\ & =pq+\frac{8}{7}p-8q-\frac{64}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-6}{8}+p)(\frac{-6}{17}-x)& =(\color{red}{p}+\color{orange}{\frac{-3}{4}}).(\color{green}{-x}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{6}{17}p+\frac{3}{4}x+\frac{3}{4}.\frac{6}{17}& \text{Uitwerken } \\ & =-px-\frac{6}{17}p+\frac{3}{4}x+\frac{18}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{6}{17}p+\frac{3}{4}x+\frac{9}{34} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(b+\frac{-6}{20})(\frac{13}{6}-a)& =(\color{red}{b}+\color{orange}{\frac{-3}{10}}).(\color{green}{-a}+\color{blue}{\frac{13}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{13}{6})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{13}{6})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{13}{6}b+\frac{3}{10}a-\frac{3}{10}.\frac{13}{6}& \text{Uitwerken } \\ & =-ab+\frac{13}{6}b+\frac{3}{10}a-\frac{39}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{13}{6}b+\frac{3}{10}a-\frac{13}{20} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-16}{12}-b)(a+\frac{-7}{5})& =(\color{red}{-b}+\color{orange}{\frac{-4}{3}}).(\color{green}{a}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{7}{5}b-\frac{4}{3}a+\frac{4}{3}.\frac{7}{5}& \text{Uitwerken } \\ & =-ab+\frac{7}{5}b-\frac{4}{3}a+\frac{28}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{5}{10}-x)(x+\frac{-6}{8})& =(\color{red}{-x}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{3}{4}x+\frac{1}{2}x-\frac{1}{2}.\frac{3}{4}& \text{Uitwerken } \\ & =-x^2+(\frac{3}{4}+\frac{1}{2})x-\frac{3}{8} & \text{Neem samen} \\ &=-x^2+\frac{5}{4}x-\frac{3}{8} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-5}{15}-a)(q-\frac{-11}{18})& =(\color{red}{-a}+\color{orange}{\frac{-1}{3}}).(\color{green}{q}+\color{blue}{\frac{11}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{18})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{11}{18})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{11}{18}a-\frac{1}{3}q-\frac{1}{3}.\frac{11}{18}& \text{Uitwerken } \\ & =-aq-\frac{11}{18}a-\frac{1}{3}q-\frac{11}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{18}{14}+b)(b+\frac{-4}{20})& =(\color{red}{b}+\color{orange}{\frac{9}{7}}).(\color{green}{b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{9}{7})} . \color{green}{(b)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{1}{5}b+\frac{9}{7}b-\frac{9}{7}.\frac{1}{5}& \text{Uitwerken } \\ & =b^2+((\frac{-1}{5})+\frac{9}{7})b-(\frac{-9}{35}) & \text{Neem samen} \\ &=b^2+\frac{38}{35}b-(\frac{-9}{35}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-14}{13})(p+(-7))& =(\color{red}{a}+\color{orange}{\frac{14}{13}}).(\color{green}{p}+\color{blue}{(-7)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-7)} + \color{orange}{(\frac{14}{13})} . \color{green}{(p)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = ap-7a+\frac{14}{13}p-\frac{14}{13}.7& \text{Uitwerken } \\ & =ap-7a+\frac{14}{13}p-\frac{98}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x-\frac{-14}{14})(b+5)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{b}+\color{blue}{5})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(5)} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = bx+5x+1b+1.5& \text{Uitwerken } \\ & =bx+5x+1b+5 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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