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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-4}{14})(\frac{-10}{10}-q)& =(\color{red}{a}+\color{orange}{\frac{-2}{7}}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-2}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -aq-1a+\frac{2}{7}q+\frac{2}{7}.1& \text{Uitwerken } \\ & =-aq-1a+\frac{2}{7}q+\frac{2}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{-20}{17})(\frac{10}{6}+b)& =(\color{red}{p}+\color{orange}{\frac{20}{17}}).(\color{green}{b}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{20}{17})} . \color{green}{(b)} + \color{orange}{(\frac{20}{17})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{3}p+\frac{20}{17}b+\frac{20}{17}.\frac{5}{3}& \text{Uitwerken } \\ & =bp+\frac{5}{3}p+\frac{20}{17}b+\frac{100}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{13}{2}-q)(b-\frac{-6}{2})& =(\color{red}{-q}+\color{orange}{\frac{13}{2}}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(3)} + \color{orange}{(\frac{13}{2})} . \color{green}{(b)} + \color{orange}{(\frac{13}{2})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -bq-3q+\frac{13}{2}b+\frac{13}{2}.3& \text{Uitwerken } \\ & =-bq-3q+\frac{13}{2}b+\frac{39}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p-\frac{-4}{5})(x+\frac{6}{4})& =(\color{red}{p}+\color{orange}{\frac{4}{5}}).(\color{green}{x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{2}p+\frac{4}{5}x+\frac{4}{5}.\frac{3}{2}& \text{Uitwerken } \\ & =px+\frac{3}{2}p+\frac{4}{5}x+\frac{12}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{3}{2}p+\frac{4}{5}x+\frac{6}{5} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(x+\frac{18}{7})(\frac{-4}{11}+x)& =(\color{red}{x}+\color{orange}{\frac{18}{7}}).(\color{green}{x}+\color{blue}{\frac{-4}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{11})} + \color{orange}{(\frac{18}{7})} . \color{green}{(x)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{-4}{11})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{4}{11}x+\frac{18}{7}x-\frac{18}{7}.\frac{4}{11}& \text{Uitwerken } \\ & =x^2+((\frac{-4}{11})+\frac{18}{7})x-(\frac{-72}{77}) & \text{Neem samen} \\ &=x^2+\frac{170}{77}x-(\frac{-72}{77}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(b+\frac{-10}{8})(\frac{19}{4}-a)& =(\color{red}{b}+\color{orange}{\frac{-5}{4}}).(\color{green}{-a}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{19}{4}b+\frac{5}{4}a-\frac{5}{4}.\frac{19}{4}& \text{Uitwerken } \\ & =-ab+\frac{19}{4}b+\frac{5}{4}a-\frac{95}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-\frac{-18}{10})(p+\frac{-5}{4})& =(\color{red}{b}+\color{orange}{\frac{9}{5}}).(\color{green}{p}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{9}{5})} . \color{green}{(p)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{4}b+\frac{9}{5}p-\frac{9}{5}.\frac{5}{4}& \text{Uitwerken } \\ & =bp-\frac{5}{4}b+\frac{9}{5}p-\frac{45}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{5}{4}b+\frac{9}{5}p-\frac{9}{4} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-20}{8})(a-\frac{11}{5})& =(\color{red}{b}+\color{orange}{\frac{-5}{2}}).(\color{green}{a}+\color{blue}{\frac{-11}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{5})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-11}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{11}{5}b-\frac{5}{2}a+\frac{5}{2}.\frac{11}{5}& \text{Uitwerken } \\ & =ab-\frac{11}{5}b-\frac{5}{2}a+\frac{55}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{11}{5}b-\frac{5}{2}a+\frac{11}{2} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-19}{6}-b)(\frac{6}{18}+b)& =(\color{red}{-b}+\color{orange}{\frac{-19}{6}}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-19}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{6})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{1}{3}b-\frac{19}{6}b-\frac{19}{6}.\frac{1}{3}& \text{Uitwerken } \\ & =-b^2+((\frac{-1}{3})+(\frac{-19}{6}))b-\frac{19}{18} & \text{Neem samen} \\ &=-b^2-\frac{21}{6}b-\frac{19}{18} & \text{Maak de som} \\ &=-b^2-\frac{7}{2}b-\frac{19}{18} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{-17}{19}+b)(a-\frac{17}{2})& =(\color{red}{b}+\color{orange}{\frac{-17}{19}}).(\color{green}{a}+\color{blue}{\frac{-17}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{2})} + \color{orange}{(\frac{-17}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(\frac{-17}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{17}{2}b-\frac{17}{19}a+\frac{17}{19}.\frac{17}{2}& \text{Uitwerken } \\ & =ab-\frac{17}{2}b-\frac{17}{19}a+\frac{289}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p-\frac{20}{4})(p+\frac{-3}{19})& =(\color{red}{p}+\color{orange}{(-5)}).(\color{green}{p}+\color{blue}{\frac{-3}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{19})} + \color{orange}{(-5)} . \color{green}{(p)} + \color{orange}{(-5)} . \color{blue}{(\frac{-3}{19})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{3}{19}p-5p+5.\frac{3}{19}& \text{Uitwerken } \\ & =p^2+((\frac{-3}{19})+(-5))p+\frac{15}{19} & \text{Neem samen} \\ &=p^2-\frac{98}{19}p+\frac{15}{19} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(14-a)(\frac{-20}{14}+x)& =(\color{red}{-a}+\color{orange}{14}).(\color{green}{x}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(14)} . \color{green}{(x)} + \color{orange}{(14)} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{10}{7}a+14x-14.\frac{10}{7}& \text{Uitwerken } \\ & =-ax+\frac{10}{7}a+14x-\frac{140}{7} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{10}{7}a+14x-20 & \text{Vereenvoudig} \\\end{align}\)
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