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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{11}{6}-p)(b-\frac{-16}{11})& =(\color{red}{-p}+\color{orange}{\frac{11}{6}}).(\color{green}{b}+\color{blue}{\frac{16}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{16}{11})} + \color{orange}{(\frac{11}{6})} . \color{green}{(b)} + \color{orange}{(\frac{11}{6})} . \color{blue}{(\frac{16}{11})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{16}{11}p+\frac{11}{6}b+\frac{11}{6}.\frac{16}{11}& \text{Uitwerken } \\ & =-bp-\frac{16}{11}p+\frac{11}{6}b+\frac{176}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{16}{11}p+\frac{11}{6}b+\frac{8}{3} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p+\frac{7}{10})(a+\frac{9}{18})& =(\color{red}{p}+\color{orange}{\frac{7}{10}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{7}{10})} . \color{green}{(a)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{2}p+\frac{7}{10}a+\frac{7}{10}.\frac{1}{2}& \text{Uitwerken } \\ & =ap+\frac{1}{2}p+\frac{7}{10}a+\frac{7}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b-\frac{-3}{3})(\frac{-4}{16}+p)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{4}b+1p-1.\frac{1}{4}& \text{Uitwerken } \\ & =bp-\frac{1}{4}b+1p-\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{8}{14})(p-\frac{-14}{7})& =(\color{red}{q}+\color{orange}{\frac{4}{7}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{4}{7})} . \color{green}{(p)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = pq+2q+\frac{4}{7}p+\frac{4}{7}.2& \text{Uitwerken } \\ & =pq+2q+\frac{4}{7}p+\frac{8}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{20}{6})(q+\frac{-18}{13})& =(\color{red}{a}+\color{orange}{\frac{-10}{3}}).(\color{green}{q}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{18}{13}a-\frac{10}{3}q+\frac{10}{3}.\frac{18}{13}& \text{Uitwerken } \\ & =aq-\frac{18}{13}a-\frac{10}{3}q+\frac{180}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{18}{13}a-\frac{10}{3}q+\frac{60}{13} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x-\frac{-20}{10})(\frac{-2}{9}-x)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{-x}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(2)} . \color{green}{(-x)} + \color{orange}{(2)} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{2}{9}x-2x-2.\frac{2}{9}& \text{Uitwerken } \\ & =-x^2+((\frac{-2}{9})+(-2))x-\frac{4}{9} & \text{Neem samen} \\ &=-x^2-\frac{20}{9}x-\frac{4}{9} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(q+\frac{17}{15})(\frac{-15}{18}+x)& =(\color{red}{q}+\color{orange}{\frac{17}{15}}).(\color{green}{x}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{17}{15})} . \color{green}{(x)} + \color{orange}{(\frac{17}{15})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{6}q+\frac{17}{15}x-\frac{17}{15}.\frac{5}{6}& \text{Uitwerken } \\ & =qx-\frac{5}{6}q+\frac{17}{15}x-\frac{85}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{5}{6}q+\frac{17}{15}x-\frac{17}{18} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-1}{9}+a)(\frac{17}{19}+b)& =(\color{red}{a}+\color{orange}{\frac{-1}{9}}).(\color{green}{b}+\color{blue}{\frac{17}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{17}{19})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{17}{19})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{19}a-\frac{1}{9}b-\frac{1}{9}.\frac{17}{19}& \text{Uitwerken } \\ & =ab+\frac{17}{19}a-\frac{1}{9}b-\frac{17}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-6}{13})(p+\frac{20}{18})& =(\color{red}{x}+\color{orange}{\frac{6}{13}}).(\color{green}{p}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{6}{13})} . \color{green}{(p)} + \color{orange}{(\frac{6}{13})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{10}{9}x+\frac{6}{13}p+\frac{6}{13}.\frac{10}{9}& \text{Uitwerken } \\ & =px+\frac{10}{9}x+\frac{6}{13}p+\frac{60}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{10}{9}x+\frac{6}{13}p+\frac{20}{39} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p-\frac{3}{20})(p+\frac{-16}{2})& =(\color{red}{p}+\color{orange}{\frac{-3}{20}}).(\color{green}{p}+\color{blue}{(-8)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-8)} + \color{orange}{(\frac{-3}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{20})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = pp-8p-\frac{3}{20}p+\frac{3}{20}.8& \text{Uitwerken } \\ & =p^2+((-8)+(\frac{-3}{20}))p+\frac{24}{20} & \text{Neem samen} \\ &=p^2-\frac{163}{20}p+\frac{24}{20} & \text{Maak de som} \\ &=p^2-\frac{163}{20}p+\frac{6}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(x-\frac{-2}{16})(b-\frac{11}{19})& =(\color{red}{x}+\color{orange}{\frac{1}{8}}).(\color{green}{b}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(\frac{1}{8})} . \color{green}{(b)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{19}x+\frac{1}{8}b-\frac{1}{8}.\frac{11}{19}& \text{Uitwerken } \\ & =bx-\frac{11}{19}x+\frac{1}{8}b-\frac{11}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(x+\frac{-1}{16})(\frac{-5}{7}+q)& =(\color{red}{x}+\color{orange}{\frac{-1}{16}}).(\color{green}{q}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{-1}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{16})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{7}x-\frac{1}{16}q+\frac{1}{16}.\frac{5}{7}& \text{Uitwerken } \\ & =qx-\frac{5}{7}x-\frac{1}{16}q+\frac{5}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-11-22 12:24:42
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