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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{7}{16})(x+\frac{10}{4})& =(\color{red}{q}+\color{orange}{\frac{7}{16}}).(\color{green}{x}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{7}{16})} . \color{green}{(x)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{2}q+\frac{7}{16}x+\frac{7}{16}.\frac{5}{2}& \text{Uitwerken } \\ & =qx+\frac{5}{2}q+\frac{7}{16}x+\frac{35}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{10}{11})(\frac{11}{8}+a)& =(\color{red}{a}+\color{orange}{\frac{-10}{11}}).(\color{green}{a}+\color{blue}{\frac{11}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{11}{8})} + \color{orange}{(\frac{-10}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(\frac{11}{8})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{11}{8}a-\frac{10}{11}a-\frac{10}{11}.\frac{11}{8}& \text{Uitwerken } \\ & =a^2+(\frac{11}{8}+(\frac{-10}{11}))a-(\frac{-110}{88}) & \text{Neem samen} \\ &=a^2+\frac{41}{88}a-(\frac{-110}{88}) & \text{Maak de som} \\ &=a^2+\frac{41}{88}a+\frac{5}{4} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(x-\frac{19}{20})(q+\frac{-8}{4})& =(\color{red}{x}+\color{orange}{\frac{-19}{20}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{-19}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = qx-2x-\frac{19}{20}q+\frac{19}{20}.2& \text{Uitwerken } \\ & =qx-2x-\frac{19}{20}q+\frac{38}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-2x-\frac{19}{20}q+\frac{19}{10} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p-\frac{16}{4})(p-\frac{3}{4})& =(\color{red}{p}+\color{orange}{(-4)}).(\color{green}{p}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(-4)} . \color{green}{(p)} + \color{orange}{(-4)} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{3}{4}p-4p+4.\frac{3}{4}& \text{Uitwerken } \\ & =p^2+((\frac{-3}{4})+(-4))p+\frac{12}{4} & \text{Neem samen} \\ &=p^2-\frac{19}{4}p+\frac{12}{4} & \text{Maak de som} \\ &=p^2-\frac{19}{4}p+3 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(p+\frac{16}{18})(q-\frac{15}{16})& =(\color{red}{p}+\color{orange}{\frac{8}{9}}).(\color{green}{q}+\color{blue}{\frac{-15}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{16})} + \color{orange}{(\frac{8}{9})} . \color{green}{(q)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{-15}{16})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{15}{16}p+\frac{8}{9}q-\frac{8}{9}.\frac{15}{16}& \text{Uitwerken } \\ & =pq-\frac{15}{16}p+\frac{8}{9}q-\frac{120}{144} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{15}{16}p+\frac{8}{9}q-\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-6}{3}+p)(b+\frac{9}{17})& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{9}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{17})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{9}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{17}p-2b-2.\frac{9}{17}& \text{Uitwerken } \\ & =bp+\frac{9}{17}p-2b-\frac{18}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-\frac{13}{6})(b+\frac{1}{16})& =(\color{red}{a}+\color{orange}{\frac{-13}{6}}).(\color{green}{b}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(\frac{-13}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{6})} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{16}a-\frac{13}{6}b-\frac{13}{6}.\frac{1}{16}& \text{Uitwerken } \\ & =ab+\frac{1}{16}a-\frac{13}{6}b-\frac{13}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-\frac{13}{18})(b+\frac{15}{11})& =(\color{red}{x}+\color{orange}{\frac{-13}{18}}).(\color{green}{b}+\color{blue}{\frac{15}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{15}{11})} + \color{orange}{(\frac{-13}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(\frac{15}{11})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{15}{11}x-\frac{13}{18}b-\frac{13}{18}.\frac{15}{11}& \text{Uitwerken } \\ & =bx+\frac{15}{11}x-\frac{13}{18}b-\frac{195}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{15}{11}x-\frac{13}{18}b-\frac{65}{66} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{15}{20}+b)(a-\frac{4}{17})& =(\color{red}{b}+\color{orange}{\frac{3}{4}}).(\color{green}{a}+\color{blue}{\frac{-4}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{17})} + \color{orange}{(\frac{3}{4})} . \color{green}{(a)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-4}{17})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{4}{17}b+\frac{3}{4}a-\frac{3}{4}.\frac{4}{17}& \text{Uitwerken } \\ & =ab-\frac{4}{17}b+\frac{3}{4}a-\frac{12}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{4}{17}b+\frac{3}{4}a-\frac{3}{17} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p+\frac{5}{8})(x+\frac{-2}{9})& =(\color{red}{p}+\color{orange}{\frac{5}{8}}).(\color{green}{x}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{5}{8})} . \color{green}{(x)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{2}{9}p+\frac{5}{8}x-\frac{5}{8}.\frac{2}{9}& \text{Uitwerken } \\ & =px-\frac{2}{9}p+\frac{5}{8}x-\frac{10}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{2}{9}p+\frac{5}{8}x-\frac{5}{36} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x-\frac{-8}{13})(\frac{-14}{6}+p)& =(\color{red}{x}+\color{orange}{\frac{8}{13}}).(\color{green}{p}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{8}{13})} . \color{green}{(p)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{7}{3}x+\frac{8}{13}p-\frac{8}{13}.\frac{7}{3}& \text{Uitwerken } \\ & =px-\frac{7}{3}x+\frac{8}{13}p-\frac{56}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b+\frac{19}{10})(x-\frac{11}{6})& =(\color{red}{b}+\color{orange}{\frac{19}{10}}).(\color{green}{x}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{19}{10})} . \color{green}{(x)} + \color{orange}{(\frac{19}{10})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{6}b+\frac{19}{10}x-\frac{19}{10}.\frac{11}{6}& \text{Uitwerken } \\ & =bx-\frac{11}{6}b+\frac{19}{10}x-\frac{209}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-03 18:20:29
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