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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{-9}{3})(x+\frac{-15}{13})& =(\color{red}{x}+\color{orange}{3}).(\color{green}{x}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(3)} . \color{green}{(x)} + \color{orange}{(3)} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{15}{13}x+3x-3.\frac{15}{13}& \text{Uitwerken } \\ & =x^2+((\frac{-15}{13})+3)x-(\frac{-45}{13}) & \text{Neem samen} \\ &=x^2+\frac{24}{13}x-(\frac{-45}{13}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(q-\frac{-2}{5})(p+\frac{20}{12})& =(\color{red}{q}+\color{orange}{\frac{2}{5}}).(\color{green}{p}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{2}{5})} . \color{green}{(p)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{3}q+\frac{2}{5}p+\frac{2}{5}.\frac{5}{3}& \text{Uitwerken } \\ & =pq+\frac{5}{3}q+\frac{2}{5}p+\frac{10}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{5}{3}q+\frac{2}{5}p+\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p+\frac{19}{8})(b-\frac{-19}{4})& =(\color{red}{p}+\color{orange}{\frac{19}{8}}).(\color{green}{b}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{19}{8})} . \color{green}{(b)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{4}p+\frac{19}{8}b+\frac{19}{8}.\frac{19}{4}& \text{Uitwerken } \\ & =bp+\frac{19}{4}p+\frac{19}{8}b+\frac{361}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{11}{3}+p)(a-\frac{-1}{8})& =(\color{red}{p}+\color{orange}{\frac{11}{3}}).(\color{green}{a}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{11}{3})} . \color{green}{(a)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{8}p+\frac{11}{3}a+\frac{11}{3}.\frac{1}{8}& \text{Uitwerken } \\ & =ap+\frac{1}{8}p+\frac{11}{3}a+\frac{11}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{16}{10}+p)(q-\frac{10}{14})& =(\color{red}{p}+\color{orange}{\frac{8}{5}}).(\color{green}{q}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{8}{5})} . \color{green}{(q)} + \color{orange}{(\frac{8}{5})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{7}p+\frac{8}{5}q-\frac{8}{5}.\frac{5}{7}& \text{Uitwerken } \\ & =pq-\frac{5}{7}p+\frac{8}{5}q-\frac{40}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{5}{7}p+\frac{8}{5}q-\frac{8}{7} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x-\frac{2}{10})(a+\frac{-11}{15})& =(\color{red}{x}+\color{orange}{\frac{-1}{5}}).(\color{green}{a}+\color{blue}{\frac{-11}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{15})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-11}{15})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{11}{15}x-\frac{1}{5}a+\frac{1}{5}.\frac{11}{15}& \text{Uitwerken } \\ & =ax-\frac{11}{15}x-\frac{1}{5}a+\frac{11}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-\frac{12}{18})(\frac{6}{17}-a)& =(\color{red}{q}+\color{orange}{\frac{-2}{3}}).(\color{green}{-a}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{6}{17}q+\frac{2}{3}a-\frac{2}{3}.\frac{6}{17}& \text{Uitwerken } \\ & =-aq+\frac{6}{17}q+\frac{2}{3}a-\frac{12}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{6}{17}q+\frac{2}{3}a-\frac{4}{17} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-14}{19})(x-\frac{13}{10})& =(\color{red}{b}+\color{orange}{\frac{-14}{19}}).(\color{green}{x}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{13}{10}b-\frac{14}{19}x+\frac{14}{19}.\frac{13}{10}& \text{Uitwerken } \\ & =bx-\frac{13}{10}b-\frac{14}{19}x+\frac{182}{190} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{13}{10}b-\frac{14}{19}x+\frac{91}{95} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-6}{9}+b)(b+\frac{-7}{18})& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{b}+\color{blue}{\frac{-7}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{18})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-7}{18})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{7}{18}b-\frac{2}{3}b+\frac{2}{3}.\frac{7}{18}& \text{Uitwerken } \\ & =b^2+((\frac{-7}{18})+(\frac{-2}{3}))b+\frac{14}{54} & \text{Neem samen} \\ &=b^2-\frac{19}{18}b+\frac{14}{54} & \text{Maak de som} \\ &=b^2-\frac{19}{18}b+\frac{7}{27} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{-2}{16}+p)(p+\frac{-12}{15})& =(\color{red}{p}+\color{orange}{\frac{-1}{8}}).(\color{green}{p}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{4}{5}p-\frac{1}{8}p+\frac{1}{8}.\frac{4}{5}& \text{Uitwerken } \\ & =p^2+((\frac{-4}{5})+(\frac{-1}{8}))p+\frac{4}{40} & \text{Neem samen} \\ &=p^2-\frac{37}{40}p+\frac{4}{40} & \text{Maak de som} \\ &=p^2-\frac{37}{40}p+\frac{1}{10} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{11}{2}+x)(a+\frac{-3}{2})& =(\color{red}{x}+\color{orange}{\frac{11}{2}}).(\color{green}{a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{11}{2})} . \color{green}{(a)} + \color{orange}{(\frac{11}{2})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{2}x+\frac{11}{2}a-\frac{11}{2}.\frac{3}{2}& \text{Uitwerken } \\ & =ax-\frac{3}{2}x+\frac{11}{2}a-\frac{33}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{10}{9}+b)(\frac{17}{11}-a)& =(\color{red}{b}+\color{orange}{\frac{10}{9}}).(\color{green}{-a}+\color{blue}{\frac{17}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{17}{11})} + \color{orange}{(\frac{10}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{17}{11})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{17}{11}b-\frac{10}{9}a+\frac{10}{9}.\frac{17}{11}& \text{Uitwerken } \\ & =-ab+\frac{17}{11}b-\frac{10}{9}a+\frac{170}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-16 10:40:54
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