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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{-6}{3})(a+\frac{-8}{6})& =(\color{red}{a}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{4}{3}a+2a-2.\frac{4}{3}& \text{Uitwerken } \\ & =a^2+((\frac{-4}{3})+2)a-(\frac{-8}{3}) & \text{Neem samen} \\ &=a^2+\frac{2}{3}a-(\frac{-8}{3}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(x-\frac{-8}{3})(p+\frac{12}{8})& =(\color{red}{x}+\color{orange}{\frac{8}{3}}).(\color{green}{p}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{8}{3})} . \color{green}{(p)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{2}x+\frac{8}{3}p+\frac{8}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =px+\frac{3}{2}x+\frac{8}{3}p+\frac{24}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{3}{2}x+\frac{8}{3}p+4 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-11}{14}-p)(\frac{14}{17}-q)& =(\color{red}{-p}+\color{orange}{\frac{-11}{14}}).(\color{green}{-q}+\color{blue}{\frac{14}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{14}{17})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(-q)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{14}{17})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{14}{17}p+\frac{11}{14}q-\frac{11}{14}.\frac{14}{17}& \text{Uitwerken } \\ & =pq-\frac{14}{17}p+\frac{11}{14}q-\frac{154}{238} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{14}{17}p+\frac{11}{14}q-\frac{11}{17} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-13}{7}+a)(p+\frac{6}{12})& =(\color{red}{a}+\color{orange}{\frac{-13}{7}}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-13}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{7})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{2}a-\frac{13}{7}p-\frac{13}{7}.\frac{1}{2}& \text{Uitwerken } \\ & =ap+\frac{1}{2}a-\frac{13}{7}p-\frac{13}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x+\frac{7}{16})(a+\frac{-15}{4})& =(\color{red}{x}+\color{orange}{\frac{7}{16}}).(\color{green}{a}+\color{blue}{\frac{-15}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{4})} + \color{orange}{(\frac{7}{16})} . \color{green}{(a)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(\frac{-15}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{15}{4}x+\frac{7}{16}a-\frac{7}{16}.\frac{15}{4}& \text{Uitwerken } \\ & =ax-\frac{15}{4}x+\frac{7}{16}a-\frac{105}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{14}{14}+b)(q+\frac{-16}{10})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{8}{5}b+1q-1.\frac{8}{5}& \text{Uitwerken } \\ & =bq-\frac{8}{5}b+1q-\frac{8}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-\frac{8}{13})(b+\frac{17}{16})& =(\color{red}{a}+\color{orange}{\frac{-8}{13}}).(\color{green}{b}+\color{blue}{\frac{17}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{17}{16})} + \color{orange}{(\frac{-8}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{13})} . \color{blue}{(\frac{17}{16})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{16}a-\frac{8}{13}b-\frac{8}{13}.\frac{17}{16}& \text{Uitwerken } \\ & =ab+\frac{17}{16}a-\frac{8}{13}b-\frac{136}{208} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{17}{16}a-\frac{8}{13}b-\frac{17}{26} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-12}{13}-b)(\frac{7}{20}-x)& =(\color{red}{-b}+\color{orange}{\frac{-12}{13}}).(\color{green}{-x}+\color{blue}{\frac{7}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{20})} + \color{orange}{(\frac{-12}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{-12}{13})} . \color{blue}{(\frac{7}{20})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{7}{20}b+\frac{12}{13}x-\frac{12}{13}.\frac{7}{20}& \text{Uitwerken } \\ & =bx-\frac{7}{20}b+\frac{12}{13}x-\frac{84}{260} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{7}{20}b+\frac{12}{13}x-\frac{21}{65} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-6}{13})(b-(-2))& =(\color{red}{x}+\color{orange}{\frac{6}{13}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{6}{13})} . \color{green}{(b)} + \color{orange}{(\frac{6}{13})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bx+2x+\frac{6}{13}b+\frac{6}{13}.2& \text{Uitwerken } \\ & =bx+2x+\frac{6}{13}b+\frac{12}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(p+\frac{12}{14})(b-\frac{-17}{5})& =(\color{red}{p}+\color{orange}{\frac{6}{7}}).(\color{green}{b}+\color{blue}{\frac{17}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{17}{5})} + \color{orange}{(\frac{6}{7})} . \color{green}{(b)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{17}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{17}{5}p+\frac{6}{7}b+\frac{6}{7}.\frac{17}{5}& \text{Uitwerken } \\ & =bp+\frac{17}{5}p+\frac{6}{7}b+\frac{102}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{4}{6}+a)(b+\frac{-19}{9})& =(\color{red}{a}+\color{orange}{\frac{2}{3}}).(\color{green}{b}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{19}{9}a+\frac{2}{3}b-\frac{2}{3}.\frac{19}{9}& \text{Uitwerken } \\ & =ab-\frac{19}{9}a+\frac{2}{3}b-\frac{38}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-18}{7}+x)(x+\frac{6}{18})& =(\color{red}{x}+\color{orange}{\frac{-18}{7}}).(\color{green}{x}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-18}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-18}{7})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{1}{3}x-\frac{18}{7}x-\frac{18}{7}.\frac{1}{3}& \text{Uitwerken } \\ & =x^2+(\frac{1}{3}+(\frac{-18}{7}))x-(\frac{-18}{21}) & \text{Neem samen} \\ &=x^2-\frac{47}{21}x-(\frac{-18}{21}) & \text{Maak de som} \\ &=x^2-\frac{47}{21}x+\frac{6}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-11 16:53:12
Een site van Busleyden Atheneum Mechelen