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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-12}{13}-p)(p+\frac{17}{8})& =(\color{red}{-p}+\color{orange}{\frac{-12}{13}}).(\color{green}{p}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(\frac{-12}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-12}{13})} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{17}{8}p-\frac{12}{13}p-\frac{12}{13}.\frac{17}{8}& \text{Uitwerken } \\ & =-p^2+((\frac{-17}{8})+(\frac{-12}{13}))p-\frac{204}{104} & \text{Neem samen} \\ &=-p^2-\frac{317}{104}p-\frac{204}{104} & \text{Maak de som} \\ &=-p^2-\frac{317}{104}p-\frac{51}{26} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{17}+p)(p-(-17))& =(\color{red}{p}+\color{orange}{\frac{8}{17}}).(\color{green}{p}+\color{blue}{17})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(17)} + \color{orange}{(\frac{8}{17})} . \color{green}{(p)} + \color{orange}{(\frac{8}{17})} . \color{blue}{(17)}& \text{Boogjes en uitschrijven} \\ & = pp+17p+\frac{8}{17}p+\frac{8}{17}.17& \text{Uitwerken } \\ & =p^2+(17+\frac{8}{17})p+\frac{136}{17} & \text{Neem samen} \\ &=p^2+\frac{297}{17}p+\frac{136}{17} & \text{Maak de som} \\ &=p^2+\frac{297}{17}p+8 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(x+\frac{14}{4})(\frac{4}{18}+x)& =(\color{red}{x}+\color{orange}{\frac{7}{2}}).(\color{green}{x}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{7}{2})} . \color{green}{(x)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{2}{9}x+\frac{7}{2}x+\frac{7}{2}.\frac{2}{9}& \text{Uitwerken } \\ & =x^2+(\frac{2}{9}+\frac{7}{2})x+\frac{14}{18} & \text{Neem samen} \\ &=x^2+\frac{67}{18}x+\frac{14}{18} & \text{Maak de som} \\ &=x^2+\frac{67}{18}x+\frac{7}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(p+\frac{-5}{9})(\frac{1}{11}-q)& =(\color{red}{p}+\color{orange}{\frac{-5}{9}}).(\color{green}{-q}+\color{blue}{\frac{1}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{11})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{1}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{11}p+\frac{5}{9}q-\frac{5}{9}.\frac{1}{11}& \text{Uitwerken } \\ & =-pq+\frac{1}{11}p+\frac{5}{9}q-\frac{5}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{12}{4}-x)(p+\frac{20}{5})& =(\color{red}{-x}+\color{orange}{3}).(\color{green}{p}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(4)} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -px-4x+3p+3.4& \text{Uitwerken } \\ & =-px-4x+3p+12 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{15}{16}+x)(\frac{6}{13}+q)& =(\color{red}{x}+\color{orange}{\frac{15}{16}}).(\color{green}{q}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{15}{16})} . \color{green}{(q)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{6}{13}x+\frac{15}{16}q+\frac{15}{16}.\frac{6}{13}& \text{Uitwerken } \\ & =qx+\frac{6}{13}x+\frac{15}{16}q+\frac{90}{208} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{6}{13}x+\frac{15}{16}q+\frac{45}{104} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-5}{16})(\frac{-14}{20}-b)& =(\color{red}{b}+\color{orange}{\frac{-5}{16}}).(\color{green}{-b}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{-5}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{16})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{7}{10}b+\frac{5}{16}b+\frac{5}{16}.\frac{7}{10}& \text{Uitwerken } \\ & =-b^2+((\frac{-7}{10})+\frac{5}{16})b+(\frac{-35}{160}) & \text{Neem samen} \\ &=-b^2-\frac{31}{80}b+(\frac{-35}{160}) & \text{Maak de som} \\ &=-b^2-\frac{31}{80}b+(\frac{-7}{32}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-15}{16})(q-\frac{-17}{14})& =(\color{red}{b}+\color{orange}{\frac{-15}{16}}).(\color{green}{q}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(\frac{-15}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{17}{14}b-\frac{15}{16}q-\frac{15}{16}.\frac{17}{14}& \text{Uitwerken } \\ & =bq+\frac{17}{14}b-\frac{15}{16}q-\frac{255}{224} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b+\frac{9}{11})(a-\frac{-19}{6})& =(\color{red}{b}+\color{orange}{\frac{9}{11}}).(\color{green}{a}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(\frac{9}{11})} . \color{green}{(a)} + \color{orange}{(\frac{9}{11})} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{19}{6}b+\frac{9}{11}a+\frac{9}{11}.\frac{19}{6}& \text{Uitwerken } \\ & =ab+\frac{19}{6}b+\frac{9}{11}a+\frac{171}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{19}{6}b+\frac{9}{11}a+\frac{57}{22} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{12}{18}+a)(\frac{-5}{20}+p)& =(\color{red}{a}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{4}a+\frac{2}{3}p-\frac{2}{3}.\frac{1}{4}& \text{Uitwerken } \\ & =ap-\frac{1}{4}a+\frac{2}{3}p-\frac{2}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{1}{4}a+\frac{2}{3}p-\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-16}{6}+a)(a-\frac{-1}{3})& =(\color{red}{a}+\color{orange}{\frac{-8}{3}}).(\color{green}{a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{3}a-\frac{8}{3}a-\frac{8}{3}.\frac{1}{3}& \text{Uitwerken } \\ & =a^2+(\frac{1}{3}+(\frac{-8}{3}))a-(\frac{-8}{9}) & \text{Neem samen} \\ &=a^2-\frac{7}{3}a-(\frac{-8}{9}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(p+\frac{2}{20})(\frac{13}{6}+x)& =(\color{red}{p}+\color{orange}{\frac{1}{10}}).(\color{green}{x}+\color{blue}{\frac{13}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{13}{6})} + \color{orange}{(\frac{1}{10})} . \color{green}{(x)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{13}{6})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{6}p+\frac{1}{10}x+\frac{1}{10}.\frac{13}{6}& \text{Uitwerken } \\ & =px+\frac{13}{6}p+\frac{1}{10}x+\frac{13}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-15 12:11:35
Een site van Busleyden Atheneum Mechelen