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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q+\frac{5}{20})(a-\frac{15}{7})& =(\color{red}{q}+\color{orange}{\frac{1}{4}}).(\color{green}{a}+\color{blue}{\frac{-15}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{7})} + \color{orange}{(\frac{1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-15}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{15}{7}q+\frac{1}{4}a-\frac{1}{4}.\frac{15}{7}& \text{Uitwerken } \\ & =aq-\frac{15}{7}q+\frac{1}{4}a-\frac{15}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-18}{19}-x)(\frac{7}{4}-a)& =(\color{red}{-x}+\color{orange}{\frac{-18}{19}}).(\color{green}{-a}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{-18}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{4}x+\frac{18}{19}a-\frac{18}{19}.\frac{7}{4}& \text{Uitwerken } \\ & =ax-\frac{7}{4}x+\frac{18}{19}a-\frac{126}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{7}{4}x+\frac{18}{19}a-\frac{63}{38} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-11}{6}+b)(a-\frac{-10}{19})& =(\color{red}{b}+\color{orange}{\frac{-11}{6}}).(\color{green}{a}+\color{blue}{\frac{10}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{10}{19})} + \color{orange}{(\frac{-11}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{6})} . \color{blue}{(\frac{10}{19})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{10}{19}b-\frac{11}{6}a-\frac{11}{6}.\frac{10}{19}& \text{Uitwerken } \\ & =ab+\frac{10}{19}b-\frac{11}{6}a-\frac{110}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{10}{19}b-\frac{11}{6}a-\frac{55}{57} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q-\frac{9}{13})(q+\frac{-19}{10})& =(\color{red}{q}+\color{orange}{\frac{-9}{13}}).(\color{green}{q}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{19}{10}q-\frac{9}{13}q+\frac{9}{13}.\frac{19}{10}& \text{Uitwerken } \\ & =q^2+((\frac{-19}{10})+(\frac{-9}{13}))q+\frac{171}{130} & \text{Neem samen} \\ &=q^2-\frac{337}{130}q+\frac{171}{130} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(a-\frac{7}{5})(\frac{10}{16}-b)& =(\color{red}{a}+\color{orange}{\frac{-7}{5}}).(\color{green}{-b}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{5}{8}a+\frac{7}{5}b-\frac{7}{5}.\frac{5}{8}& \text{Uitwerken } \\ & =-ab+\frac{5}{8}a+\frac{7}{5}b-\frac{35}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{5}{8}a+\frac{7}{5}b-\frac{7}{8} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x-\frac{-12}{19})(x+\frac{-6}{8})& =(\color{red}{x}+\color{orange}{\frac{12}{19}}).(\color{green}{x}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{12}{19})} . \color{green}{(x)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{3}{4}x+\frac{12}{19}x-\frac{12}{19}.\frac{3}{4}& \text{Uitwerken } \\ & =x^2+((\frac{-3}{4})+\frac{12}{19})x-(\frac{-36}{76}) & \text{Neem samen} \\ &=x^2-\frac{9}{76}x-(\frac{-36}{76}) & \text{Maak de som} \\ &=x^2-\frac{9}{76}x+\frac{9}{19} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(\frac{-1}{20}-a)(p+\frac{-12}{12})& =(\color{red}{-a}+\color{orange}{\frac{-1}{20}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{20})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ap+1a-\frac{1}{20}p+\frac{1}{20}.1& \text{Uitwerken } \\ & =-ap+1a-\frac{1}{20}p+\frac{1}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-12}{20}-x)(q+\frac{-13}{11})& =(\color{red}{-x}+\color{orange}{\frac{-3}{5}}).(\color{green}{q}+\color{blue}{\frac{-13}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-13}{11})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-13}{11})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{13}{11}x-\frac{3}{5}q+\frac{3}{5}.\frac{13}{11}& \text{Uitwerken } \\ & =-qx+\frac{13}{11}x-\frac{3}{5}q+\frac{39}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a-\frac{12}{6})(a+\frac{12}{15})& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{4}{5}a-2a-2.\frac{4}{5}& \text{Uitwerken } \\ & =a^2+(\frac{4}{5}+(-2))a-(\frac{-8}{5}) & \text{Neem samen} \\ &=a^2-\frac{6}{5}a-(\frac{-8}{5}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(p+(-15))(\frac{-9}{14}+b)& =(\color{red}{p}+\color{orange}{(-15)}).(\color{green}{b}+\color{blue}{\frac{-9}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{14})} + \color{orange}{(-15)} . \color{green}{(b)} + \color{orange}{(-15)} . \color{blue}{(\frac{-9}{14})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{9}{14}p-15b+15.\frac{9}{14}& \text{Uitwerken } \\ & =bp-\frac{9}{14}p-15b+\frac{135}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a-\frac{9}{13})(a+\frac{14}{12})& =(\color{red}{a}+\color{orange}{\frac{-9}{13}}).(\color{green}{a}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{7}{6}a-\frac{9}{13}a-\frac{9}{13}.\frac{7}{6}& \text{Uitwerken } \\ & =a^2+(\frac{7}{6}+(\frac{-9}{13}))a-(\frac{-63}{78}) & \text{Neem samen} \\ &=a^2+\frac{37}{78}a-(\frac{-63}{78}) & \text{Maak de som} \\ &=a^2+\frac{37}{78}a+\frac{21}{26} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(x-\frac{9}{17})(p-\frac{7}{20})& =(\color{red}{x}+\color{orange}{\frac{-9}{17}}).(\color{green}{p}+\color{blue}{\frac{-7}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{20})} + \color{orange}{(\frac{-9}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{17})} . \color{blue}{(\frac{-7}{20})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{7}{20}x-\frac{9}{17}p+\frac{9}{17}.\frac{7}{20}& \text{Uitwerken } \\ & =px-\frac{7}{20}x-\frac{9}{17}p+\frac{63}{340} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-22 14:49:44
Een site van Busleyden Atheneum Mechelen