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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{19}{19})(b+\frac{1}{17})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{1}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{17})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{17})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{17}q-1b-1.\frac{1}{17}& \text{Uitwerken } \\ & =bq+\frac{1}{17}q-1b-\frac{1}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-16}{14})(q-\frac{16}{11})& =(\color{red}{a}+\color{orange}{\frac{8}{7}}).(\color{green}{q}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(\frac{8}{7})} . \color{green}{(q)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{16}{11}a+\frac{8}{7}q-\frac{8}{7}.\frac{16}{11}& \text{Uitwerken } \\ & =aq-\frac{16}{11}a+\frac{8}{7}q-\frac{128}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{17}{6}+x)(x-\frac{-12}{16})& =(\color{red}{x}+\color{orange}{\frac{17}{6}}).(\color{green}{x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{17}{6})} . \color{green}{(x)} + \color{orange}{(\frac{17}{6})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{3}{4}x+\frac{17}{6}x+\frac{17}{6}.\frac{3}{4}& \text{Uitwerken } \\ & =x^2+(\frac{3}{4}+\frac{17}{6})x+\frac{51}{24} & \text{Neem samen} \\ &=x^2+\frac{43}{12}x+\frac{51}{24} & \text{Maak de som} \\ &=x^2+\frac{43}{12}x+\frac{17}{8} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{4}{16}+a)(a-\frac{6}{10})& =(\color{red}{a}+\color{orange}{\frac{1}{4}}).(\color{green}{a}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{1}{4})} . \color{green}{(a)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{3}{5}a+\frac{1}{4}a-\frac{1}{4}.\frac{3}{5}& \text{Uitwerken } \\ & =a^2+((\frac{-3}{5})+\frac{1}{4})a-(\frac{-3}{20}) & \text{Neem samen} \\ &=a^2-\frac{7}{20}a-(\frac{-3}{20}) & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-7}{6}+b)(\frac{14}{13}+p)& =(\color{red}{b}+\color{orange}{\frac{-7}{6}}).(\color{green}{p}+\color{blue}{\frac{14}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{14}{13})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{14}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{14}{13}b-\frac{7}{6}p-\frac{7}{6}.\frac{14}{13}& \text{Uitwerken } \\ & =bp+\frac{14}{13}b-\frac{7}{6}p-\frac{98}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{14}{13}b-\frac{7}{6}p-\frac{49}{39} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{1}{15}-b)(p+\frac{9}{13})& =(\color{red}{-b}+\color{orange}{\frac{1}{15}}).(\color{green}{p}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{1}{15})} . \color{green}{(p)} + \color{orange}{(\frac{1}{15})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{9}{13}b+\frac{1}{15}p+\frac{1}{15}.\frac{9}{13}& \text{Uitwerken } \\ & =-bp-\frac{9}{13}b+\frac{1}{15}p+\frac{9}{195} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{9}{13}b+\frac{1}{15}p+\frac{3}{65} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-17}{8}-b)(\frac{-3}{4}+b)& =(\color{red}{-b}+\color{orange}{\frac{-17}{8}}).(\color{green}{b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-17}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{8})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{3}{4}b-\frac{17}{8}b+\frac{17}{8}.\frac{3}{4}& \text{Uitwerken } \\ & =-b^2+(\frac{3}{4}+(\frac{-17}{8}))b+(\frac{-51}{32}) & \text{Neem samen} \\ &=-b^2-\frac{11}{8}b+(\frac{-51}{32}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-13}{4})(x-\frac{13}{5})& =(\color{red}{x}+\color{orange}{\frac{13}{4}}).(\color{green}{x}+\color{blue}{\frac{-13}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{5})} + \color{orange}{(\frac{13}{4})} . \color{green}{(x)} + \color{orange}{(\frac{13}{4})} . \color{blue}{(\frac{-13}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{13}{5}x+\frac{13}{4}x-\frac{13}{4}.\frac{13}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-13}{5})+\frac{13}{4})x-(\frac{-169}{20}) & \text{Neem samen} \\ &=x^2+\frac{13}{20}x-(\frac{-169}{20}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(a+\frac{-5}{5})(15+b)& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{15})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(15)} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(15)}& \text{Boogjes en uitschrijven} \\ & = ab+15a-1b-1.15& \text{Uitwerken } \\ & =ab+15a-1b-15 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a+\frac{19}{18})(x+\frac{9}{10})& =(\color{red}{a}+\color{orange}{\frac{19}{18}}).(\color{green}{x}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{19}{18})} . \color{green}{(x)} + \color{orange}{(\frac{19}{18})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{10}a+\frac{19}{18}x+\frac{19}{18}.\frac{9}{10}& \text{Uitwerken } \\ & =ax+\frac{9}{10}a+\frac{19}{18}x+\frac{171}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{9}{10}a+\frac{19}{18}x+\frac{19}{20} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x-\frac{2}{19})(8-x)& =(\color{red}{x}+\color{orange}{\frac{-2}{19}}).(\color{green}{-x}+\color{blue}{8})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(8)} + \color{orange}{(\frac{-2}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{-2}{19})} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = -xx+8x+\frac{2}{19}x-\frac{2}{19}.8& \text{Uitwerken } \\ & =-x^2+(8+\frac{2}{19})x-\frac{16}{19} & \text{Neem samen} \\ &=-x^2+\frac{154}{19}x-\frac{16}{19} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(p+\frac{12}{10})(\frac{17}{5}+x)& =(\color{red}{p}+\color{orange}{\frac{6}{5}}).(\color{green}{x}+\color{blue}{\frac{17}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{17}{5})} + \color{orange}{(\frac{6}{5})} . \color{green}{(x)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{17}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{17}{5}p+\frac{6}{5}x+\frac{6}{5}.\frac{17}{5}& \text{Uitwerken } \\ & =px+\frac{17}{5}p+\frac{6}{5}x+\frac{102}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-10 03:34:34
Een site van Busleyden Atheneum Mechelen