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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{19}{6}-b)(p-\frac{11}{7})& =(\color{red}{-b}+\color{orange}{\frac{19}{6}}).(\color{green}{p}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(\frac{19}{6})} . \color{green}{(p)} + \color{orange}{(\frac{19}{6})} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{11}{7}b+\frac{19}{6}p-\frac{19}{6}.\frac{11}{7}& \text{Uitwerken } \\ & =-bp+\frac{11}{7}b+\frac{19}{6}p-\frac{209}{42} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-5}{17})(a-\frac{8}{18})& =(\color{red}{a}+\color{orange}{\frac{5}{17}}).(\color{green}{a}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{5}{17})} . \color{green}{(a)} + \color{orange}{(\frac{5}{17})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{4}{9}a+\frac{5}{17}a-\frac{5}{17}.\frac{4}{9}& \text{Uitwerken } \\ & =a^2+((\frac{-4}{9})+\frac{5}{17})a-(\frac{-20}{153}) & \text{Neem samen} \\ &=a^2-\frac{23}{153}a-(\frac{-20}{153}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(b+\frac{-5}{19})(\frac{16}{20}+x)& =(\color{red}{b}+\color{orange}{\frac{-5}{19}}).(\color{green}{x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-5}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{4}{5}b-\frac{5}{19}x-\frac{5}{19}.\frac{4}{5}& \text{Uitwerken } \\ & =bx+\frac{4}{5}b-\frac{5}{19}x-\frac{20}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{4}{5}b-\frac{5}{19}x-\frac{4}{19} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(6+x)(b-\frac{-2}{2})& =(\color{red}{x}+\color{orange}{6}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(6)} . \color{green}{(b)} + \color{orange}{(6)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx+1x+6b+6.1& \text{Uitwerken } \\ & =bx+1x+6b+6 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a-\frac{-12}{3})(x+\frac{-13}{6})& =(\color{red}{a}+\color{orange}{4}).(\color{green}{x}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(4)} . \color{green}{(x)} + \color{orange}{(4)} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{13}{6}a+4x-4.\frac{13}{6}& \text{Uitwerken } \\ & =ax-\frac{13}{6}a+4x-\frac{52}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{13}{6}a+4x-\frac{26}{3} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{4}{18}-x)(\frac{12}{13}-x)& =(\color{red}{-x}+\color{orange}{\frac{2}{9}}).(\color{green}{-x}+\color{blue}{\frac{12}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(\frac{12}{13})} + \color{orange}{(\frac{2}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{12}{13})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{12}{13}x-\frac{2}{9}x+\frac{2}{9}.\frac{12}{13}& \text{Uitwerken } \\ & =x^2+((\frac{-12}{13})+(\frac{-2}{9}))x+\frac{24}{117} & \text{Neem samen} \\ &=x^2-\frac{134}{117}x+\frac{24}{117} & \text{Maak de som} \\ &=x^2-\frac{134}{117}x+\frac{8}{39} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{20}{15}-b)(b+\frac{-13}{13})& =(\color{red}{-b}+\color{orange}{\frac{4}{3}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(-1)} + \color{orange}{(\frac{4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bb+1b+\frac{4}{3}b-\frac{4}{3}.1& \text{Uitwerken } \\ & =-b^2+(1+\frac{4}{3})b-\frac{4}{3} & \text{Neem samen} \\ &=-b^2+\frac{7}{3}b-\frac{4}{3} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{15}{6}+a)(q+\frac{19}{7})& =(\color{red}{a}+\color{orange}{\frac{5}{2}}).(\color{green}{q}+\color{blue}{\frac{19}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{19}{7})} + \color{orange}{(\frac{5}{2})} . \color{green}{(q)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{19}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{19}{7}a+\frac{5}{2}q+\frac{5}{2}.\frac{19}{7}& \text{Uitwerken } \\ & =aq+\frac{19}{7}a+\frac{5}{2}q+\frac{95}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{6}{3})(p-\frac{-5}{18})& =(\color{red}{a}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{5}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{5}{18})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{5}{18})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{5}{18}a+2p+2.\frac{5}{18}& \text{Uitwerken } \\ & =ap+\frac{5}{18}a+2p+\frac{10}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{5}{18}a+2p+\frac{5}{9} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a-13)(\frac{1}{16}+x)& =(\color{red}{a}+\color{orange}{(-13)}).(\color{green}{x}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(-13)} . \color{green}{(x)} + \color{orange}{(-13)} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{16}a-13x-13.\frac{1}{16}& \text{Uitwerken } \\ & =ax+\frac{1}{16}a-13x-\frac{13}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a+\frac{17}{3})(q-\frac{-15}{6})& =(\color{red}{a}+\color{orange}{\frac{17}{3}}).(\color{green}{q}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{17}{3})} . \color{green}{(q)} + \color{orange}{(\frac{17}{3})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{2}a+\frac{17}{3}q+\frac{17}{3}.\frac{5}{2}& \text{Uitwerken } \\ & =aq+\frac{5}{2}a+\frac{17}{3}q+\frac{85}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a-\frac{-17}{12})(\frac{9}{10}+b)& =(\color{red}{a}+\color{orange}{\frac{17}{12}}).(\color{green}{b}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{17}{12})} . \color{green}{(b)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{9}{10}a+\frac{17}{12}b+\frac{17}{12}.\frac{9}{10}& \text{Uitwerken } \\ & =ab+\frac{9}{10}a+\frac{17}{12}b+\frac{153}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{9}{10}a+\frac{17}{12}b+\frac{51}{40} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-11 01:52:57
Een site van Busleyden Atheneum Mechelen