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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}((-10)-a)(\frac{-1}{16}+p)& =(\color{red}{-a}+\color{orange}{(-10)}).(\color{green}{p}+\color{blue}{\frac{-1}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{16})} + \color{orange}{(-10)} . \color{green}{(p)} + \color{orange}{(-10)} . \color{blue}{(\frac{-1}{16})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{16}a-10p+10.\frac{1}{16}& \text{Uitwerken } \\ & =-ap+\frac{1}{16}a-10p+\frac{10}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{1}{16}a-10p+\frac{5}{8} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-19}{19}-a)(b-\frac{-7}{13})& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{7}{13}a-1b-1.\frac{7}{13}& \text{Uitwerken } \\ & =-ab-\frac{7}{13}a-1b-\frac{7}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-19}{17}+p)(\frac{-17}{17}-a)& =(\color{red}{p}+\color{orange}{\frac{-19}{17}}).(\color{green}{-a}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-19}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{17})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ap-1p+\frac{19}{17}a+\frac{19}{17}.1& \text{Uitwerken } \\ & =-ap-1p+\frac{19}{17}a+\frac{19}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{20}{5}+p)(\frac{-8}{6}+x)& =(\color{red}{p}+\color{orange}{4}).(\color{green}{x}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(4)} . \color{green}{(x)} + \color{orange}{(4)} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{4}{3}p+4x-4.\frac{4}{3}& \text{Uitwerken } \\ & =px-\frac{4}{3}p+4x-\frac{16}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{11}{3}-a)(\frac{17}{14}-b)& =(\color{red}{-a}+\color{orange}{\frac{11}{3}}).(\color{green}{-b}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(\frac{11}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{17}{14}a-\frac{11}{3}b+\frac{11}{3}.\frac{17}{14}& \text{Uitwerken } \\ & =ab-\frac{17}{14}a-\frac{11}{3}b+\frac{187}{42} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{10}{9}-a)(\frac{-1}{11}-a)& =(\color{red}{-a}+\color{orange}{\frac{10}{9}}).(\color{green}{-a}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{10}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{10}{9})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{11}a-\frac{10}{9}a-\frac{10}{9}.\frac{1}{11}& \text{Uitwerken } \\ & =a^2+(\frac{1}{11}+(\frac{-10}{9}))a-(\frac{-10}{99}) & \text{Neem samen} \\ &=a^2-\frac{101}{99}a-(\frac{-10}{99}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{4}{2}-q)(\frac{1}{5}+q)& =(\color{red}{-q}+\color{orange}{2}).(\color{green}{q}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{1}{5}q+2q+2.\frac{1}{5}& \text{Uitwerken } \\ & =-q^2+((\frac{-1}{5})+2)q+(\frac{-2}{5}) & \text{Neem samen} \\ &=-q^2+\frac{9}{5}q+(\frac{-2}{5}) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(q+\frac{-8}{4})(a+\frac{7}{8})& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{8}q-2a-2.\frac{7}{8}& \text{Uitwerken } \\ & =aq+\frac{7}{8}q-2a-\frac{14}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{7}{8}q-2a-\frac{7}{4} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{7}{18}-b)(p+\frac{-18}{20})& =(\color{red}{-b}+\color{orange}{\frac{7}{18}}).(\color{green}{p}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{7}{18})} . \color{green}{(p)} + \color{orange}{(\frac{7}{18})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{9}{10}b+\frac{7}{18}p-\frac{7}{18}.\frac{9}{10}& \text{Uitwerken } \\ & =-bp+\frac{9}{10}b+\frac{7}{18}p-\frac{63}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{9}{10}b+\frac{7}{18}p-\frac{7}{20} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(a-\frac{15}{9})(\frac{6}{7}+p)& =(\color{red}{a}+\color{orange}{\frac{-5}{3}}).(\color{green}{p}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{6}{7}a-\frac{5}{3}p-\frac{5}{3}.\frac{6}{7}& \text{Uitwerken } \\ & =ap+\frac{6}{7}a-\frac{5}{3}p-\frac{30}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{6}{7}a-\frac{5}{3}p-\frac{10}{7} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(p+\frac{5}{19})(\frac{9}{16}+p)& =(\color{red}{p}+\color{orange}{\frac{5}{19}}).(\color{green}{p}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(\frac{5}{19})} . \color{green}{(p)} + \color{orange}{(\frac{5}{19})} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{9}{16}p+\frac{5}{19}p+\frac{5}{19}.\frac{9}{16}& \text{Uitwerken } \\ & =p^2+(\frac{9}{16}+\frac{5}{19})p+\frac{45}{304} & \text{Neem samen} \\ &=p^2+\frac{251}{304}p+\frac{45}{304} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(a+\frac{18}{6})(p+\frac{5}{9})& =(\color{red}{a}+\color{orange}{3}).(\color{green}{p}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{5}{9}a+3p+3.\frac{5}{9}& \text{Uitwerken } \\ & =ap+\frac{5}{9}a+3p+\frac{15}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{5}{9}a+3p+\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-10 22:45:25
Een site van Busleyden Atheneum Mechelen