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

Hoofdmenu Eentje per keer 

Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{6}{20}+x)(p-\frac{6}{16})& =(\color{red}{x}+\color{orange}{\frac{3}{10}}).(\color{green}{p}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{3}{10})} . \color{green}{(p)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{3}{8}x+\frac{3}{10}p-\frac{3}{10}.\frac{3}{8}& \text{Uitwerken } \\ & =px-\frac{3}{8}x+\frac{3}{10}p-\frac{9}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{20}{15}+b)(x+\frac{-8}{7})& =(\color{red}{b}+\color{orange}{\frac{4}{3}}).(\color{green}{x}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{8}{7}b+\frac{4}{3}x-\frac{4}{3}.\frac{8}{7}& \text{Uitwerken } \\ & =bx-\frac{8}{7}b+\frac{4}{3}x-\frac{32}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{19}{4}-x)(\frac{2}{12}-a)& =(\color{red}{-x}+\color{orange}{\frac{19}{4}}).(\color{green}{-a}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{19}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{6}x-\frac{19}{4}a+\frac{19}{4}.\frac{1}{6}& \text{Uitwerken } \\ & =ax-\frac{1}{6}x-\frac{19}{4}a+\frac{19}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{18}{7}-a)(q+\frac{-6}{9})& =(\color{red}{-a}+\color{orange}{\frac{18}{7}}).(\color{green}{q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{18}{7})} . \color{green}{(q)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{2}{3}a+\frac{18}{7}q-\frac{18}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =-aq+\frac{2}{3}a+\frac{18}{7}q-\frac{36}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{2}{3}a+\frac{18}{7}q-\frac{12}{7} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-11}{17}+x)(p-\frac{-9}{8})& =(\color{red}{x}+\color{orange}{\frac{-11}{17}}).(\color{green}{p}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{-11}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{17})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{9}{8}x-\frac{11}{17}p-\frac{11}{17}.\frac{9}{8}& \text{Uitwerken } \\ & =px+\frac{9}{8}x-\frac{11}{17}p-\frac{99}{136} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{5}{12})(\frac{17}{12}-p)& =(\color{red}{p}+\color{orange}{\frac{5}{12}}).(\color{green}{-p}+\color{blue}{\frac{17}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{17}{12})} + \color{orange}{(\frac{5}{12})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{12})} . \color{blue}{(\frac{17}{12})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{17}{12}p-\frac{5}{12}p+\frac{5}{12}.\frac{17}{12}& \text{Uitwerken } \\ & =-p^2+(\frac{17}{12}+(\frac{-5}{12}))p+(\frac{-85}{144}) & \text{Neem samen} \\ &=-p^2+\frac{12}{12}p+(\frac{-85}{144}) & \text{Maak de som} \\ &=-p^2+1p+(\frac{-85}{144}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{8}-p)(\frac{6}{11}-a)& =(\color{red}{-p}+\color{orange}{1}).(\color{green}{-a}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(1)} . \color{green}{(-a)} + \color{orange}{(1)} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{6}{11}p-1a+1.\frac{6}{11}& \text{Uitwerken } \\ & =ap-\frac{6}{11}p-1a+\frac{6}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{-18}{17})(q+\frac{7}{10})& =(\color{red}{q}+\color{orange}{\frac{-18}{17}}).(\color{green}{q}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{7}{10}q-\frac{18}{17}q-\frac{18}{17}.\frac{7}{10}& \text{Uitwerken } \\ & =q^2+(\frac{7}{10}+(\frac{-18}{17}))q-(\frac{-126}{170}) & \text{Neem samen} \\ &=q^2-\frac{61}{170}q-(\frac{-126}{170}) & \text{Maak de som} \\ &=q^2-\frac{61}{170}q+\frac{63}{85} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(p-\frac{19}{2})(a-\frac{2}{18})& =(\color{red}{p}+\color{orange}{\frac{-19}{2}}).(\color{green}{a}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{-19}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{9}p-\frac{19}{2}a+\frac{19}{2}.\frac{1}{9}& \text{Uitwerken } \\ & =ap-\frac{1}{9}p-\frac{19}{2}a+\frac{19}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x-\frac{10}{12})(\frac{-14}{20}-x)& =(\color{red}{x}+\color{orange}{\frac{-5}{6}}).(\color{green}{-x}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{7}{10}x+\frac{5}{6}x+\frac{5}{6}.\frac{7}{10}& \text{Uitwerken } \\ & =-x^2+((\frac{-7}{10})+\frac{5}{6})x+(\frac{-35}{60}) & \text{Neem samen} \\ &=-x^2+\frac{4}{30}x+(\frac{-35}{60}) & \text{Maak de som} \\ &=-x^2+\frac{2}{15}x+(\frac{-7}{12}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(\frac{10}{13}+x)(\frac{18}{12}+q)& =(\color{red}{x}+\color{orange}{\frac{10}{13}}).(\color{green}{q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{10}{13})} . \color{green}{(q)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{2}x+\frac{10}{13}q+\frac{10}{13}.\frac{3}{2}& \text{Uitwerken } \\ & =qx+\frac{3}{2}x+\frac{10}{13}q+\frac{30}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{3}{2}x+\frac{10}{13}q+\frac{15}{13} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-20}{3}+a)(b-\frac{8}{10})& =(\color{red}{a}+\color{orange}{\frac{-20}{3}}).(\color{green}{b}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-20}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{4}{5}a-\frac{20}{3}b+\frac{20}{3}.\frac{4}{5}& \text{Uitwerken } \\ & =ab-\frac{4}{5}a-\frac{20}{3}b+\frac{80}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{4}{5}a-\frac{20}{3}b+\frac{16}{3} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-30 19:01:42
Een site van Busleyden Atheneum Mechelen