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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{18}{3})(\frac{-7}{8}+p)& =(\color{red}{p}+\color{orange}{6}).(\color{green}{p}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(6)} . \color{green}{(p)} + \color{orange}{(6)} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{7}{8}p+6p-6.\frac{7}{8}& \text{Uitwerken } \\ & =p^2+((\frac{-7}{8})+6)p-(\frac{-42}{8}) & \text{Neem samen} \\ &=p^2+\frac{41}{8}p-(\frac{-42}{8}) & \text{Maak de som} \\ &=p^2+\frac{41}{8}p+\frac{21}{4} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(\frac{14}{16}+q)(\frac{9}{15}-a)& =(\color{red}{q}+\color{orange}{\frac{7}{8}}).(\color{green}{-a}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{7}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{3}{5}q-\frac{7}{8}a+\frac{7}{8}.\frac{3}{5}& \text{Uitwerken } \\ & =-aq+\frac{3}{5}q-\frac{7}{8}a+\frac{21}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-11}{6}-a)(x+\frac{12}{11})& =(\color{red}{-a}+\color{orange}{\frac{-11}{6}}).(\color{green}{x}+\color{blue}{\frac{12}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{12}{11})} + \color{orange}{(\frac{-11}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{6})} . \color{blue}{(\frac{12}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{12}{11}a-\frac{11}{6}x-\frac{11}{6}.\frac{12}{11}& \text{Uitwerken } \\ & =-ax-\frac{12}{11}a-\frac{11}{6}x-\frac{132}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{12}{11}a-\frac{11}{6}x-2 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a-\frac{3}{8})(\frac{-5}{20}+p)& =(\color{red}{a}+\color{orange}{\frac{-3}{8}}).(\color{green}{p}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{4}a-\frac{3}{8}p+\frac{3}{8}.\frac{1}{4}& \text{Uitwerken } \\ & =ap-\frac{1}{4}a-\frac{3}{8}p+\frac{3}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{4}{18}+x)(x+\frac{-6}{19})& =(\color{red}{x}+\color{orange}{\frac{2}{9}}).(\color{green}{x}+\color{blue}{\frac{-6}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{19})} + \color{orange}{(\frac{2}{9})} . \color{green}{(x)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{-6}{19})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{6}{19}x+\frac{2}{9}x-\frac{2}{9}.\frac{6}{19}& \text{Uitwerken } \\ & =x^2+((\frac{-6}{19})+\frac{2}{9})x-(\frac{-12}{171}) & \text{Neem samen} \\ &=x^2-\frac{16}{171}x-(\frac{-12}{171}) & \text{Maak de som} \\ &=x^2-\frac{16}{171}x+\frac{4}{57} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  6. \(\begin{align}(\frac{1}{6}+q)(b-\frac{-4}{19})& =(\color{red}{q}+\color{orange}{\frac{1}{6}}).(\color{green}{b}+\color{blue}{\frac{4}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{4}{19})} + \color{orange}{(\frac{1}{6})} . \color{green}{(b)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{4}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{4}{19}q+\frac{1}{6}b+\frac{1}{6}.\frac{4}{19}& \text{Uitwerken } \\ & =bq+\frac{4}{19}q+\frac{1}{6}b+\frac{4}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{4}{19}q+\frac{1}{6}b+\frac{2}{57} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(q+\frac{-7}{15})(\frac{-14}{13}-p)& =(\color{red}{q}+\color{orange}{\frac{-7}{15}}).(\color{green}{-p}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(\frac{-7}{15})} . \color{green}{(-p)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{14}{13}q+\frac{7}{15}p+\frac{7}{15}.\frac{14}{13}& \text{Uitwerken } \\ & =-pq-\frac{14}{13}q+\frac{7}{15}p+\frac{98}{195} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{1}{19}+b)(b+\frac{2}{6})& =(\color{red}{b}+\color{orange}{\frac{1}{19}}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{1}{19})} . \color{green}{(b)} + \color{orange}{(\frac{1}{19})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{3}b+\frac{1}{19}b+\frac{1}{19}.\frac{1}{3}& \text{Uitwerken } \\ & =b^2+(\frac{1}{3}+\frac{1}{19})b+\frac{1}{57} & \text{Neem samen} \\ &=b^2+\frac{22}{57}b+\frac{1}{57} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{6}{4}-a)(q+\frac{7}{2})& =(\color{red}{-a}+\color{orange}{\frac{3}{2}}).(\color{green}{q}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(\frac{3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{7}{2}a+\frac{3}{2}q+\frac{3}{2}.\frac{7}{2}& \text{Uitwerken } \\ & =-aq-\frac{7}{2}a+\frac{3}{2}q+\frac{21}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-20}{6}-p)(a+\frac{15}{20})& =(\color{red}{-p}+\color{orange}{\frac{-10}{3}}).(\color{green}{a}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{3}{4}p-\frac{10}{3}a-\frac{10}{3}.\frac{3}{4}& \text{Uitwerken } \\ & =-ap-\frac{3}{4}p-\frac{10}{3}a-\frac{30}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{3}{4}p-\frac{10}{3}a-\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{10}{15}-p)(x-(-9))& =(\color{red}{-p}+\color{orange}{\frac{2}{3}}).(\color{green}{x}+\color{blue}{9})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(9)} + \color{orange}{(\frac{2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = -px-9p+\frac{2}{3}x+\frac{2}{3}.9& \text{Uitwerken } \\ & =-px-9p+\frac{2}{3}x+\frac{18}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-9p+\frac{2}{3}x+6 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{13}{12}+x)(\frac{8}{3}+a)& =(\color{red}{x}+\color{orange}{\frac{13}{12}}).(\color{green}{a}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(\frac{13}{12})} . \color{green}{(a)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{8}{3}x+\frac{13}{12}a+\frac{13}{12}.\frac{8}{3}& \text{Uitwerken } \\ & =ax+\frac{8}{3}x+\frac{13}{12}a+\frac{104}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{8}{3}x+\frac{13}{12}a+\frac{26}{9} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-15 14:35:33
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