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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-19}{18}-p)(\frac{16}{15}+x)& =(\color{red}{-p}+\color{orange}{\frac{-19}{18}}).(\color{green}{x}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{-19}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{18})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{16}{15}p-\frac{19}{18}x-\frac{19}{18}.\frac{16}{15}& \text{Uitwerken } \\ & =-px-\frac{16}{15}p-\frac{19}{18}x-\frac{304}{270} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{16}{15}p-\frac{19}{18}x-\frac{152}{135} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{5}{6}+x)(p+10)& =(\color{red}{x}+\color{orange}{\frac{5}{6}}).(\color{green}{p}+\color{blue}{10})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(10)} + \color{orange}{(\frac{5}{6})} . \color{green}{(p)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = px+10x+\frac{5}{6}p+\frac{5}{6}.10& \text{Uitwerken } \\ & =px+10x+\frac{5}{6}p+\frac{50}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+10x+\frac{5}{6}p+\frac{25}{3} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-16}{17}+q)(q-(-3))& =(\color{red}{q}+\color{orange}{\frac{-16}{17}}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{-16}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{17})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = qq+3q-\frac{16}{17}q-\frac{16}{17}.3& \text{Uitwerken } \\ & =q^2+(3+(\frac{-16}{17}))q-(\frac{-48}{17}) & \text{Neem samen} \\ &=q^2+\frac{35}{17}q-(\frac{-48}{17}) & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(b+\frac{5}{8})(a+\frac{-20}{17})& =(\color{red}{b}+\color{orange}{\frac{5}{8}}).(\color{green}{a}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(\frac{5}{8})} . \color{green}{(a)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{20}{17}b+\frac{5}{8}a-\frac{5}{8}.\frac{20}{17}& \text{Uitwerken } \\ & =ab-\frac{20}{17}b+\frac{5}{8}a-\frac{100}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{20}{17}b+\frac{5}{8}a-\frac{25}{34} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(b-\frac{10}{17})(\frac{3}{12}-x)& =(\color{red}{b}+\color{orange}{\frac{-10}{17}}).(\color{green}{-x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-10}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-10}{17})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{4}b+\frac{10}{17}x-\frac{10}{17}.\frac{1}{4}& \text{Uitwerken } \\ & =-bx+\frac{1}{4}b+\frac{10}{17}x-\frac{10}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{1}{4}b+\frac{10}{17}x-\frac{5}{34} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-19}{6}+p)(a-\frac{-3}{6})& =(\color{red}{p}+\color{orange}{\frac{-19}{6}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-19}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{6})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{2}p-\frac{19}{6}a-\frac{19}{6}.\frac{1}{2}& \text{Uitwerken } \\ & =ap+\frac{1}{2}p-\frac{19}{6}a-\frac{19}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-14}{2})(q-\frac{-14}{18})& =(\color{red}{p}+\color{orange}{7}).(\color{green}{q}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(7)} . \color{green}{(q)} + \color{orange}{(7)} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{7}{9}p+7q+7.\frac{7}{9}& \text{Uitwerken } \\ & =pq+\frac{7}{9}p+7q+\frac{49}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-17}{13})(\frac{-8}{2}+b)& =(\color{red}{b}+\color{orange}{\frac{-17}{13}}).(\color{green}{b}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(-4)} + \color{orange}{(\frac{-17}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{13})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = bb-4b-\frac{17}{13}b+\frac{17}{13}.4& \text{Uitwerken } \\ & =b^2+((-4)+(\frac{-17}{13}))b+\frac{68}{13} & \text{Neem samen} \\ &=b^2-\frac{69}{13}b+\frac{68}{13} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{8}{12}-a)(p-\frac{16}{18})& =(\color{red}{-a}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{8}{9}a+\frac{2}{3}p-\frac{2}{3}.\frac{8}{9}& \text{Uitwerken } \\ & =-ap+\frac{8}{9}a+\frac{2}{3}p-\frac{16}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a+\frac{16}{8})(b+\frac{10}{11})& =(\color{red}{a}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{10}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{10}{11})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{10}{11})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{10}{11}a+2b+2.\frac{10}{11}& \text{Uitwerken } \\ & =ab+\frac{10}{11}a+2b+\frac{20}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(18-b)(\frac{17}{16}-b)& =(\color{red}{-b}+\color{orange}{18}).(\color{green}{-b}+\color{blue}{\frac{17}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{17}{16})} + \color{orange}{(18)} . \color{green}{(-b)} + \color{orange}{(18)} . \color{blue}{(\frac{17}{16})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{17}{16}b-18b+18.\frac{17}{16}& \text{Uitwerken } \\ & =b^2+((\frac{-17}{16})+(-18))b+\frac{306}{16} & \text{Neem samen} \\ &=b^2-\frac{305}{16}b+\frac{306}{16} & \text{Maak de som} \\ &=b^2-\frac{305}{16}b+\frac{153}{8} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  12. \(\begin{align}(\frac{3}{2}-a)(b+\frac{3}{7})& =(\color{red}{-a}+\color{orange}{\frac{3}{2}}).(\color{green}{b}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{3}{7}a+\frac{3}{2}b+\frac{3}{2}.\frac{3}{7}& \text{Uitwerken } \\ & =-ab-\frac{3}{7}a+\frac{3}{2}b+\frac{9}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-19 11:28:36
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