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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{20}{14}+a)(b-\frac{20}{14})& =(\color{red}{a}+\color{orange}{\frac{10}{7}}).(\color{green}{b}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{10}{7})} . \color{green}{(b)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{10}{7}a+\frac{10}{7}b-\frac{10}{7}.\frac{10}{7}& \text{Uitwerken } \\ & =ab-\frac{10}{7}a+\frac{10}{7}b-\frac{100}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p+\frac{20}{16})(x-\frac{-18}{13})& =(\color{red}{p}+\color{orange}{\frac{5}{4}}).(\color{green}{x}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{18}{13}p+\frac{5}{4}x+\frac{5}{4}.\frac{18}{13}& \text{Uitwerken } \\ & =px+\frac{18}{13}p+\frac{5}{4}x+\frac{90}{52} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{18}{13}p+\frac{5}{4}x+\frac{45}{26} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{14}{15}-p)(\frac{16}{5}-a)& =(\color{red}{-p}+\color{orange}{\frac{14}{15}}).(\color{green}{-a}+\color{blue}{\frac{16}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{16}{5})} + \color{orange}{(\frac{14}{15})} . \color{green}{(-a)} + \color{orange}{(\frac{14}{15})} . \color{blue}{(\frac{16}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{16}{5}p-\frac{14}{15}a+\frac{14}{15}.\frac{16}{5}& \text{Uitwerken } \\ & =ap-\frac{16}{5}p-\frac{14}{15}a+\frac{224}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{-16}{2})(a-\frac{-5}{7})& =(\color{red}{a}+\color{orange}{8}).(\color{green}{a}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(8)} . \color{green}{(a)} + \color{orange}{(8)} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{5}{7}a+8a+8.\frac{5}{7}& \text{Uitwerken } \\ & =a^2+(\frac{5}{7}+8)a+\frac{40}{7} & \text{Neem samen} \\ &=a^2+\frac{61}{7}a+\frac{40}{7} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(\frac{-5}{5}+b)(\frac{-2}{19}-a)& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{-a}+\color{blue}{\frac{-2}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{19})} + \color{orange}{(-1)} . \color{green}{(-a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-2}{19})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{2}{19}b+1a+1.\frac{2}{19}& \text{Uitwerken } \\ & =-ab-\frac{2}{19}b+1a+\frac{2}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{14}{7}+x)(\frac{3}{13}-b)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{-b}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(2)} . \color{green}{(-b)} + \color{orange}{(2)} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{3}{13}x-2b+2.\frac{3}{13}& \text{Uitwerken } \\ & =-bx+\frac{3}{13}x-2b+\frac{6}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-\frac{2}{6})(a+\frac{-10}{20})& =(\color{red}{q}+\color{orange}{\frac{-1}{3}}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{2}q-\frac{1}{3}a+\frac{1}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =aq-\frac{1}{2}q-\frac{1}{3}a+\frac{1}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-13}{6}+q)(\frac{-14}{9}-p)& =(\color{red}{q}+\color{orange}{\frac{-13}{6}}).(\color{green}{-p}+\color{blue}{\frac{-14}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{9})} + \color{orange}{(\frac{-13}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{-13}{6})} . \color{blue}{(\frac{-14}{9})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{14}{9}q+\frac{13}{6}p+\frac{13}{6}.\frac{14}{9}& \text{Uitwerken } \\ & =-pq-\frac{14}{9}q+\frac{13}{6}p+\frac{182}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{14}{9}q+\frac{13}{6}p+\frac{91}{27} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-11}{4}+b)(\frac{-14}{10}+x)& =(\color{red}{b}+\color{orange}{\frac{-11}{4}}).(\color{green}{x}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-11}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{4})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{7}{5}b-\frac{11}{4}x+\frac{11}{4}.\frac{7}{5}& \text{Uitwerken } \\ & =bx-\frac{7}{5}b-\frac{11}{4}x+\frac{77}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}((-8)-p)(\frac{10}{14}-x)& =(\color{red}{-p}+\color{orange}{(-8)}).(\color{green}{-x}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(-8)} . \color{green}{(-x)} + \color{orange}{(-8)} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{5}{7}p+8x-8.\frac{5}{7}& \text{Uitwerken } \\ & =px-\frac{5}{7}p+8x-\frac{40}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q-\frac{-1}{16})(\frac{-11}{17}-p)& =(\color{red}{q}+\color{orange}{\frac{1}{16}}).(\color{green}{-p}+\color{blue}{\frac{-11}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{17})} + \color{orange}{(\frac{1}{16})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{16})} . \color{blue}{(\frac{-11}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{11}{17}q-\frac{1}{16}p-\frac{1}{16}.\frac{11}{17}& \text{Uitwerken } \\ & =-pq-\frac{11}{17}q-\frac{1}{16}p-\frac{11}{272} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{-3}{17})(p+\frac{15}{10})& =(\color{red}{a}+\color{orange}{\frac{-3}{17}}).(\color{green}{p}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-3}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{17})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{2}a-\frac{3}{17}p-\frac{3}{17}.\frac{3}{2}& \text{Uitwerken } \\ & =ap+\frac{3}{2}a-\frac{3}{17}p-\frac{9}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-20 17:06:55
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