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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{19}{8})(10+a)& =(\color{red}{b}+\color{orange}{\frac{19}{8}}).(\color{green}{a}+\color{blue}{10})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(10)} + \color{orange}{(\frac{19}{8})} . \color{green}{(a)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = ab+10b+\frac{19}{8}a+\frac{19}{8}.10& \text{Uitwerken } \\ & =ab+10b+\frac{19}{8}a+\frac{190}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+10b+\frac{19}{8}a+\frac{95}{4} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q+\frac{-14}{11})(p-\frac{-15}{17})& =(\color{red}{q}+\color{orange}{\frac{-14}{11}}).(\color{green}{p}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(\frac{-14}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{15}{17}q-\frac{14}{11}p-\frac{14}{11}.\frac{15}{17}& \text{Uitwerken } \\ & =pq+\frac{15}{17}q-\frac{14}{11}p-\frac{210}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-19}{12})(\frac{-12}{15}-b)& =(\color{red}{x}+\color{orange}{\frac{-19}{12}}).(\color{green}{-b}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{4}{5}x+\frac{19}{12}b+\frac{19}{12}.\frac{4}{5}& \text{Uitwerken } \\ & =-bx-\frac{4}{5}x+\frac{19}{12}b+\frac{76}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{4}{5}x+\frac{19}{12}b+\frac{19}{15} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{15}{19}-p)(\frac{-9}{17}+a)& =(\color{red}{-p}+\color{orange}{\frac{15}{19}}).(\color{green}{a}+\color{blue}{\frac{-9}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-9}{17})} + \color{orange}{(\frac{15}{19})} . \color{green}{(a)} + \color{orange}{(\frac{15}{19})} . \color{blue}{(\frac{-9}{17})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{9}{17}p+\frac{15}{19}a-\frac{15}{19}.\frac{9}{17}& \text{Uitwerken } \\ & =-ap+\frac{9}{17}p+\frac{15}{19}a-\frac{135}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{-11}{17})(a-\frac{13}{12})& =(\color{red}{p}+\color{orange}{\frac{11}{17}}).(\color{green}{a}+\color{blue}{\frac{-13}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{12})} + \color{orange}{(\frac{11}{17})} . \color{green}{(a)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{-13}{12})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{13}{12}p+\frac{11}{17}a-\frac{11}{17}.\frac{13}{12}& \text{Uitwerken } \\ & =ap-\frac{13}{12}p+\frac{11}{17}a-\frac{143}{204} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-10}{7})(\frac{-14}{6}-q)& =(\color{red}{a}+\color{orange}{\frac{-10}{7}}).(\color{green}{-q}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{7}{3}a+\frac{10}{7}q+\frac{10}{7}.\frac{7}{3}& \text{Uitwerken } \\ & =-aq-\frac{7}{3}a+\frac{10}{7}q+\frac{70}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{7}{3}a+\frac{10}{7}q+\frac{10}{3} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(a+\frac{-9}{9})(\frac{-12}{16}-b)& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{-b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(-1)} . \color{green}{(-b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{3}{4}a+1b+1.\frac{3}{4}& \text{Uitwerken } \\ & =-ab-\frac{3}{4}a+1b+\frac{3}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p-\frac{6}{8})(\frac{13}{9}-b)& =(\color{red}{p}+\color{orange}{\frac{-3}{4}}).(\color{green}{-b}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{13}{9}p+\frac{3}{4}b-\frac{3}{4}.\frac{13}{9}& \text{Uitwerken } \\ & =-bp+\frac{13}{9}p+\frac{3}{4}b-\frac{39}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{13}{9}p+\frac{3}{4}b-\frac{13}{12} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(15+p)(\frac{10}{9}-b)& =(\color{red}{p}+\color{orange}{15}).(\color{green}{-b}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(15)} . \color{green}{(-b)} + \color{orange}{(15)} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{10}{9}p-15b+15.\frac{10}{9}& \text{Uitwerken } \\ & =-bp+\frac{10}{9}p-15b+\frac{150}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{10}{9}p-15b+\frac{50}{3} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{2}{5}+x)(\frac{8}{13}-x)& =(\color{red}{x}+\color{orange}{\frac{2}{5}}).(\color{green}{-x}+\color{blue}{\frac{8}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{8}{13})} + \color{orange}{(\frac{2}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{8}{13})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{8}{13}x-\frac{2}{5}x+\frac{2}{5}.\frac{8}{13}& \text{Uitwerken } \\ & =-x^2+(\frac{8}{13}+(\frac{-2}{5}))x+(\frac{-16}{65}) & \text{Neem samen} \\ &=-x^2+\frac{14}{65}x+(\frac{-16}{65}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(p+\frac{11}{7})(x+\frac{11}{6})& =(\color{red}{p}+\color{orange}{\frac{11}{7}}).(\color{green}{x}+\color{blue}{\frac{11}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{11}{6})} + \color{orange}{(\frac{11}{7})} . \color{green}{(x)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(\frac{11}{6})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{11}{6}p+\frac{11}{7}x+\frac{11}{7}.\frac{11}{6}& \text{Uitwerken } \\ & =px+\frac{11}{6}p+\frac{11}{7}x+\frac{121}{42} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-11}{10}-a)(p+\frac{20}{16})& =(\color{red}{-a}+\color{orange}{\frac{-11}{10}}).(\color{green}{p}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-11}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{10})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{5}{4}a-\frac{11}{10}p-\frac{11}{10}.\frac{5}{4}& \text{Uitwerken } \\ & =-ap-\frac{5}{4}a-\frac{11}{10}p-\frac{55}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{5}{4}a-\frac{11}{10}p-\frac{11}{8} & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-06 09:20:44
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