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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{16}{6})(\frac{13}{20}-q)& =(\color{red}{x}+\color{orange}{\frac{-8}{3}}).(\color{green}{-q}+\color{blue}{\frac{13}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{13}{20})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{13}{20})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{13}{20}x+\frac{8}{3}q-\frac{8}{3}.\frac{13}{20}& \text{Uitwerken } \\ & =-qx+\frac{13}{20}x+\frac{8}{3}q-\frac{104}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{13}{20}x+\frac{8}{3}q-\frac{26}{15} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q+\frac{11}{18})(\frac{9}{9}-p)& =(\color{red}{q}+\color{orange}{\frac{11}{18}}).(\color{green}{-p}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{11}{18})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -pq+1q-\frac{11}{18}p+\frac{11}{18}.1& \text{Uitwerken } \\ & =-pq+1q-\frac{11}{18}p+\frac{11}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{12}{20}-a)(\frac{10}{6}-a)& =(\color{red}{-a}+\color{orange}{\frac{3}{5}}).(\color{green}{-a}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-a)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{3}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{5}{3}a-\frac{3}{5}a+\frac{3}{5}.\frac{5}{3}& \text{Uitwerken } \\ & =a^2+((\frac{-5}{3})+(\frac{-3}{5}))a+\frac{15}{15} & \text{Neem samen} \\ &=a^2-\frac{34}{15}a+\frac{15}{15} & \text{Maak de som} \\ &=a^2-\frac{34}{15}a+1 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{-14}{4}-b)(x-\frac{-16}{19})& =(\color{red}{-b}+\color{orange}{\frac{-7}{2}}).(\color{green}{x}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{16}{19}b-\frac{7}{2}x-\frac{7}{2}.\frac{16}{19}& \text{Uitwerken } \\ & =-bx-\frac{16}{19}b-\frac{7}{2}x-\frac{112}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{16}{19}b-\frac{7}{2}x-\frac{56}{19} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-7}{3}+b)(a-\frac{-3}{15})& =(\color{red}{b}+\color{orange}{\frac{-7}{3}}).(\color{green}{a}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{5}b-\frac{7}{3}a-\frac{7}{3}.\frac{1}{5}& \text{Uitwerken } \\ & =ab+\frac{1}{5}b-\frac{7}{3}a-\frac{7}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-18}{9}-a)(\frac{-8}{9}-x)& =(\color{red}{-a}+\color{orange}{(-2)}).(\color{green}{-x}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(-2)} . \color{green}{(-x)} + \color{orange}{(-2)} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{8}{9}a+2x+2.\frac{8}{9}& \text{Uitwerken } \\ & =ax+\frac{8}{9}a+2x+\frac{16}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(p+\frac{5}{6})(x+\frac{-3}{4})& =(\color{red}{p}+\color{orange}{\frac{5}{6}}).(\color{green}{x}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{5}{6})} . \color{green}{(x)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{3}{4}p+\frac{5}{6}x-\frac{5}{6}.\frac{3}{4}& \text{Uitwerken } \\ & =px-\frac{3}{4}p+\frac{5}{6}x-\frac{15}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{3}{4}p+\frac{5}{6}x-\frac{5}{8} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{16}{2}+p)(q+\frac{1}{13})& =(\color{red}{p}+\color{orange}{8}).(\color{green}{q}+\color{blue}{\frac{1}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{13})} + \color{orange}{(8)} . \color{green}{(q)} + \color{orange}{(8)} . \color{blue}{(\frac{1}{13})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{13}p+8q+8.\frac{1}{13}& \text{Uitwerken } \\ & =pq+\frac{1}{13}p+8q+\frac{8}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{4}{14}-b)(\frac{3}{13}+p)& =(\color{red}{-b}+\color{orange}{\frac{2}{7}}).(\color{green}{p}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(\frac{2}{7})} . \color{green}{(p)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{3}{13}b+\frac{2}{7}p+\frac{2}{7}.\frac{3}{13}& \text{Uitwerken } \\ & =-bp-\frac{3}{13}b+\frac{2}{7}p+\frac{6}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-9}{14}+a)(\frac{-15}{11}-x)& =(\color{red}{a}+\color{orange}{\frac{-9}{14}}).(\color{green}{-x}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(-x)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{15}{11}a+\frac{9}{14}x+\frac{9}{14}.\frac{15}{11}& \text{Uitwerken } \\ & =-ax-\frac{15}{11}a+\frac{9}{14}x+\frac{135}{154} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(b-\frac{-15}{8})(a+\frac{-15}{2})& =(\color{red}{b}+\color{orange}{\frac{15}{8}}).(\color{green}{a}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{15}{8})} . \color{green}{(a)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{15}{2}b+\frac{15}{8}a-\frac{15}{8}.\frac{15}{2}& \text{Uitwerken } \\ & =ab-\frac{15}{2}b+\frac{15}{8}a-\frac{225}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{13}{14}-x)(\frac{-6}{16}+p)& =(\color{red}{-x}+\color{orange}{\frac{13}{14}}).(\color{green}{p}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{13}{14})} . \color{green}{(p)} + \color{orange}{(\frac{13}{14})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{3}{8}x+\frac{13}{14}p-\frac{13}{14}.\frac{3}{8}& \text{Uitwerken } \\ & =-px+\frac{3}{8}x+\frac{13}{14}p-\frac{39}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-06 08:26:54
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