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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+6)(\frac{-20}{9}-a)& =(\color{red}{a}+\color{orange}{6}).(\color{green}{-a}+\color{blue}{\frac{-20}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{9})} + \color{orange}{(6)} . \color{green}{(-a)} + \color{orange}{(6)} . \color{blue}{(\frac{-20}{9})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{20}{9}a-6a-6.\frac{20}{9}& \text{Uitwerken } \\ & =-a^2+((\frac{-20}{9})+(-6))a-\frac{120}{9} & \text{Neem samen} \\ &=-a^2-\frac{74}{9}a-\frac{120}{9} & \text{Maak de som} \\ &=-a^2-\frac{74}{9}a-\frac{40}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{-9}{3}+b)(\frac{-10}{5}-p)& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{-p}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(-3)} . \color{green}{(-p)} + \color{orange}{(-3)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -bp-2b+3p+3.2& \text{Uitwerken } \\ & =-bp-2b+3p+6 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(18-x)(\frac{3}{7}+p)& =(\color{red}{-x}+\color{orange}{18}).(\color{green}{p}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(18)} . \color{green}{(p)} + \color{orange}{(18)} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{3}{7}x+18p+18.\frac{3}{7}& \text{Uitwerken } \\ & =-px-\frac{3}{7}x+18p+\frac{54}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-7}{19})(q+\frac{-15}{16})& =(\color{red}{x}+\color{orange}{\frac{7}{19}}).(\color{green}{q}+\color{blue}{\frac{-15}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{16})} + \color{orange}{(\frac{7}{19})} . \color{green}{(q)} + \color{orange}{(\frac{7}{19})} . \color{blue}{(\frac{-15}{16})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{15}{16}x+\frac{7}{19}q-\frac{7}{19}.\frac{15}{16}& \text{Uitwerken } \\ & =qx-\frac{15}{16}x+\frac{7}{19}q-\frac{105}{304} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{4}{19}+q)(q-\frac{-7}{11})& =(\color{red}{q}+\color{orange}{\frac{4}{19}}).(\color{green}{q}+\color{blue}{\frac{7}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{7}{11})} + \color{orange}{(\frac{4}{19})} . \color{green}{(q)} + \color{orange}{(\frac{4}{19})} . \color{blue}{(\frac{7}{11})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{7}{11}q+\frac{4}{19}q+\frac{4}{19}.\frac{7}{11}& \text{Uitwerken } \\ & =q^2+(\frac{7}{11}+\frac{4}{19})q+\frac{28}{209} & \text{Neem samen} \\ &=q^2+\frac{177}{209}q+\frac{28}{209} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{7}{4}+x)(b-\frac{2}{2})& =(\color{red}{x}+\color{orange}{\frac{7}{4}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{7}{4})} . \color{green}{(b)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bx-1x+\frac{7}{4}b-\frac{7}{4}.1& \text{Uitwerken } \\ & =bx-1x+\frac{7}{4}b-\frac{7}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b+\frac{-18}{16})(x+\frac{8}{3})& =(\color{red}{b}+\color{orange}{\frac{-9}{8}}).(\color{green}{x}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{8}{3}b-\frac{9}{8}x-\frac{9}{8}.\frac{8}{3}& \text{Uitwerken } \\ & =bx+\frac{8}{3}b-\frac{9}{8}x-\frac{72}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{8}{3}b-\frac{9}{8}x-3 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-18}{12}+a)(\frac{14}{2}-x)& =(\color{red}{a}+\color{orange}{\frac{-3}{2}}).(\color{green}{-x}+\color{blue}{7})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(7)} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = -ax+7a+\frac{3}{2}x-\frac{3}{2}.7& \text{Uitwerken } \\ & =-ax+7a+\frac{3}{2}x-\frac{21}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-16}{3}-p)(\frac{-11}{20}-b)& =(\color{red}{-p}+\color{orange}{\frac{-16}{3}}).(\color{green}{-b}+\color{blue}{\frac{-11}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-11}{20})} + \color{orange}{(\frac{-16}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-16}{3})} . \color{blue}{(\frac{-11}{20})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{11}{20}p+\frac{16}{3}b+\frac{16}{3}.\frac{11}{20}& \text{Uitwerken } \\ & =bp+\frac{11}{20}p+\frac{16}{3}b+\frac{176}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{11}{20}p+\frac{16}{3}b+\frac{44}{15} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p-\frac{13}{9})(\frac{-10}{2}+p)& =(\color{red}{p}+\color{orange}{\frac{-13}{9}}).(\color{green}{p}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-5)} + \color{orange}{(\frac{-13}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{9})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = pp-5p-\frac{13}{9}p+\frac{13}{9}.5& \text{Uitwerken } \\ & =p^2+((-5)+(\frac{-13}{9}))p+\frac{65}{9} & \text{Neem samen} \\ &=p^2-\frac{58}{9}p+\frac{65}{9} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(p+\frac{-12}{19})(p+\frac{3}{16})& =(\color{red}{p}+\color{orange}{\frac{-12}{19}}).(\color{green}{p}+\color{blue}{\frac{3}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{3}{16})} + \color{orange}{(\frac{-12}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-12}{19})} . \color{blue}{(\frac{3}{16})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{3}{16}p-\frac{12}{19}p-\frac{12}{19}.\frac{3}{16}& \text{Uitwerken } \\ & =p^2+(\frac{3}{16}+(\frac{-12}{19}))p-(\frac{-36}{304}) & \text{Neem samen} \\ &=p^2-\frac{135}{304}p-(\frac{-36}{304}) & \text{Maak de som} \\ &=p^2-\frac{135}{304}p+\frac{9}{76} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{-11}{13}+q)(p+\frac{-20}{14})& =(\color{red}{q}+\color{orange}{\frac{-11}{13}}).(\color{green}{p}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{10}{7}q-\frac{11}{13}p+\frac{11}{13}.\frac{10}{7}& \text{Uitwerken } \\ & =pq-\frac{10}{7}q-\frac{11}{13}p+\frac{110}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-04-10 21:20:59
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