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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{12}{2}+q)(\frac{-15}{20}+q)& =(\color{red}{q}+\color{orange}{6}).(\color{green}{q}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(6)} . \color{green}{(q)} + \color{orange}{(6)} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{3}{4}q+6q-6.\frac{3}{4}& \text{Uitwerken } \\ & =q^2+((\frac{-3}{4})+6)q-(\frac{-18}{4}) & \text{Neem samen} \\ &=q^2+\frac{21}{4}q-(\frac{-18}{4}) & \text{Maak de som} \\ &=q^2+\frac{21}{4}q+\frac{9}{2} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-5}{20})(\frac{8}{10}+p)& =(\color{red}{b}+\color{orange}{\frac{-1}{4}}).(\color{green}{p}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{5}b-\frac{1}{4}p-\frac{1}{4}.\frac{4}{5}& \text{Uitwerken } \\ & =bp+\frac{4}{5}b-\frac{1}{4}p-\frac{4}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{4}{5}b-\frac{1}{4}p-\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p-\frac{4}{13})(\frac{-16}{19}+x)& =(\color{red}{p}+\color{orange}{\frac{-4}{13}}).(\color{green}{x}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{16}{19}p-\frac{4}{13}x+\frac{4}{13}.\frac{16}{19}& \text{Uitwerken } \\ & =px-\frac{16}{19}p-\frac{4}{13}x+\frac{64}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p+\frac{-7}{10})((-7)+p)& =(\color{red}{p}+\color{orange}{\frac{-7}{10}}).(\color{green}{p}+\color{blue}{(-7)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-7)} + \color{orange}{(\frac{-7}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = pp-7p-\frac{7}{10}p+\frac{7}{10}.7& \text{Uitwerken } \\ & =p^2+((-7)+(\frac{-7}{10}))p+\frac{49}{10} & \text{Neem samen} \\ &=p^2-\frac{77}{10}p+\frac{49}{10} & \text{Maak de som} \\\end{align}\)
  5. \(\begin{align}(q-\frac{-16}{11})(\frac{14}{18}+b)& =(\color{red}{q}+\color{orange}{\frac{16}{11}}).(\color{green}{b}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{16}{11})} . \color{green}{(b)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{9}q+\frac{16}{11}b+\frac{16}{11}.\frac{7}{9}& \text{Uitwerken } \\ & =bq+\frac{7}{9}q+\frac{16}{11}b+\frac{112}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{16}{20}+b)(a-\frac{-19}{8})& =(\color{red}{b}+\color{orange}{\frac{4}{5}}).(\color{green}{a}+\color{blue}{\frac{19}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{19}{8})} + \color{orange}{(\frac{4}{5})} . \color{green}{(a)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{19}{8})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{19}{8}b+\frac{4}{5}a+\frac{4}{5}.\frac{19}{8}& \text{Uitwerken } \\ & =ab+\frac{19}{8}b+\frac{4}{5}a+\frac{76}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{19}{8}b+\frac{4}{5}a+\frac{19}{10} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-4}{2}+x)(p-\frac{-3}{3})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = px+1x-2p-2.1& \text{Uitwerken } \\ & =px+1x-2p-2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{-12}{15})(p+\frac{9}{16})& =(\color{red}{q}+\color{orange}{\frac{-4}{5}}).(\color{green}{p}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{9}{16}q-\frac{4}{5}p-\frac{4}{5}.\frac{9}{16}& \text{Uitwerken } \\ & =pq+\frac{9}{16}q-\frac{4}{5}p-\frac{36}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{9}{16}q-\frac{4}{5}p-\frac{9}{20} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-6}{7}-p)(\frac{-20}{9}-p)& =(\color{red}{-p}+\color{orange}{\frac{-6}{7}}).(\color{green}{-p}+\color{blue}{\frac{-20}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{-20}{9})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{-20}{9})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{20}{9}p+\frac{6}{7}p+\frac{6}{7}.\frac{20}{9}& \text{Uitwerken } \\ & =p^2+(\frac{20}{9}+\frac{6}{7})p+\frac{120}{63} & \text{Neem samen} \\ &=p^2+\frac{194}{63}p+\frac{120}{63} & \text{Maak de som} \\ &=p^2+\frac{194}{63}p+\frac{40}{21} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{9}{16}+a)(q+\frac{16}{13})& =(\color{red}{a}+\color{orange}{\frac{9}{16}}).(\color{green}{q}+\color{blue}{\frac{16}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{16}{13})} + \color{orange}{(\frac{9}{16})} . \color{green}{(q)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{16}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{16}{13}a+\frac{9}{16}q+\frac{9}{16}.\frac{16}{13}& \text{Uitwerken } \\ & =aq+\frac{16}{13}a+\frac{9}{16}q+\frac{144}{208} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{16}{13}a+\frac{9}{16}q+\frac{9}{13} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q+\frac{-18}{3})(a+\frac{-9}{13})& =(\color{red}{q}+\color{orange}{(-6)}).(\color{green}{a}+\color{blue}{\frac{-9}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{13})} + \color{orange}{(-6)} . \color{green}{(a)} + \color{orange}{(-6)} . \color{blue}{(\frac{-9}{13})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{9}{13}q-6a+6.\frac{9}{13}& \text{Uitwerken } \\ & =aq-\frac{9}{13}q-6a+\frac{54}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-11}{9}-p)(4+p)& =(\color{red}{-p}+\color{orange}{\frac{-11}{9}}).(\color{green}{p}+\color{blue}{4})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(4)} + \color{orange}{(\frac{-11}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -pp-4p-\frac{11}{9}p-\frac{11}{9}.4& \text{Uitwerken } \\ & =-p^2+((-4)+(\frac{-11}{9}))p-\frac{44}{9} & \text{Neem samen} \\ &=-p^2-\frac{47}{9}p-\frac{44}{9} & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-18 06:18:35
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