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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{15}{6})(x-\frac{14}{18})& =(\color{red}{x}+\color{orange}{\frac{-5}{2}}).(\color{green}{x}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{7}{9}x-\frac{5}{2}x+\frac{5}{2}.\frac{7}{9}& \text{Uitwerken } \\ & =x^2+((\frac{-7}{9})+(\frac{-5}{2}))x+\frac{35}{18} & \text{Neem samen} \\ &=x^2-\frac{59}{18}x+\frac{35}{18} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{15}{11}-q)(\frac{-13}{13}-q)& =(\color{red}{-q}+\color{orange}{\frac{15}{11}}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(-1)} + \color{orange}{(\frac{15}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{15}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qq+1q-\frac{15}{11}q-\frac{15}{11}.1& \text{Uitwerken } \\ & =q^2+(1+(\frac{-15}{11}))q-(\frac{-15}{11}) & \text{Neem samen} \\ &=q^2-\frac{4}{11}q-(\frac{-15}{11}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{-9}{19}+a)(\frac{10}{17}+b)& =(\color{red}{a}+\color{orange}{\frac{-9}{19}}).(\color{green}{b}+\color{blue}{\frac{10}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{10}{17})} + \color{orange}{(\frac{-9}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{19})} . \color{blue}{(\frac{10}{17})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{10}{17}a-\frac{9}{19}b-\frac{9}{19}.\frac{10}{17}& \text{Uitwerken } \\ & =ab+\frac{10}{17}a-\frac{9}{19}b-\frac{90}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-11}{13}+p)(\frac{-14}{7}+a)& =(\color{red}{p}+\color{orange}{\frac{-11}{13}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-11}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ap-2p-\frac{11}{13}a+\frac{11}{13}.2& \text{Uitwerken } \\ & =ap-2p-\frac{11}{13}a+\frac{22}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(b+\frac{7}{15})(a-\frac{4}{5})& =(\color{red}{b}+\color{orange}{\frac{7}{15}}).(\color{green}{a}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{7}{15})} . \color{green}{(a)} + \color{orange}{(\frac{7}{15})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{4}{5}b+\frac{7}{15}a-\frac{7}{15}.\frac{4}{5}& \text{Uitwerken } \\ & =ab-\frac{4}{5}b+\frac{7}{15}a-\frac{28}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q-\frac{10}{10})(q+\frac{11}{12})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{11}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{11}{12})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{11}{12})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{11}{12}q-1q-1.\frac{11}{12}& \text{Uitwerken } \\ & =q^2+(\frac{11}{12}+(-1))q-(\frac{-11}{12}) & \text{Neem samen} \\ &=q^2-\frac{1}{12}q-(\frac{-11}{12}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{8}{2}-q)(\frac{-12}{16}+q)& =(\color{red}{-q}+\color{orange}{4}).(\color{green}{q}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(4)} . \color{green}{(q)} + \color{orange}{(4)} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{3}{4}q+4q-4.\frac{3}{4}& \text{Uitwerken } \\ & =-q^2+(\frac{3}{4}+4)q-\frac{12}{4} & \text{Neem samen} \\ &=-q^2+\frac{19}{4}q-\frac{12}{4} & \text{Maak de som} \\ &=-q^2+\frac{19}{4}q-3 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(b+\frac{-10}{18})(q-18)& =(\color{red}{b}+\color{orange}{\frac{-5}{9}}).(\color{green}{q}+\color{blue}{(-18)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-18)} + \color{orange}{(\frac{-5}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(-18)}& \text{Boogjes en uitschrijven} \\ & = bq-18b-\frac{5}{9}q+\frac{5}{9}.18& \text{Uitwerken } \\ & =bq-18b-\frac{5}{9}q+\frac{90}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-18b-\frac{5}{9}q+10 & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(q+\frac{-20}{5})(\frac{5}{17}-x)& =(\color{red}{q}+\color{orange}{(-4)}).(\color{green}{-x}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(-4)} . \color{green}{(-x)} + \color{orange}{(-4)} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{5}{17}q+4x-4.\frac{5}{17}& \text{Uitwerken } \\ & =-qx+\frac{5}{17}q+4x-\frac{20}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{13}{19}+q)(\frac{13}{19}+x)& =(\color{red}{q}+\color{orange}{\frac{13}{19}}).(\color{green}{x}+\color{blue}{\frac{13}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{13}{19})} + \color{orange}{(\frac{13}{19})} . \color{green}{(x)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{13}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{13}{19}q+\frac{13}{19}x+\frac{13}{19}.\frac{13}{19}& \text{Uitwerken } \\ & =qx+\frac{13}{19}q+\frac{13}{19}x+\frac{169}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{4}{11}+p)(b-\frac{-5}{18})& =(\color{red}{p}+\color{orange}{\frac{4}{11}}).(\color{green}{b}+\color{blue}{\frac{5}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{5}{18})} + \color{orange}{(\frac{4}{11})} . \color{green}{(b)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(\frac{5}{18})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{18}p+\frac{4}{11}b+\frac{4}{11}.\frac{5}{18}& \text{Uitwerken } \\ & =bp+\frac{5}{18}p+\frac{4}{11}b+\frac{20}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{5}{18}p+\frac{4}{11}b+\frac{10}{99} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(p+\frac{-18}{3})(a+\frac{20}{5})& =(\color{red}{p}+\color{orange}{(-6)}).(\color{green}{a}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(4)} + \color{orange}{(-6)} . \color{green}{(a)} + \color{orange}{(-6)} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = ap+4p-6a-6.4& \text{Uitwerken } \\ & =ap+4p-6a-24 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-11-21 12:23:03