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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{13}{5}-a)(a+\frac{1}{10})& =(\color{red}{-a}+\color{orange}{\frac{13}{5}}).(\color{green}{a}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{13}{5})} . \color{green}{(a)} + \color{orange}{(\frac{13}{5})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{1}{10}a+\frac{13}{5}a+\frac{13}{5}.\frac{1}{10}& \text{Uitwerken } \\ & =-a^2+((\frac{-1}{10})+\frac{13}{5})a+(\frac{-13}{50}) & \text{Neem samen} \\ &=-a^2+\frac{25}{10}a+(\frac{-13}{50}) & \text{Maak de som} \\ &=-a^2+\frac{5}{2}a+(\frac{-13}{50}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(a-\frac{-9}{19})(a-\frac{8}{12})& =(\color{red}{a}+\color{orange}{\frac{9}{19}}).(\color{green}{a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{9}{19})} . \color{green}{(a)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{2}{3}a+\frac{9}{19}a-\frac{9}{19}.\frac{2}{3}& \text{Uitwerken } \\ & =a^2+((\frac{-2}{3})+\frac{9}{19})a-(\frac{-18}{57}) & \text{Neem samen} \\ &=a^2-\frac{11}{57}a-(\frac{-18}{57}) & \text{Maak de som} \\ &=a^2-\frac{11}{57}a+\frac{6}{19} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  3. \(\begin{align}(\frac{-16}{3}+b)(\frac{-8}{3}+b)& =(\color{red}{b}+\color{orange}{\frac{-16}{3}}).(\color{green}{b}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-16}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{3})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{8}{3}b-\frac{16}{3}b+\frac{16}{3}.\frac{8}{3}& \text{Uitwerken } \\ & =b^2+((\frac{-8}{3})+(\frac{-16}{3}))b+\frac{128}{9} & \text{Neem samen} \\ &=b^2-\frac{24}{3}b+\frac{128}{9} & \text{Maak de som} \\ &=b^2-8b+\frac{128}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{-6}{12}+q)(\frac{-6}{5}-x)& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{-x}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{6}{5}q+\frac{1}{2}x+\frac{1}{2}.\frac{6}{5}& \text{Uitwerken } \\ & =-qx-\frac{6}{5}q+\frac{1}{2}x+\frac{6}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{6}{5}q+\frac{1}{2}x+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{13}{19}-a)(\frac{-20}{3}+q)& =(\color{red}{-a}+\color{orange}{\frac{13}{19}}).(\color{green}{q}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(\frac{13}{19})} . \color{green}{(q)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{20}{3}a+\frac{13}{19}q-\frac{13}{19}.\frac{20}{3}& \text{Uitwerken } \\ & =-aq+\frac{20}{3}a+\frac{13}{19}q-\frac{260}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a+\frac{-15}{10})(a-\frac{-13}{2})& =(\color{red}{a}+\color{orange}{\frac{-3}{2}}).(\color{green}{a}+\color{blue}{\frac{13}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{13}{2})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{13}{2})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{13}{2}a-\frac{3}{2}a-\frac{3}{2}.\frac{13}{2}& \text{Uitwerken } \\ & =a^2+(\frac{13}{2}+(\frac{-3}{2}))a-(\frac{-39}{4}) & \text{Neem samen} \\ &=a^2+\frac{10}{2}a-(\frac{-39}{4}) & \text{Maak de som} \\ &=a^2+5a+\frac{39}{4} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(a-19)(\frac{-3}{3}-p)& =(\color{red}{a}+\color{orange}{(-19)}).(\color{green}{-p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(-19)} . \color{green}{(-p)} + \color{orange}{(-19)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ap-1a+19p+19.1& \text{Uitwerken } \\ & =-ap-1a+19p+19 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{-8}{13})(a+\frac{-16}{4})& =(\color{red}{a}+\color{orange}{\frac{-8}{13}}).(\color{green}{a}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-4)} + \color{orange}{(\frac{-8}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{13})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = aa-4a-\frac{8}{13}a+\frac{8}{13}.4& \text{Uitwerken } \\ & =a^2+((-4)+(\frac{-8}{13}))a+\frac{32}{13} & \text{Neem samen} \\ &=a^2-\frac{60}{13}a+\frac{32}{13} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(x+\frac{-13}{20})(p-\frac{14}{7})& =(\color{red}{x}+\color{orange}{\frac{-13}{20}}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{-13}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = px-2x-\frac{13}{20}p+\frac{13}{20}.2& \text{Uitwerken } \\ & =px-2x-\frac{13}{20}p+\frac{26}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-2x-\frac{13}{20}p+\frac{13}{10} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-20}{16})(a+\frac{12}{14})& =(\color{red}{b}+\color{orange}{\frac{5}{4}}).(\color{green}{a}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{5}{4})} . \color{green}{(a)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{6}{7}b+\frac{5}{4}a+\frac{5}{4}.\frac{6}{7}& \text{Uitwerken } \\ & =ab+\frac{6}{7}b+\frac{5}{4}a+\frac{30}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{6}{7}b+\frac{5}{4}a+\frac{15}{14} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(14+x)(a+\frac{9}{18})& =(\color{red}{x}+\color{orange}{14}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(14)} . \color{green}{(a)} + \color{orange}{(14)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{2}x+14a+14.\frac{1}{2}& \text{Uitwerken } \\ & =ax+\frac{1}{2}x+14a+\frac{14}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{1}{2}x+14a+7 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}((-2)+b)(p-\frac{-7}{2})& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{2}b-2p-2.\frac{7}{2}& \text{Uitwerken } \\ & =bp+\frac{7}{2}b-2p-\frac{14}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{7}{2}b-2p-7 & \text{Vereenvoudig} \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-02 02:29:19