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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{10}{17})(\frac{-9}{8}+a)& =(\color{red}{p}+\color{orange}{\frac{-10}{17}}).(\color{green}{a}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{-10}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{17})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{9}{8}p-\frac{10}{17}a+\frac{10}{17}.\frac{9}{8}& \text{Uitwerken } \\ & =ap-\frac{9}{8}p-\frac{10}{17}a+\frac{90}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{9}{8}p-\frac{10}{17}a+\frac{45}{68} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-12}{12}-a)(\frac{-20}{5}+p)& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(-4)} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -ap+4a-1p+1.4& \text{Uitwerken } \\ & =-ap+4a-1p+4 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{19}{12}+b)(\frac{-9}{18}-x)& =(\color{red}{b}+\color{orange}{\frac{19}{12}}).(\color{green}{-x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{19}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{12})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{2}b-\frac{19}{12}x-\frac{19}{12}.\frac{1}{2}& \text{Uitwerken } \\ & =-bx-\frac{1}{2}b-\frac{19}{12}x-\frac{19}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p+\frac{18}{7})(\frac{1}{20}+a)& =(\color{red}{p}+\color{orange}{\frac{18}{7}}).(\color{green}{a}+\color{blue}{\frac{1}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{20})} + \color{orange}{(\frac{18}{7})} . \color{green}{(a)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{1}{20})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{20}p+\frac{18}{7}a+\frac{18}{7}.\frac{1}{20}& \text{Uitwerken } \\ & =ap+\frac{1}{20}p+\frac{18}{7}a+\frac{18}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{1}{20}p+\frac{18}{7}a+\frac{9}{70} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(a-\frac{3}{12})(q-\frac{-17}{19})& =(\color{red}{a}+\color{orange}{\frac{-1}{4}}).(\color{green}{q}+\color{blue}{\frac{17}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{17}{19})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{17}{19})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{17}{19}a-\frac{1}{4}q-\frac{1}{4}.\frac{17}{19}& \text{Uitwerken } \\ & =aq+\frac{17}{19}a-\frac{1}{4}q-\frac{17}{76} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-20}{15}-x)(\frac{-4}{10}-b)& =(\color{red}{-x}+\color{orange}{\frac{-4}{3}}).(\color{green}{-b}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{2}{5}x+\frac{4}{3}b+\frac{4}{3}.\frac{2}{5}& \text{Uitwerken } \\ & =bx+\frac{2}{5}x+\frac{4}{3}b+\frac{8}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q-\frac{-2}{3})(q-\frac{-20}{7})& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{20}{7}q+\frac{2}{3}q+\frac{2}{3}.\frac{20}{7}& \text{Uitwerken } \\ & =q^2+(\frac{20}{7}+\frac{2}{3})q+\frac{40}{21} & \text{Neem samen} \\ &=q^2+\frac{74}{21}q+\frac{40}{21} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-5}{16}-b)(\frac{18}{19}-b)& =(\color{red}{-b}+\color{orange}{\frac{-5}{16}}).(\color{green}{-b}+\color{blue}{\frac{18}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{18}{19})} + \color{orange}{(\frac{-5}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{16})} . \color{blue}{(\frac{18}{19})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{18}{19}b+\frac{5}{16}b-\frac{5}{16}.\frac{18}{19}& \text{Uitwerken } \\ & =b^2+((\frac{-18}{19})+\frac{5}{16})b-(\frac{-90}{304}) & \text{Neem samen} \\ &=b^2-\frac{193}{304}b-(\frac{-90}{304}) & \text{Maak de som} \\ &=b^2-\frac{193}{304}b+\frac{45}{152} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  9. \(\begin{align}(\frac{15}{18}+b)((-2)-a)& =(\color{red}{b}+\color{orange}{\frac{5}{6}}).(\color{green}{-a}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{5}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -ab-2b-\frac{5}{6}a-\frac{5}{6}.2& \text{Uitwerken } \\ & =-ab-2b-\frac{5}{6}a-\frac{10}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-2b-\frac{5}{6}a-\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(b+\frac{2}{4})(b-\frac{3}{14})& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{3}{14}b+\frac{1}{2}b-\frac{1}{2}.\frac{3}{14}& \text{Uitwerken } \\ & =b^2+((\frac{-3}{14})+\frac{1}{2})b-(\frac{-3}{28}) & \text{Neem samen} \\ &=b^2+\frac{4}{14}b-(\frac{-3}{28}) & \text{Maak de som} \\ &=b^2+\frac{2}{7}b+\frac{3}{28} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(a+(-20))(\frac{-2}{14}-p)& =(\color{red}{a}+\color{orange}{(-20)}).(\color{green}{-p}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(-20)} . \color{green}{(-p)} + \color{orange}{(-20)} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{7}a+20p+20.\frac{1}{7}& \text{Uitwerken } \\ & =-ap-\frac{1}{7}a+20p+\frac{20}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a-\frac{20}{13})(\frac{-9}{17}-a)& =(\color{red}{a}+\color{orange}{\frac{-20}{13}}).(\color{green}{-a}+\color{blue}{\frac{-9}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{17})} + \color{orange}{(\frac{-20}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{-20}{13})} . \color{blue}{(\frac{-9}{17})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{9}{17}a+\frac{20}{13}a+\frac{20}{13}.\frac{9}{17}& \text{Uitwerken } \\ & =-a^2+((\frac{-9}{17})+\frac{20}{13})a+(\frac{-180}{221}) & \text{Neem samen} \\ &=-a^2+\frac{223}{221}a+(\frac{-180}{221}) & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-27 18:37:49
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