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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-17}{6}-x)(\frac{12}{7}-b)& =(\color{red}{-x}+\color{orange}{\frac{-17}{6}}).(\color{green}{-b}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(\frac{-17}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{-17}{6})} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{12}{7}x+\frac{17}{6}b-\frac{17}{6}.\frac{12}{7}& \text{Uitwerken } \\ & =bx-\frac{12}{7}x+\frac{17}{6}b-\frac{204}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{12}{7}x+\frac{17}{6}b-\frac{34}{7} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(q+\frac{-18}{6})(\frac{6}{13}-p)& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{-p}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(-3)} . \color{green}{(-p)} + \color{orange}{(-3)} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{6}{13}q+3p-3.\frac{6}{13}& \text{Uitwerken } \\ & =-pq+\frac{6}{13}q+3p-\frac{18}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{16}{8}+p)(\frac{18}{6}+b)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bp+3p+2b+2.3& \text{Uitwerken } \\ & =bp+3p+2b+6 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{5}{10}+x)(p-\frac{-18}{16})& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{9}{8}x+\frac{1}{2}p+\frac{1}{2}.\frac{9}{8}& \text{Uitwerken } \\ & =px+\frac{9}{8}x+\frac{1}{2}p+\frac{9}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(p-\frac{20}{11})(x-\frac{13}{13})& =(\color{red}{p}+\color{orange}{\frac{-20}{11}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-20}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1p-\frac{20}{11}x+\frac{20}{11}.1& \text{Uitwerken } \\ & =px-1p-\frac{20}{11}x+\frac{20}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(x-\frac{19}{3})(\frac{18}{4}+p)& =(\color{red}{x}+\color{orange}{\frac{-19}{3}}).(\color{green}{p}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-19}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{3})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{9}{2}x-\frac{19}{3}p-\frac{19}{3}.\frac{9}{2}& \text{Uitwerken } \\ & =px+\frac{9}{2}x-\frac{19}{3}p-\frac{171}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{9}{2}x-\frac{19}{3}p-\frac{57}{2} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{5}{7}-x)(2-b)& =(\color{red}{-x}+\color{orange}{\frac{5}{7}}).(\color{green}{-b}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(2)} + \color{orange}{(\frac{5}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bx-2x-\frac{5}{7}b+\frac{5}{7}.2& \text{Uitwerken } \\ & =bx-2x-\frac{5}{7}b+\frac{10}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{20}{19}+q)(\frac{16}{3}+x)& =(\color{red}{q}+\color{orange}{\frac{20}{19}}).(\color{green}{x}+\color{blue}{\frac{16}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{16}{3})} + \color{orange}{(\frac{20}{19})} . \color{green}{(x)} + \color{orange}{(\frac{20}{19})} . \color{blue}{(\frac{16}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{16}{3}q+\frac{20}{19}x+\frac{20}{19}.\frac{16}{3}& \text{Uitwerken } \\ & =qx+\frac{16}{3}q+\frac{20}{19}x+\frac{320}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-19}{9}+x)(q+\frac{-2}{2})& =(\color{red}{x}+\color{orange}{\frac{-19}{9}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-19}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx-1x-\frac{19}{9}q+\frac{19}{9}.1& \text{Uitwerken } \\ & =qx-1x-\frac{19}{9}q+\frac{19}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-11}{3}+p)(\frac{17}{13}+a)& =(\color{red}{p}+\color{orange}{\frac{-11}{3}}).(\color{green}{a}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{17}{13})} + \color{orange}{(\frac{-11}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{3})} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{17}{13}p-\frac{11}{3}a-\frac{11}{3}.\frac{17}{13}& \text{Uitwerken } \\ & =ap+\frac{17}{13}p-\frac{11}{3}a-\frac{187}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a+\frac{-16}{16})(q-\frac{-6}{9})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{2}{3}a-1q-1.\frac{2}{3}& \text{Uitwerken } \\ & =aq+\frac{2}{3}a-1q-\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{19}{10}+p)(\frac{-17}{13}-a)& =(\color{red}{p}+\color{orange}{\frac{19}{10}}).(\color{green}{-a}+\color{blue}{\frac{-17}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{13})} + \color{orange}{(\frac{19}{10})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{10})} . \color{blue}{(\frac{-17}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{17}{13}p-\frac{19}{10}a-\frac{19}{10}.\frac{17}{13}& \text{Uitwerken } \\ & =-ap-\frac{17}{13}p-\frac{19}{10}a-\frac{323}{130} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-15 15:31:06
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