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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{9}{14}+q)(\frac{-18}{4}-q)& =(\color{red}{q}+\color{orange}{\frac{9}{14}}).(\color{green}{-q}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{9}{14})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{9}{2}q-\frac{9}{14}q-\frac{9}{14}.\frac{9}{2}& \text{Uitwerken } \\ & =-q^2+((\frac{-9}{2})+(\frac{-9}{14}))q-\frac{81}{28} & \text{Neem samen} \\ &=-q^2-\frac{72}{14}q-\frac{81}{28} & \text{Maak de som} \\ &=-q^2-\frac{36}{7}q-\frac{81}{28} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{7}-a)(q+\frac{-10}{3})& =(\color{red}{-a}+\color{orange}{\frac{8}{7}}).(\color{green}{q}+\color{blue}{\frac{-10}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-10}{3})} + \color{orange}{(\frac{8}{7})} . \color{green}{(q)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-10}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{10}{3}a+\frac{8}{7}q-\frac{8}{7}.\frac{10}{3}& \text{Uitwerken } \\ & =-aq+\frac{10}{3}a+\frac{8}{7}q-\frac{80}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{6}{6}-a)(p-\frac{-20}{11})& =(\color{red}{-a}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{20}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{20}{11})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{20}{11})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{20}{11}a+1p+1.\frac{20}{11}& \text{Uitwerken } \\ & =-ap-\frac{20}{11}a+1p+\frac{20}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{4}{6}-x)(a-\frac{11}{9})& =(\color{red}{-x}+\color{orange}{\frac{2}{3}}).(\color{green}{a}+\color{blue}{\frac{-11}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-11}{9})} + \color{orange}{(\frac{2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-11}{9})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{11}{9}x+\frac{2}{3}a-\frac{2}{3}.\frac{11}{9}& \text{Uitwerken } \\ & =-ax+\frac{11}{9}x+\frac{2}{3}a-\frac{22}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-5}{19}+a)(\frac{3}{19}-q)& =(\color{red}{a}+\color{orange}{\frac{-5}{19}}).(\color{green}{-q}+\color{blue}{\frac{3}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{3}{19})} + \color{orange}{(\frac{-5}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(\frac{3}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{3}{19}a+\frac{5}{19}q-\frac{5}{19}.\frac{3}{19}& \text{Uitwerken } \\ & =-aq+\frac{3}{19}a+\frac{5}{19}q-\frac{15}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p+\frac{-16}{17})(\frac{1}{3}-p)& =(\color{red}{p}+\color{orange}{\frac{-16}{17}}).(\color{green}{-p}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-16}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-16}{17})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{1}{3}p+\frac{16}{17}p-\frac{16}{17}.\frac{1}{3}& \text{Uitwerken } \\ & =-p^2+(\frac{1}{3}+\frac{16}{17})p-\frac{16}{51} & \text{Neem samen} \\ &=-p^2+\frac{65}{51}p-\frac{16}{51} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(x-\frac{-12}{14})(\frac{-14}{16}+q)& =(\color{red}{x}+\color{orange}{\frac{6}{7}}).(\color{green}{q}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{6}{7})} . \color{green}{(q)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{7}{8}x+\frac{6}{7}q-\frac{6}{7}.\frac{7}{8}& \text{Uitwerken } \\ & =qx-\frac{7}{8}x+\frac{6}{7}q-\frac{42}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{7}{8}x+\frac{6}{7}q-\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-12}{3}-a)(q-\frac{-2}{20})& =(\color{red}{-a}+\color{orange}{(-4)}).(\color{green}{q}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(-4)} . \color{green}{(q)} + \color{orange}{(-4)} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{10}a-4q-4.\frac{1}{10}& \text{Uitwerken } \\ & =-aq-\frac{1}{10}a-4q-\frac{4}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{1}{10}a-4q-\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-16}{10}-b)(\frac{-19}{9}+b)& =(\color{red}{-b}+\color{orange}{\frac{-8}{5}}).(\color{green}{b}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{19}{9}b-\frac{8}{5}b+\frac{8}{5}.\frac{19}{9}& \text{Uitwerken } \\ & =-b^2+(\frac{19}{9}+(\frac{-8}{5}))b+(\frac{-152}{45}) & \text{Neem samen} \\ &=-b^2+\frac{23}{45}b+(\frac{-152}{45}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(\frac{6}{14}-b)(p-3)& =(\color{red}{-b}+\color{orange}{\frac{3}{7}}).(\color{green}{p}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(-3)} + \color{orange}{(\frac{3}{7})} . \color{green}{(p)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -bp+3b+\frac{3}{7}p-\frac{3}{7}.3& \text{Uitwerken } \\ & =-bp+3b+\frac{3}{7}p-\frac{9}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q+\frac{-4}{7})(\frac{-6}{9}-q)& =(\color{red}{q}+\color{orange}{\frac{-4}{7}}).(\color{green}{-q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{2}{3}q+\frac{4}{7}q+\frac{4}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =-q^2+((\frac{-2}{3})+\frac{4}{7})q+(\frac{-8}{21}) & \text{Neem samen} \\ &=-q^2-\frac{2}{21}q+(\frac{-8}{21}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(a-\frac{-15}{19})(\frac{-4}{18}+x)& =(\color{red}{a}+\color{orange}{\frac{15}{19}}).(\color{green}{x}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{15}{19})} . \color{green}{(x)} + \color{orange}{(\frac{15}{19})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{2}{9}a+\frac{15}{19}x-\frac{15}{19}.\frac{2}{9}& \text{Uitwerken } \\ & =ax-\frac{2}{9}a+\frac{15}{19}x-\frac{30}{171} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{2}{9}a+\frac{15}{19}x-\frac{10}{57} & \text{Vereenvoudig} \\\end{align}\)
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