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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{-8}{18})(\frac{-1}{14}-q)& =(\color{red}{a}+\color{orange}{\frac{-4}{9}}).(\color{green}{-q}+\color{blue}{\frac{-1}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{14})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{-1}{14})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{14}a+\frac{4}{9}q+\frac{4}{9}.\frac{1}{14}& \text{Uitwerken } \\ & =-aq-\frac{1}{14}a+\frac{4}{9}q+\frac{4}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{1}{14}a+\frac{4}{9}q+\frac{2}{63} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a-\frac{2}{10})(\frac{12}{14}-a)& =(\color{red}{a}+\color{orange}{\frac{-1}{5}}).(\color{green}{-a}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{6}{7}a+\frac{1}{5}a-\frac{1}{5}.\frac{6}{7}& \text{Uitwerken } \\ & =-a^2+(\frac{6}{7}+\frac{1}{5})a-\frac{6}{35} & \text{Neem samen} \\ &=-a^2+\frac{37}{35}a-\frac{6}{35} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{17}{17}-b)(a-\frac{-18}{13})& =(\color{red}{-b}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{18}{13}b+1a+1.\frac{18}{13}& \text{Uitwerken } \\ & =-ab-\frac{18}{13}b+1a+\frac{18}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{12}{15}+p)(\frac{-9}{3}+b)& =(\color{red}{p}+\color{orange}{\frac{4}{5}}).(\color{green}{b}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-3)} + \color{orange}{(\frac{4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bp-3p+\frac{4}{5}b-\frac{4}{5}.3& \text{Uitwerken } \\ & =bp-3p+\frac{4}{5}b-\frac{12}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{2}{14}-b)(p-\frac{18}{6})& =(\color{red}{-b}+\color{orange}{\frac{1}{7}}).(\color{green}{p}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(-3)} + \color{orange}{(\frac{1}{7})} . \color{green}{(p)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -bp+3b+\frac{1}{7}p-\frac{1}{7}.3& \text{Uitwerken } \\ & =-bp+3b+\frac{1}{7}p-\frac{3}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(b+\frac{10}{6})(\frac{-5}{6}-x)& =(\color{red}{b}+\color{orange}{\frac{5}{3}}).(\color{green}{-x}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{5}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{6}b-\frac{5}{3}x-\frac{5}{3}.\frac{5}{6}& \text{Uitwerken } \\ & =-bx-\frac{5}{6}b-\frac{5}{3}x-\frac{25}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a+\frac{11}{3})(\frac{-6}{10}+p)& =(\color{red}{a}+\color{orange}{\frac{11}{3}}).(\color{green}{p}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{11}{3})} . \color{green}{(p)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{5}a+\frac{11}{3}p-\frac{11}{3}.\frac{3}{5}& \text{Uitwerken } \\ & =ap-\frac{3}{5}a+\frac{11}{3}p-\frac{33}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{3}{5}a+\frac{11}{3}p-\frac{11}{5} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-4}{6}-x)(q+\frac{10}{3})& =(\color{red}{-x}+\color{orange}{\frac{-2}{3}}).(\color{green}{q}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{10}{3}x-\frac{2}{3}q-\frac{2}{3}.\frac{10}{3}& \text{Uitwerken } \\ & =-qx-\frac{10}{3}x-\frac{2}{3}q-\frac{20}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-15}{7}-q)(\frac{-15}{19}-x)& =(\color{red}{-q}+\color{orange}{\frac{-15}{7}}).(\color{green}{-x}+\color{blue}{\frac{-15}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{-15}{19})} + \color{orange}{(\frac{-15}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{-15}{7})} . \color{blue}{(\frac{-15}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{15}{19}q+\frac{15}{7}x+\frac{15}{7}.\frac{15}{19}& \text{Uitwerken } \\ & =qx+\frac{15}{19}q+\frac{15}{7}x+\frac{225}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b+\frac{-19}{12})(p-\frac{11}{19})& =(\color{red}{b}+\color{orange}{\frac{-19}{12}}).(\color{green}{p}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{11}{19}b-\frac{19}{12}p+\frac{19}{12}.\frac{11}{19}& \text{Uitwerken } \\ & =bp-\frac{11}{19}b-\frac{19}{12}p+\frac{209}{228} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{11}{19}b-\frac{19}{12}p+\frac{11}{12} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a+\frac{18}{19})(\frac{-8}{13}+q)& =(\color{red}{a}+\color{orange}{\frac{18}{19}}).(\color{green}{q}+\color{blue}{\frac{-8}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-8}{13})} + \color{orange}{(\frac{18}{19})} . \color{green}{(q)} + \color{orange}{(\frac{18}{19})} . \color{blue}{(\frac{-8}{13})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{8}{13}a+\frac{18}{19}q-\frac{18}{19}.\frac{8}{13}& \text{Uitwerken } \\ & =aq-\frac{8}{13}a+\frac{18}{19}q-\frac{144}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-14}{9}-x)(\frac{-7}{13}+x)& =(\color{red}{-x}+\color{orange}{\frac{-14}{9}}).(\color{green}{x}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(\frac{-14}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{9})} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{7}{13}x-\frac{14}{9}x+\frac{14}{9}.\frac{7}{13}& \text{Uitwerken } \\ & =-x^2+(\frac{7}{13}+(\frac{-14}{9}))x+(\frac{-98}{117}) & \text{Neem samen} \\ &=-x^2-\frac{119}{117}x+(\frac{-98}{117}) & \text{Maak de som} \\\end{align}\)
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