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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{19}{8}-q)(\frac{-15}{12}+b)& =(\color{red}{-q}+\color{orange}{\frac{19}{8}}).(\color{green}{b}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{19}{8})} . \color{green}{(b)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{4}q+\frac{19}{8}b-\frac{19}{8}.\frac{5}{4}& \text{Uitwerken } \\ & =-bq+\frac{5}{4}q+\frac{19}{8}b-\frac{95}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(q+\frac{-12}{13})(a-\frac{20}{9})& =(\color{red}{q}+\color{orange}{\frac{-12}{13}}).(\color{green}{a}+\color{blue}{\frac{-20}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{9})} + \color{orange}{(\frac{-12}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-12}{13})} . \color{blue}{(\frac{-20}{9})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{20}{9}q-\frac{12}{13}a+\frac{12}{13}.\frac{20}{9}& \text{Uitwerken } \\ & =aq-\frac{20}{9}q-\frac{12}{13}a+\frac{240}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{20}{9}q-\frac{12}{13}a+\frac{80}{39} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(a+\frac{-17}{4})(\frac{-11}{4}-x)& =(\color{red}{a}+\color{orange}{\frac{-17}{4}}).(\color{green}{-x}+\color{blue}{\frac{-11}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{4})} + \color{orange}{(\frac{-17}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-17}{4})} . \color{blue}{(\frac{-11}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{11}{4}a+\frac{17}{4}x+\frac{17}{4}.\frac{11}{4}& \text{Uitwerken } \\ & =-ax-\frac{11}{4}a+\frac{17}{4}x+\frac{187}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a-\frac{9}{8})(b-\frac{-3}{18})& =(\color{red}{a}+\color{orange}{\frac{-9}{8}}).(\color{green}{b}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{6}a-\frac{9}{8}b-\frac{9}{8}.\frac{1}{6}& \text{Uitwerken } \\ & =ab+\frac{1}{6}a-\frac{9}{8}b-\frac{9}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{1}{6}a-\frac{9}{8}b-\frac{3}{16} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p+\frac{-14}{4})(\frac{20}{7}+b)& =(\color{red}{p}+\color{orange}{\frac{-7}{2}}).(\color{green}{b}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{20}{7}p-\frac{7}{2}b-\frac{7}{2}.\frac{20}{7}& \text{Uitwerken } \\ & =bp+\frac{20}{7}p-\frac{7}{2}b-\frac{140}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{20}{7}p-\frac{7}{2}b-10 & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{11}{3}-x)(x+\frac{-11}{19})& =(\color{red}{-x}+\color{orange}{\frac{11}{3}}).(\color{green}{x}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(\frac{11}{3})} . \color{green}{(x)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{11}{19}x+\frac{11}{3}x-\frac{11}{3}.\frac{11}{19}& \text{Uitwerken } \\ & =-x^2+(\frac{11}{19}+\frac{11}{3})x-\frac{121}{57} & \text{Neem samen} \\ &=-x^2+\frac{242}{57}x-\frac{121}{57} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{9}{2}-q)(\frac{-19}{16}-b)& =(\color{red}{-q}+\color{orange}{\frac{9}{2}}).(\color{green}{-b}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(\frac{9}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{19}{16}q-\frac{9}{2}b-\frac{9}{2}.\frac{19}{16}& \text{Uitwerken } \\ & =bq+\frac{19}{16}q-\frac{9}{2}b-\frac{171}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p-\frac{-1}{2})(b+\frac{18}{13})& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{18}{13}p+\frac{1}{2}b+\frac{1}{2}.\frac{18}{13}& \text{Uitwerken } \\ & =bp+\frac{18}{13}p+\frac{1}{2}b+\frac{18}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{18}{13}p+\frac{1}{2}b+\frac{9}{13} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b-\frac{19}{15})(p+(-16))& =(\color{red}{b}+\color{orange}{\frac{-19}{15}}).(\color{green}{p}+\color{blue}{(-16)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-16)} + \color{orange}{(\frac{-19}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{15})} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = bp-16b-\frac{19}{15}p+\frac{19}{15}.16& \text{Uitwerken } \\ & =bp-16b-\frac{19}{15}p+\frac{304}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{18}{13}-a)(\frac{3}{20}-p)& =(\color{red}{-a}+\color{orange}{\frac{18}{13}}).(\color{green}{-p}+\color{blue}{\frac{3}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{20})} + \color{orange}{(\frac{18}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{18}{13})} . \color{blue}{(\frac{3}{20})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{20}a-\frac{18}{13}p+\frac{18}{13}.\frac{3}{20}& \text{Uitwerken } \\ & =ap-\frac{3}{20}a-\frac{18}{13}p+\frac{54}{260} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{3}{20}a-\frac{18}{13}p+\frac{27}{130} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a+\frac{6}{5})(x+\frac{-19}{14})& =(\color{red}{a}+\color{orange}{\frac{6}{5}}).(\color{green}{x}+\color{blue}{\frac{-19}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{14})} + \color{orange}{(\frac{6}{5})} . \color{green}{(x)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-19}{14})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{19}{14}a+\frac{6}{5}x-\frac{6}{5}.\frac{19}{14}& \text{Uitwerken } \\ & =ax-\frac{19}{14}a+\frac{6}{5}x-\frac{114}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{19}{14}a+\frac{6}{5}x-\frac{57}{35} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(a+\frac{1}{20})(\frac{-16}{2}+q)& =(\color{red}{a}+\color{orange}{\frac{1}{20}}).(\color{green}{q}+\color{blue}{(-8)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-8)} + \color{orange}{(\frac{1}{20})} . \color{green}{(q)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = aq-8a+\frac{1}{20}q-\frac{1}{20}.8& \text{Uitwerken } \\ & =aq-8a+\frac{1}{20}q-\frac{8}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-8a+\frac{1}{20}q-\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
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