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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-13}{12}+x)(b+\frac{18}{10})& =(\color{red}{x}+\color{orange}{\frac{-13}{12}}).(\color{green}{b}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(\frac{-13}{12})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{12})} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{9}{5}x-\frac{13}{12}b-\frac{13}{12}.\frac{9}{5}& \text{Uitwerken } \\ & =bx+\frac{9}{5}x-\frac{13}{12}b-\frac{117}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{9}{5}x-\frac{13}{12}b-\frac{39}{20} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(b+\frac{-3}{2})(\frac{16}{20}-x)& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{-x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{4}{5}b+\frac{3}{2}x-\frac{3}{2}.\frac{4}{5}& \text{Uitwerken } \\ & =-bx+\frac{4}{5}b+\frac{3}{2}x-\frac{12}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{4}{5}b+\frac{3}{2}x-\frac{6}{5} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b+\frac{-14}{19})(p-\frac{13}{2})& =(\color{red}{b}+\color{orange}{\frac{-14}{19}}).(\color{green}{p}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(\frac{-14}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-14}{19})} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{13}{2}b-\frac{14}{19}p+\frac{14}{19}.\frac{13}{2}& \text{Uitwerken } \\ & =bp-\frac{13}{2}b-\frac{14}{19}p+\frac{182}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{13}{2}b-\frac{14}{19}p+\frac{91}{19} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p-16)(a+\frac{-11}{20})& =(\color{red}{p}+\color{orange}{(-16)}).(\color{green}{a}+\color{blue}{\frac{-11}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{20})} + \color{orange}{(-16)} . \color{green}{(a)} + \color{orange}{(-16)} . \color{blue}{(\frac{-11}{20})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{11}{20}p-16a+16.\frac{11}{20}& \text{Uitwerken } \\ & =ap-\frac{11}{20}p-16a+\frac{176}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{11}{20}p-16a+\frac{44}{5} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-15}{15}-b)(q+\frac{-4}{20})& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{5}b-1q+1.\frac{1}{5}& \text{Uitwerken } \\ & =-bq+\frac{1}{5}b-1q+\frac{1}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{4}{8}-p)(\frac{-15}{11}-p)& =(\color{red}{-p}+\color{orange}{\frac{1}{2}}).(\color{green}{-p}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{15}{11}p-\frac{1}{2}p-\frac{1}{2}.\frac{15}{11}& \text{Uitwerken } \\ & =p^2+(\frac{15}{11}+(\frac{-1}{2}))p-(\frac{-15}{22}) & \text{Neem samen} \\ &=p^2+\frac{19}{22}p-(\frac{-15}{22}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(x+\frac{19}{9})(\frac{-12}{13}+q)& =(\color{red}{x}+\color{orange}{\frac{19}{9}}).(\color{green}{q}+\color{blue}{\frac{-12}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-12}{13})} + \color{orange}{(\frac{19}{9})} . \color{green}{(q)} + \color{orange}{(\frac{19}{9})} . \color{blue}{(\frac{-12}{13})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{12}{13}x+\frac{19}{9}q-\frac{19}{9}.\frac{12}{13}& \text{Uitwerken } \\ & =qx-\frac{12}{13}x+\frac{19}{9}q-\frac{228}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{12}{13}x+\frac{19}{9}q-\frac{76}{39} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-5}{18}+q)(\frac{4}{5}+b)& =(\color{red}{q}+\color{orange}{\frac{-5}{18}}).(\color{green}{b}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-5}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{4}{5}q-\frac{5}{18}b-\frac{5}{18}.\frac{4}{5}& \text{Uitwerken } \\ & =bq+\frac{4}{5}q-\frac{5}{18}b-\frac{20}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{4}{5}q-\frac{5}{18}b-\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{-11}{6}-p)(q+\frac{3}{17})& =(\color{red}{-p}+\color{orange}{\frac{-11}{6}}).(\color{green}{q}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{-11}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{6})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{3}{17}p-\frac{11}{6}q-\frac{11}{6}.\frac{3}{17}& \text{Uitwerken } \\ & =-pq-\frac{3}{17}p-\frac{11}{6}q-\frac{33}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{3}{17}p-\frac{11}{6}q-\frac{11}{34} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{3}{10}-a)(q-12)& =(\color{red}{-a}+\color{orange}{\frac{3}{10}}).(\color{green}{q}+\color{blue}{(-12)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(-12)} + \color{orange}{(\frac{3}{10})} . \color{green}{(q)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(-12)}& \text{Boogjes en uitschrijven} \\ & = -aq+12a+\frac{3}{10}q-\frac{3}{10}.12& \text{Uitwerken } \\ & =-aq+12a+\frac{3}{10}q-\frac{36}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+12a+\frac{3}{10}q-\frac{18}{5} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x+\frac{-18}{17})(x-\frac{-14}{11})& =(\color{red}{x}+\color{orange}{\frac{-18}{17}}).(\color{green}{x}+\color{blue}{\frac{14}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{14}{11})} + \color{orange}{(\frac{-18}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-18}{17})} . \color{blue}{(\frac{14}{11})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{14}{11}x-\frac{18}{17}x-\frac{18}{17}.\frac{14}{11}& \text{Uitwerken } \\ & =x^2+(\frac{14}{11}+(\frac{-18}{17}))x-(\frac{-252}{187}) & \text{Neem samen} \\ &=x^2+\frac{40}{187}x-(\frac{-252}{187}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(q+\frac{11}{7})(\frac{-16}{18}+b)& =(\color{red}{q}+\color{orange}{\frac{11}{7}}).(\color{green}{b}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{11}{7})} . \color{green}{(b)} + \color{orange}{(\frac{11}{7})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{8}{9}q+\frac{11}{7}b-\frac{11}{7}.\frac{8}{9}& \text{Uitwerken } \\ & =bq-\frac{8}{9}q+\frac{11}{7}b-\frac{88}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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