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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-3}{16}-x)(p+\frac{14}{20})& =(\color{red}{-x}+\color{orange}{\frac{-3}{16}}).(\color{green}{p}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{-3}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{16})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{7}{10}x-\frac{3}{16}p-\frac{3}{16}.\frac{7}{10}& \text{Uitwerken } \\ & =-px-\frac{7}{10}x-\frac{3}{16}p-\frac{21}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x+\frac{12}{4})(\frac{-16}{2}-b)& =(\color{red}{x}+\color{orange}{3}).(\color{green}{-b}+\color{blue}{(-8)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(-8)} + \color{orange}{(3)} . \color{green}{(-b)} + \color{orange}{(3)} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = -bx-8x-3b-3.8& \text{Uitwerken } \\ & =-bx-8x-3b-24 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(a+\frac{19}{11})(\frac{-4}{15}+b)& =(\color{red}{a}+\color{orange}{\frac{19}{11}}).(\color{green}{b}+\color{blue}{\frac{-4}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{15})} + \color{orange}{(\frac{19}{11})} . \color{green}{(b)} + \color{orange}{(\frac{19}{11})} . \color{blue}{(\frac{-4}{15})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{4}{15}a+\frac{19}{11}b-\frac{19}{11}.\frac{4}{15}& \text{Uitwerken } \\ & =ab-\frac{4}{15}a+\frac{19}{11}b-\frac{76}{165} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p-\frac{-16}{9})(\frac{-1}{14}+b)& =(\color{red}{p}+\color{orange}{\frac{16}{9}}).(\color{green}{b}+\color{blue}{\frac{-1}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{14})} + \color{orange}{(\frac{16}{9})} . \color{green}{(b)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(\frac{-1}{14})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{14}p+\frac{16}{9}b-\frac{16}{9}.\frac{1}{14}& \text{Uitwerken } \\ & =bp-\frac{1}{14}p+\frac{16}{9}b-\frac{16}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{1}{14}p+\frac{16}{9}b-\frac{8}{63} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(x-\frac{-7}{20})(\frac{-8}{19}+p)& =(\color{red}{x}+\color{orange}{\frac{7}{20}}).(\color{green}{p}+\color{blue}{\frac{-8}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{19})} + \color{orange}{(\frac{7}{20})} . \color{green}{(p)} + \color{orange}{(\frac{7}{20})} . \color{blue}{(\frac{-8}{19})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{8}{19}x+\frac{7}{20}p-\frac{7}{20}.\frac{8}{19}& \text{Uitwerken } \\ & =px-\frac{8}{19}x+\frac{7}{20}p-\frac{56}{380} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{8}{19}x+\frac{7}{20}p-\frac{14}{95} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(p-\frac{-6}{9})(q+(-10))& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{(-10)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-10)} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = pq-10p+\frac{2}{3}q-\frac{2}{3}.10& \text{Uitwerken } \\ & =pq-10p+\frac{2}{3}q-\frac{20}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(q+\frac{-14}{16})(\frac{-7}{2}-x)& =(\color{red}{q}+\color{orange}{\frac{-7}{8}}).(\color{green}{-x}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{7}{2}q+\frac{7}{8}x+\frac{7}{8}.\frac{7}{2}& \text{Uitwerken } \\ & =-qx-\frac{7}{2}q+\frac{7}{8}x+\frac{49}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-3}{5}-b)(x-\frac{4}{5})& =(\color{red}{-b}+\color{orange}{\frac{-3}{5}}).(\color{green}{x}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{4}{5}b-\frac{3}{5}x+\frac{3}{5}.\frac{4}{5}& \text{Uitwerken } \\ & =-bx+\frac{4}{5}b-\frac{3}{5}x+\frac{12}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{19}{2}-q)(b-\frac{5}{4})& =(\color{red}{-q}+\color{orange}{\frac{19}{2}}).(\color{green}{b}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{19}{2})} . \color{green}{(b)} + \color{orange}{(\frac{19}{2})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{4}q+\frac{19}{2}b-\frac{19}{2}.\frac{5}{4}& \text{Uitwerken } \\ & =-bq+\frac{5}{4}q+\frac{19}{2}b-\frac{95}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b-\frac{-6}{14})(q+\frac{-14}{6})& =(\color{red}{b}+\color{orange}{\frac{3}{7}}).(\color{green}{q}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{3}{7})} . \color{green}{(q)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{3}b+\frac{3}{7}q-\frac{3}{7}.\frac{7}{3}& \text{Uitwerken } \\ & =bq-\frac{7}{3}b+\frac{3}{7}q-\frac{21}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{7}{3}b+\frac{3}{7}q-1 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x-\frac{-3}{13})(b+\frac{5}{17})& =(\color{red}{x}+\color{orange}{\frac{3}{13}}).(\color{green}{b}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(\frac{3}{13})} . \color{green}{(b)} + \color{orange}{(\frac{3}{13})} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{17}x+\frac{3}{13}b+\frac{3}{13}.\frac{5}{17}& \text{Uitwerken } \\ & =bx+\frac{5}{17}x+\frac{3}{13}b+\frac{15}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{20}{19}+b)(q-\frac{1}{6})& =(\color{red}{b}+\color{orange}{\frac{20}{19}}).(\color{green}{q}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{20}{19})} . \color{green}{(q)} + \color{orange}{(\frac{20}{19})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{6}b+\frac{20}{19}q-\frac{20}{19}.\frac{1}{6}& \text{Uitwerken } \\ & =bq-\frac{1}{6}b+\frac{20}{19}q-\frac{20}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{1}{6}b+\frac{20}{19}q-\frac{10}{57} & \text{Vereenvoudig} \\\end{align}\)
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