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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{1}{11})(\frac{-14}{14}+x)& =(\color{red}{a}+\color{orange}{\frac{-1}{11}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1a-\frac{1}{11}x+\frac{1}{11}.1& \text{Uitwerken } \\ & =ax-1a-\frac{1}{11}x+\frac{1}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-16)(\frac{-1}{13}-p)& =(\color{red}{a}+\color{orange}{(-16)}).(\color{green}{-p}+\color{blue}{\frac{-1}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{13})} + \color{orange}{(-16)} . \color{green}{(-p)} + \color{orange}{(-16)} . \color{blue}{(\frac{-1}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{13}a+16p+16.\frac{1}{13}& \text{Uitwerken } \\ & =-ap-\frac{1}{13}a+16p+\frac{16}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-18}{4}+a)(\frac{17}{20}-x)& =(\color{red}{a}+\color{orange}{\frac{-9}{2}}).(\color{green}{-x}+\color{blue}{\frac{17}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{17}{20})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{17}{20})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{17}{20}a+\frac{9}{2}x-\frac{9}{2}.\frac{17}{20}& \text{Uitwerken } \\ & =-ax+\frac{17}{20}a+\frac{9}{2}x-\frac{153}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-20}{8}-b)(q-\frac{11}{6})& =(\color{red}{-b}+\color{orange}{\frac{-5}{2}}).(\color{green}{q}+\color{blue}{\frac{-11}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-11}{6})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-11}{6})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{11}{6}b-\frac{5}{2}q+\frac{5}{2}.\frac{11}{6}& \text{Uitwerken } \\ & =-bq+\frac{11}{6}b-\frac{5}{2}q+\frac{55}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-15}{3}-a)(p+6)& =(\color{red}{-a}+\color{orange}{(-5)}).(\color{green}{p}+\color{blue}{6})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(6)} + \color{orange}{(-5)} . \color{green}{(p)} + \color{orange}{(-5)} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = -ap-6a-5p-5.6& \text{Uitwerken } \\ & =-ap-6a-5p-30 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-17}{12})((-12)+x)& =(\color{red}{a}+\color{orange}{\frac{17}{12}}).(\color{green}{x}+\color{blue}{(-12)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-12)} + \color{orange}{(\frac{17}{12})} . \color{green}{(x)} + \color{orange}{(\frac{17}{12})} . \color{blue}{(-12)}& \text{Boogjes en uitschrijven} \\ & = ax-12a+\frac{17}{12}x-\frac{17}{12}.12& \text{Uitwerken } \\ & =ax-12a+\frac{17}{12}x-\frac{204}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-12a+\frac{17}{12}x-17 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-7}{7})(\frac{9}{7}+q)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{9}{7}p+1q+1.\frac{9}{7}& \text{Uitwerken } \\ & =pq+\frac{9}{7}p+1q+\frac{9}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-6}{17}+b)(\frac{-20}{16}-x)& =(\color{red}{b}+\color{orange}{\frac{-6}{17}}).(\color{green}{-x}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-6}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-6}{17})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{5}{4}b+\frac{6}{17}x+\frac{6}{17}.\frac{5}{4}& \text{Uitwerken } \\ & =-bx-\frac{5}{4}b+\frac{6}{17}x+\frac{30}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{5}{4}b+\frac{6}{17}x+\frac{15}{34} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(p-\frac{-1}{8})(q-\frac{3}{15})& =(\color{red}{p}+\color{orange}{\frac{1}{8}}).(\color{green}{q}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{1}{8})} . \color{green}{(q)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{5}p+\frac{1}{8}q-\frac{1}{8}.\frac{1}{5}& \text{Uitwerken } \\ & =pq-\frac{1}{5}p+\frac{1}{8}q-\frac{1}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{-14}{18}+x)(p-\frac{13}{11})& =(\color{red}{x}+\color{orange}{\frac{-7}{9}}).(\color{green}{p}+\color{blue}{\frac{-13}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{11})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{-13}{11})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{13}{11}x-\frac{7}{9}p+\frac{7}{9}.\frac{13}{11}& \text{Uitwerken } \\ & =px-\frac{13}{11}x-\frac{7}{9}p+\frac{91}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p+\frac{17}{20})(x-\frac{8}{17})& =(\color{red}{p}+\color{orange}{\frac{17}{20}}).(\color{green}{x}+\color{blue}{\frac{-8}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{17})} + \color{orange}{(\frac{17}{20})} . \color{green}{(x)} + \color{orange}{(\frac{17}{20})} . \color{blue}{(\frac{-8}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{8}{17}p+\frac{17}{20}x-\frac{17}{20}.\frac{8}{17}& \text{Uitwerken } \\ & =px-\frac{8}{17}p+\frac{17}{20}x-\frac{136}{340} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{8}{17}p+\frac{17}{20}x-\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(a+\frac{13}{15})(p-\frac{-20}{3})& =(\color{red}{a}+\color{orange}{\frac{13}{15}}).(\color{green}{p}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{13}{15})} . \color{green}{(p)} + \color{orange}{(\frac{13}{15})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{20}{3}a+\frac{13}{15}p+\frac{13}{15}.\frac{20}{3}& \text{Uitwerken } \\ & =ap+\frac{20}{3}a+\frac{13}{15}p+\frac{260}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{20}{3}a+\frac{13}{15}p+\frac{52}{9} & \text{Vereenvoudig} \\\end{align}\)
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