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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(4+b)(\frac{-1}{8}-q)& =(\color{red}{b}+\color{orange}{4}).(\color{green}{-q}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(4)} . \color{green}{(-q)} + \color{orange}{(4)} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{8}b-4q-4.\frac{1}{8}& \text{Uitwerken } \\ & =-bq-\frac{1}{8}b-4q-\frac{4}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{1}{8}b-4q-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{20}{9}+b)(\frac{-10}{20}-b)& =(\color{red}{b}+\color{orange}{\frac{20}{9}}).(\color{green}{-b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{20}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{1}{2}b-\frac{20}{9}b-\frac{20}{9}.\frac{1}{2}& \text{Uitwerken } \\ & =-b^2+((\frac{-1}{2})+(\frac{-20}{9}))b-\frac{20}{18} & \text{Neem samen} \\ &=-b^2-\frac{49}{18}b-\frac{20}{18} & \text{Maak de som} \\ &=-b^2-\frac{49}{18}b-\frac{10}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(p-\frac{-12}{14})(b-\frac{-16}{12})& =(\color{red}{p}+\color{orange}{\frac{6}{7}}).(\color{green}{b}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{6}{7})} . \color{green}{(b)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{4}{3}p+\frac{6}{7}b+\frac{6}{7}.\frac{4}{3}& \text{Uitwerken } \\ & =bp+\frac{4}{3}p+\frac{6}{7}b+\frac{24}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{4}{3}p+\frac{6}{7}b+\frac{8}{7} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x+\frac{20}{19})(\frac{6}{11}-p)& =(\color{red}{x}+\color{orange}{\frac{20}{19}}).(\color{green}{-p}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(\frac{20}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{20}{19})} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{6}{11}x-\frac{20}{19}p+\frac{20}{19}.\frac{6}{11}& \text{Uitwerken } \\ & =-px+\frac{6}{11}x-\frac{20}{19}p+\frac{120}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(q+\frac{-20}{3})(\frac{12}{17}+x)& =(\color{red}{q}+\color{orange}{\frac{-20}{3}}).(\color{green}{x}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{-20}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{12}{17}q-\frac{20}{3}x-\frac{20}{3}.\frac{12}{17}& \text{Uitwerken } \\ & =qx+\frac{12}{17}q-\frac{20}{3}x-\frac{240}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{12}{17}q-\frac{20}{3}x-\frac{80}{17} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-11}{3}-x)(b+\frac{13}{4})& =(\color{red}{-x}+\color{orange}{\frac{-11}{3}}).(\color{green}{b}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{-11}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{3})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{13}{4}x-\frac{11}{3}b-\frac{11}{3}.\frac{13}{4}& \text{Uitwerken } \\ & =-bx-\frac{13}{4}x-\frac{11}{3}b-\frac{143}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-2}{3}+q)(\frac{14}{17}-p)& =(\color{red}{q}+\color{orange}{\frac{-2}{3}}).(\color{green}{-p}+\color{blue}{\frac{14}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{14}{17})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{14}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{14}{17}q+\frac{2}{3}p-\frac{2}{3}.\frac{14}{17}& \text{Uitwerken } \\ & =-pq+\frac{14}{17}q+\frac{2}{3}p-\frac{28}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-20}{9})(\frac{17}{7}-p)& =(\color{red}{x}+\color{orange}{\frac{20}{9}}).(\color{green}{-p}+\color{blue}{\frac{17}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{17}{7})} + \color{orange}{(\frac{20}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{17}{7})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{17}{7}x-\frac{20}{9}p+\frac{20}{9}.\frac{17}{7}& \text{Uitwerken } \\ & =-px+\frac{17}{7}x-\frac{20}{9}p+\frac{340}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{-8}{2})(\frac{11}{2}+x)& =(\color{red}{b}+\color{orange}{4}).(\color{green}{x}+\color{blue}{\frac{11}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{11}{2})} + \color{orange}{(4)} . \color{green}{(x)} + \color{orange}{(4)} . \color{blue}{(\frac{11}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{2}b+4x+4.\frac{11}{2}& \text{Uitwerken } \\ & =bx+\frac{11}{2}b+4x+\frac{44}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{11}{2}b+4x+22 & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-9}{16}-a)(q-\frac{1}{19})& =(\color{red}{-a}+\color{orange}{\frac{-9}{16}}).(\color{green}{q}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{-9}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{19}a-\frac{9}{16}q+\frac{9}{16}.\frac{1}{19}& \text{Uitwerken } \\ & =-aq+\frac{1}{19}a-\frac{9}{16}q+\frac{9}{304} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q-\frac{-9}{19})(\frac{15}{4}+q)& =(\color{red}{q}+\color{orange}{\frac{9}{19}}).(\color{green}{q}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{9}{19})} . \color{green}{(q)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{15}{4}q+\frac{9}{19}q+\frac{9}{19}.\frac{15}{4}& \text{Uitwerken } \\ & =q^2+(\frac{15}{4}+\frac{9}{19})q+\frac{135}{76} & \text{Neem samen} \\ &=q^2+\frac{321}{76}q+\frac{135}{76} & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(b-\frac{19}{11})(a+\frac{2}{19})& =(\color{red}{b}+\color{orange}{\frac{-19}{11}}).(\color{green}{a}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{19}b-\frac{19}{11}a-\frac{19}{11}.\frac{2}{19}& \text{Uitwerken } \\ & =ab+\frac{2}{19}b-\frac{19}{11}a-\frac{38}{209} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{2}{19}b-\frac{19}{11}a-\frac{2}{11} & \text{Vereenvoudig} \\\end{align}\)
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