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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{13}{10})(\frac{-3}{20}+x)& =(\color{red}{q}+\color{orange}{\frac{-13}{10}}).(\color{green}{x}+\color{blue}{\frac{-3}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{20})} + \color{orange}{(\frac{-13}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(\frac{-3}{20})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{3}{20}q-\frac{13}{10}x+\frac{13}{10}.\frac{3}{20}& \text{Uitwerken } \\ & =qx-\frac{3}{20}q-\frac{13}{10}x+\frac{39}{200} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(a-6)(a-\frac{4}{13})& =(\color{red}{a}+\color{orange}{(-6)}).(\color{green}{a}+\color{blue}{\frac{-4}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{13})} + \color{orange}{(-6)} . \color{green}{(a)} + \color{orange}{(-6)} . \color{blue}{(\frac{-4}{13})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{4}{13}a-6a+6.\frac{4}{13}& \text{Uitwerken } \\ & =a^2+((\frac{-4}{13})+(-6))a+\frac{24}{13} & \text{Neem samen} \\ &=a^2-\frac{82}{13}a+\frac{24}{13} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{13}{2}+a)(\frac{-4}{16}-p)& =(\color{red}{a}+\color{orange}{\frac{13}{2}}).(\color{green}{-p}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{13}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{13}{2})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{4}a-\frac{13}{2}p-\frac{13}{2}.\frac{1}{4}& \text{Uitwerken } \\ & =-ap-\frac{1}{4}a-\frac{13}{2}p-\frac{13}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-5}{14}+a)(x+\frac{4}{14})& =(\color{red}{a}+\color{orange}{\frac{-5}{14}}).(\color{green}{x}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{-5}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{14})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{7}a-\frac{5}{14}x-\frac{5}{14}.\frac{2}{7}& \text{Uitwerken } \\ & =ax+\frac{2}{7}a-\frac{5}{14}x-\frac{10}{98} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{2}{7}a-\frac{5}{14}x-\frac{5}{49} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(x+\frac{6}{3})(x+\frac{-4}{19})& =(\color{red}{x}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{4}{19}x+2x-2.\frac{4}{19}& \text{Uitwerken } \\ & =x^2+((\frac{-4}{19})+2)x-(\frac{-8}{19}) & \text{Neem samen} \\ &=x^2+\frac{34}{19}x-(\frac{-8}{19}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(x+\frac{18}{10})(\frac{10}{4}+q)& =(\color{red}{x}+\color{orange}{\frac{9}{5}}).(\color{green}{q}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{9}{5})} . \color{green}{(q)} + \color{orange}{(\frac{9}{5})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{2}x+\frac{9}{5}q+\frac{9}{5}.\frac{5}{2}& \text{Uitwerken } \\ & =qx+\frac{5}{2}x+\frac{9}{5}q+\frac{45}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{5}{2}x+\frac{9}{5}q+\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(x-\frac{8}{3})(\frac{13}{4}-x)& =(\color{red}{x}+\color{orange}{\frac{-8}{3}}).(\color{green}{-x}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{13}{4}x+\frac{8}{3}x-\frac{8}{3}.\frac{13}{4}& \text{Uitwerken } \\ & =-x^2+(\frac{13}{4}+\frac{8}{3})x-\frac{104}{12} & \text{Neem samen} \\ &=-x^2+\frac{71}{12}x-\frac{104}{12} & \text{Maak de som} \\ &=-x^2+\frac{71}{12}x-\frac{26}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(b-\frac{18}{19})(\frac{18}{18}+p)& =(\color{red}{b}+\color{orange}{\frac{-18}{19}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-18}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-18}{19})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp+1b-\frac{18}{19}p-\frac{18}{19}.1& \text{Uitwerken } \\ & =bp+1b-\frac{18}{19}p-\frac{18}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{9}{7}-b)(b-\frac{-14}{2})& =(\color{red}{-b}+\color{orange}{\frac{9}{7}}).(\color{green}{b}+\color{blue}{7})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(7)} + \color{orange}{(\frac{9}{7})} . \color{green}{(b)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = -bb-7b+\frac{9}{7}b+\frac{9}{7}.7& \text{Uitwerken } \\ & =-b^2+((-7)+\frac{9}{7})b+(\frac{-63}{7}) & \text{Neem samen} \\ &=-b^2-\frac{40}{7}b+(\frac{-63}{7}) & \text{Maak de som} \\ &=-b^2-\frac{40}{7}b+(-9) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(q-\frac{5}{11})(\frac{14}{13}+a)& =(\color{red}{q}+\color{orange}{\frac{-5}{11}}).(\color{green}{a}+\color{blue}{\frac{14}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{14}{13})} + \color{orange}{(\frac{-5}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(\frac{14}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{14}{13}q-\frac{5}{11}a-\frac{5}{11}.\frac{14}{13}& \text{Uitwerken } \\ & =aq+\frac{14}{13}q-\frac{5}{11}a-\frac{70}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q+\frac{-15}{5})(p+\frac{-19}{8})& =(\color{red}{q}+\color{orange}{(-3)}).(\color{green}{p}+\color{blue}{\frac{-19}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{8})} + \color{orange}{(-3)} . \color{green}{(p)} + \color{orange}{(-3)} . \color{blue}{(\frac{-19}{8})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{8}q-3p+3.\frac{19}{8}& \text{Uitwerken } \\ & =pq-\frac{19}{8}q-3p+\frac{57}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(p-\frac{8}{11})(a-\frac{15}{2})& =(\color{red}{p}+\color{orange}{\frac{-8}{11}}).(\color{green}{a}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{-8}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{11})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{15}{2}p-\frac{8}{11}a+\frac{8}{11}.\frac{15}{2}& \text{Uitwerken } \\ & =ap-\frac{15}{2}p-\frac{8}{11}a+\frac{120}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{15}{2}p-\frac{8}{11}a+\frac{60}{11} & \text{Vereenvoudig} \\\end{align}\)
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