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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{2}{2}+q)(x-(-15))& =(\color{red}{q}+\color{orange}{1}).(\color{green}{x}+\color{blue}{15})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(15)} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(15)}& \text{Boogjes en uitschrijven} \\ & = qx+15q+1x+1.15& \text{Uitwerken } \\ & =qx+15q+1x+15 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{3}{4}-a)((-16)-x)& =(\color{red}{-a}+\color{orange}{\frac{3}{4}}).(\color{green}{-x}+\color{blue}{(-16)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(-16)} + \color{orange}{(\frac{3}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = ax+16a-\frac{3}{4}x-\frac{3}{4}.16& \text{Uitwerken } \\ & =ax+16a-\frac{3}{4}x-\frac{48}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+16a-\frac{3}{4}x-12 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(p+\frac{-5}{15})(\frac{-2}{17}-b)& =(\color{red}{p}+\color{orange}{\frac{-1}{3}}).(\color{green}{-b}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{2}{17}p+\frac{1}{3}b+\frac{1}{3}.\frac{2}{17}& \text{Uitwerken } \\ & =-bp-\frac{2}{17}p+\frac{1}{3}b+\frac{2}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b-\frac{15}{8})(b-\frac{16}{10})& =(\color{red}{b}+\color{orange}{\frac{-15}{8}}).(\color{green}{b}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{-15}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{8})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{8}{5}b-\frac{15}{8}b+\frac{15}{8}.\frac{8}{5}& \text{Uitwerken } \\ & =b^2+((\frac{-8}{5})+(\frac{-15}{8}))b+\frac{120}{40} & \text{Neem samen} \\ &=b^2-\frac{139}{40}b+\frac{120}{40} & \text{Maak de som} \\ &=b^2-\frac{139}{40}b+3 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(x-\frac{3}{19})(\frac{3}{8}+x)& =(\color{red}{x}+\color{orange}{\frac{-3}{19}}).(\color{green}{x}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{-3}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{19})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{3}{8}x-\frac{3}{19}x-\frac{3}{19}.\frac{3}{8}& \text{Uitwerken } \\ & =x^2+(\frac{3}{8}+(\frac{-3}{19}))x-(\frac{-9}{152}) & \text{Neem samen} \\ &=x^2+\frac{33}{152}x-(\frac{-9}{152}) & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{-13}{20}+a)(p+\frac{20}{7})& =(\color{red}{a}+\color{orange}{\frac{-13}{20}}).(\color{green}{p}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{20}{7}a-\frac{13}{20}p-\frac{13}{20}.\frac{20}{7}& \text{Uitwerken } \\ & =ap+\frac{20}{7}a-\frac{13}{20}p-\frac{260}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{20}{7}a-\frac{13}{20}p-\frac{13}{7} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(p-\frac{-19}{10})(p+\frac{12}{17})& =(\color{red}{p}+\color{orange}{\frac{19}{10}}).(\color{green}{p}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{19}{10})} . \color{green}{(p)} + \color{orange}{(\frac{19}{10})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{12}{17}p+\frac{19}{10}p+\frac{19}{10}.\frac{12}{17}& \text{Uitwerken } \\ & =p^2+(\frac{12}{17}+\frac{19}{10})p+\frac{228}{170} & \text{Neem samen} \\ &=p^2+\frac{443}{170}p+\frac{228}{170} & \text{Maak de som} \\ &=p^2+\frac{443}{170}p+\frac{114}{85} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  8. \(\begin{align}(b-\frac{-8}{9})(b-\frac{-20}{5})& =(\color{red}{b}+\color{orange}{\frac{8}{9}}).(\color{green}{b}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(4)} + \color{orange}{(\frac{8}{9})} . \color{green}{(b)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = bb+4b+\frac{8}{9}b+\frac{8}{9}.4& \text{Uitwerken } \\ & =b^2+(4+\frac{8}{9})b+\frac{32}{9} & \text{Neem samen} \\ &=b^2+\frac{44}{9}b+\frac{32}{9} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(p-\frac{8}{10})(q+\frac{16}{11})& =(\color{red}{p}+\color{orange}{\frac{-4}{5}}).(\color{green}{q}+\color{blue}{\frac{16}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{16}{11})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{16}{11})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{16}{11}p-\frac{4}{5}q-\frac{4}{5}.\frac{16}{11}& \text{Uitwerken } \\ & =pq+\frac{16}{11}p-\frac{4}{5}q-\frac{64}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{17}{11}+p)(x-\frac{-16}{4})& =(\color{red}{p}+\color{orange}{\frac{17}{11}}).(\color{green}{x}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(4)} + \color{orange}{(\frac{17}{11})} . \color{green}{(x)} + \color{orange}{(\frac{17}{11})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = px+4p+\frac{17}{11}x+\frac{17}{11}.4& \text{Uitwerken } \\ & =px+4p+\frac{17}{11}x+\frac{68}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-3}{6})(\frac{3}{4}-p)& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{-p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{3}{4}a-\frac{1}{2}p+\frac{1}{2}.\frac{3}{4}& \text{Uitwerken } \\ & =-ap+\frac{3}{4}a-\frac{1}{2}p+\frac{3}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a-\frac{-7}{5})(\frac{13}{14}+p)& =(\color{red}{a}+\color{orange}{\frac{7}{5}}).(\color{green}{p}+\color{blue}{\frac{13}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{13}{14})} + \color{orange}{(\frac{7}{5})} . \color{green}{(p)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{13}{14})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{14}a+\frac{7}{5}p+\frac{7}{5}.\frac{13}{14}& \text{Uitwerken } \\ & =ap+\frac{13}{14}a+\frac{7}{5}p+\frac{91}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{13}{14}a+\frac{7}{5}p+\frac{13}{10} & \text{Vereenvoudig} \\\end{align}\)
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