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

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Werk uit en vereenvoudig

  1. \((\frac{-8}{9}-a)(\frac{13}{16}-p)\)
  2. \((a-\frac{11}{10})(b+\frac{-13}{9})\)
  3. \((\frac{3}{14}+b)(\frac{20}{17}+p)\)
  4. \((q+\frac{5}{13})(p+\frac{4}{13})\)
  5. \((\frac{-7}{4}-b)(12+b)\)
  6. \((q-\frac{5}{19})(a+\frac{-15}{11})\)
  7. \((\frac{-18}{2}-b)(18-b)\)
  8. \((p-\frac{-3}{3})(b+18)\)
  9. \((p+(-9))(p-\frac{-19}{6})\)
  10. \((p-\frac{-20}{9})(\frac{-7}{3}-x)\)
  11. \((\frac{-5}{7}+b)(\frac{20}{3}+p)\)
  12. \((\frac{17}{8}+x)(\frac{-4}{18}+x)\)

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-8}{9}-a)(\frac{13}{16}-p)& =(\color{red}{-a}+\color{orange}{\frac{-8}{9}}).(\color{green}{-p}+\color{blue}{\frac{13}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{13}{16})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{13}{16})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{13}{16}a+\frac{8}{9}p-\frac{8}{9}.\frac{13}{16}& \text{Uitwerken } \\ & =ap-\frac{13}{16}a+\frac{8}{9}p-\frac{104}{144} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{13}{16}a+\frac{8}{9}p-\frac{13}{18} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(a-\frac{11}{10})(b+\frac{-13}{9})& =(\color{red}{a}+\color{orange}{\frac{-11}{10}}).(\color{green}{b}+\color{blue}{\frac{-13}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{9})} + \color{orange}{(\frac{-11}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{10})} . \color{blue}{(\frac{-13}{9})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{9}a-\frac{11}{10}b+\frac{11}{10}.\frac{13}{9}& \text{Uitwerken } \\ & =ab-\frac{13}{9}a-\frac{11}{10}b+\frac{143}{90} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{3}{14}+b)(\frac{20}{17}+p)& =(\color{red}{b}+\color{orange}{\frac{3}{14}}).(\color{green}{p}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(\frac{3}{14})} . \color{green}{(p)} + \color{orange}{(\frac{3}{14})} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{20}{17}b+\frac{3}{14}p+\frac{3}{14}.\frac{20}{17}& \text{Uitwerken } \\ & =bp+\frac{20}{17}b+\frac{3}{14}p+\frac{60}{238} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{20}{17}b+\frac{3}{14}p+\frac{30}{119} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(q+\frac{5}{13})(p+\frac{4}{13})& =(\color{red}{q}+\color{orange}{\frac{5}{13}}).(\color{green}{p}+\color{blue}{\frac{4}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{4}{13})} + \color{orange}{(\frac{5}{13})} . \color{green}{(p)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(\frac{4}{13})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{13}q+\frac{5}{13}p+\frac{5}{13}.\frac{4}{13}& \text{Uitwerken } \\ & =pq+\frac{4}{13}q+\frac{5}{13}p+\frac{20}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-7}{4}-b)(12+b)& =(\color{red}{-b}+\color{orange}{\frac{-7}{4}}).(\color{green}{b}+\color{blue}{12})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(12)} + \color{orange}{(\frac{-7}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = -bb-12b-\frac{7}{4}b-\frac{7}{4}.12& \text{Uitwerken } \\ & =-b^2+((-12)+(\frac{-7}{4}))b-\frac{84}{4} & \text{Neem samen} \\ &=-b^2-\frac{55}{4}b-\frac{84}{4} & \text{Maak de som} \\ &=-b^2-\frac{55}{4}b-21 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(q-\frac{5}{19})(a+\frac{-15}{11})& =(\color{red}{q}+\color{orange}{\frac{-5}{19}}).(\color{green}{a}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(\frac{-5}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{19})} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{15}{11}q-\frac{5}{19}a+\frac{5}{19}.\frac{15}{11}& \text{Uitwerken } \\ & =aq-\frac{15}{11}q-\frac{5}{19}a+\frac{75}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-18}{2}-b)(18-b)& =(\color{red}{-b}+\color{orange}{(-9)}).(\color{green}{-b}+\color{blue}{18})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(18)} + \color{orange}{(-9)} . \color{green}{(-b)} + \color{orange}{(-9)} . \color{blue}{(18)}& \text{Boogjes en uitschrijven} \\ & = bb-18b+9b-9.18& \text{Uitwerken } \\ & =b^2+((-18)+9)b-(-162) & \text{Neem samen} \\ &=b^2-9b-(-162) & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(p-\frac{-3}{3})(b+18)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{b}+\color{blue}{18})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(18)} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(18)}& \text{Boogjes en uitschrijven} \\ & = bp+18p+1b+1.18& \text{Uitwerken } \\ & =bp+18p+1b+18 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p+(-9))(p-\frac{-19}{6})& =(\color{red}{p}+\color{orange}{(-9)}).(\color{green}{p}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(-9)} . \color{green}{(p)} + \color{orange}{(-9)} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{19}{6}p-9p-9.\frac{19}{6}& \text{Uitwerken } \\ & =p^2+(\frac{19}{6}+(-9))p-(\frac{-171}{6}) & \text{Neem samen} \\ &=p^2-\frac{35}{6}p-(\frac{-171}{6}) & \text{Maak de som} \\ &=p^2-\frac{35}{6}p+\frac{57}{2} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  10. \(\begin{align}(p-\frac{-20}{9})(\frac{-7}{3}-x)& =(\color{red}{p}+\color{orange}{\frac{20}{9}}).(\color{green}{-x}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{20}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{7}{3}p-\frac{20}{9}x-\frac{20}{9}.\frac{7}{3}& \text{Uitwerken } \\ & =-px-\frac{7}{3}p-\frac{20}{9}x-\frac{140}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-5}{7}+b)(\frac{20}{3}+p)& =(\color{red}{b}+\color{orange}{\frac{-5}{7}}).(\color{green}{p}+\color{blue}{\frac{20}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{20}{3})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{20}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{20}{3}b-\frac{5}{7}p-\frac{5}{7}.\frac{20}{3}& \text{Uitwerken } \\ & =bp+\frac{20}{3}b-\frac{5}{7}p-\frac{100}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{17}{8}+x)(\frac{-4}{18}+x)& =(\color{red}{x}+\color{orange}{\frac{17}{8}}).(\color{green}{x}+\color{blue}{\frac{-2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{9})} + \color{orange}{(\frac{17}{8})} . \color{green}{(x)} + \color{orange}{(\frac{17}{8})} . \color{blue}{(\frac{-2}{9})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{2}{9}x+\frac{17}{8}x-\frac{17}{8}.\frac{2}{9}& \text{Uitwerken } \\ & =x^2+((\frac{-2}{9})+\frac{17}{8})x-(\frac{-34}{72}) & \text{Neem samen} \\ &=x^2+\frac{137}{72}x-(\frac{-34}{72}) & \text{Maak de som} \\ &=x^2+\frac{137}{72}x+\frac{17}{36} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
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