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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b-\frac{-15}{16})(b-\frac{15}{17})& =(\color{red}{b}+\color{orange}{\frac{15}{16}}).(\color{green}{b}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(\frac{15}{16})} . \color{green}{(b)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{15}{17}b+\frac{15}{16}b-\frac{15}{16}.\frac{15}{17}& \text{Uitwerken } \\ & =b^2+((\frac{-15}{17})+\frac{15}{16})b-(\frac{-225}{272}) & \text{Neem samen} \\ &=b^2+\frac{15}{272}b-(\frac{-225}{272}) & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(\frac{10}{19}+x)(a+\frac{16}{19})& =(\color{red}{x}+\color{orange}{\frac{10}{19}}).(\color{green}{a}+\color{blue}{\frac{16}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{16}{19})} + \color{orange}{(\frac{10}{19})} . \color{green}{(a)} + \color{orange}{(\frac{10}{19})} . \color{blue}{(\frac{16}{19})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{16}{19}x+\frac{10}{19}a+\frac{10}{19}.\frac{16}{19}& \text{Uitwerken } \\ & =ax+\frac{16}{19}x+\frac{10}{19}a+\frac{160}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-11}{12}-b)(q+\frac{8}{9})& =(\color{red}{-b}+\color{orange}{\frac{-11}{12}}).(\color{green}{q}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{-11}{12})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{12})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{8}{9}b-\frac{11}{12}q-\frac{11}{12}.\frac{8}{9}& \text{Uitwerken } \\ & =-bq-\frac{8}{9}b-\frac{11}{12}q-\frac{88}{108} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{8}{9}b-\frac{11}{12}q-\frac{22}{27} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(p-\frac{2}{9})(\frac{-7}{6}-p)& =(\color{red}{p}+\color{orange}{\frac{-2}{9}}).(\color{green}{-p}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{7}{6}p+\frac{2}{9}p+\frac{2}{9}.\frac{7}{6}& \text{Uitwerken } \\ & =-p^2+((\frac{-7}{6})+\frac{2}{9})p+(\frac{-14}{54}) & \text{Neem samen} \\ &=-p^2-\frac{17}{18}p+(\frac{-14}{54}) & \text{Maak de som} \\ &=-p^2-\frac{17}{18}p+(\frac{-7}{27}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(b-\frac{10}{5})(\frac{16}{11}+q)& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{16}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{16}{11})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{16}{11})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{16}{11}b-2q-2.\frac{16}{11}& \text{Uitwerken } \\ & =bq+\frac{16}{11}b-2q-\frac{32}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(p-\frac{7}{3})(b+\frac{-4}{13})& =(\color{red}{p}+\color{orange}{\frac{-7}{3}}).(\color{green}{b}+\color{blue}{\frac{-4}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{13})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{-4}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{13}p-\frac{7}{3}b+\frac{7}{3}.\frac{4}{13}& \text{Uitwerken } \\ & =bp-\frac{4}{13}p-\frac{7}{3}b+\frac{28}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-17}{13}-x)(\frac{-9}{18}-b)& =(\color{red}{-x}+\color{orange}{\frac{-17}{13}}).(\color{green}{-b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-17}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-17}{13})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{2}x+\frac{17}{13}b+\frac{17}{13}.\frac{1}{2}& \text{Uitwerken } \\ & =bx+\frac{1}{2}x+\frac{17}{13}b+\frac{17}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{10}{3})(\frac{-4}{12}+b)& =(\color{red}{q}+\color{orange}{\frac{10}{3}}).(\color{green}{b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{10}{3})} . \color{green}{(b)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{3}q+\frac{10}{3}b-\frac{10}{3}.\frac{1}{3}& \text{Uitwerken } \\ & =bq-\frac{1}{3}q+\frac{10}{3}b-\frac{10}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-5}{18}+q)(\frac{8}{13}+b)& =(\color{red}{q}+\color{orange}{\frac{-5}{18}}).(\color{green}{b}+\color{blue}{\frac{8}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{8}{13})} + \color{orange}{(\frac{-5}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{18})} . \color{blue}{(\frac{8}{13})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{8}{13}q-\frac{5}{18}b-\frac{5}{18}.\frac{8}{13}& \text{Uitwerken } \\ & =bq+\frac{8}{13}q-\frac{5}{18}b-\frac{40}{234} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{8}{13}q-\frac{5}{18}b-\frac{20}{117} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{15}{18}-b)(\frac{-20}{9}-a)& =(\color{red}{-b}+\color{orange}{\frac{5}{6}}).(\color{green}{-a}+\color{blue}{\frac{-20}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-20}{9})} + \color{orange}{(\frac{5}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-20}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{20}{9}b-\frac{5}{6}a-\frac{5}{6}.\frac{20}{9}& \text{Uitwerken } \\ & =ab+\frac{20}{9}b-\frac{5}{6}a-\frac{100}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{20}{9}b-\frac{5}{6}a-\frac{50}{27} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{15}{18}+a)(\frac{-1}{15}+a)& =(\color{red}{a}+\color{orange}{\frac{5}{6}}).(\color{green}{a}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(\frac{5}{6})} . \color{green}{(a)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{15}a+\frac{5}{6}a-\frac{5}{6}.\frac{1}{15}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{15})+\frac{5}{6})a-(\frac{-5}{90}) & \text{Neem samen} \\ &=a^2+\frac{23}{30}a-(\frac{-5}{90}) & \text{Maak de som} \\ &=a^2+\frac{23}{30}a+\frac{1}{18} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{9}{8}-p)(\frac{5}{2}-p)& =(\color{red}{-p}+\color{orange}{\frac{9}{8}}).(\color{green}{-p}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{9}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{5}{2}p-\frac{9}{8}p+\frac{9}{8}.\frac{5}{2}& \text{Uitwerken } \\ & =p^2+((\frac{-5}{2})+(\frac{-9}{8}))p+\frac{45}{16} & \text{Neem samen} \\ &=p^2-\frac{29}{8}p+\frac{45}{16} & \text{Maak de som} \\\end{align}\)
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