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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(b+\frac{15}{8})(x-\frac{-5}{20})& =(\color{red}{b}+\color{orange}{\frac{15}{8}}).(\color{green}{x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{15}{8})} . \color{green}{(x)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{4}b+\frac{15}{8}x+\frac{15}{8}.\frac{1}{4}& \text{Uitwerken } \\ & =bx+\frac{1}{4}b+\frac{15}{8}x+\frac{15}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{-12}{14}-b)(\frac{16}{10}+b)& =(\color{red}{-b}+\color{orange}{\frac{-6}{7}}).(\color{green}{b}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{8}{5}b-\frac{6}{7}b-\frac{6}{7}.\frac{8}{5}& \text{Uitwerken } \\ & =-b^2+((\frac{-8}{5})+(\frac{-6}{7}))b-\frac{48}{35} & \text{Neem samen} \\ &=-b^2-\frac{86}{35}b-\frac{48}{35} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(a+\frac{-19}{6})(\frac{4}{3}+a)& =(\color{red}{a}+\color{orange}{\frac{-19}{6}}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-19}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{6})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{4}{3}a-\frac{19}{6}a-\frac{19}{6}.\frac{4}{3}& \text{Uitwerken } \\ & =a^2+(\frac{4}{3}+(\frac{-19}{6}))a-(\frac{-76}{18}) & \text{Neem samen} \\ &=a^2-\frac{11}{6}a-(\frac{-76}{18}) & \text{Maak de som} \\ &=a^2-\frac{11}{6}a+\frac{38}{9} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  4. \(\begin{align}(b+\frac{15}{7})(15-p)& =(\color{red}{b}+\color{orange}{\frac{15}{7}}).(\color{green}{-p}+\color{blue}{15})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(15)} + \color{orange}{(\frac{15}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{15}{7})} . \color{blue}{(15)}& \text{Boogjes en uitschrijven} \\ & = -bp+15b-\frac{15}{7}p+\frac{15}{7}.15& \text{Uitwerken } \\ & =-bp+15b-\frac{15}{7}p+\frac{225}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(x-\frac{9}{2})(x+\frac{8}{5})& =(\color{red}{x}+\color{orange}{\frac{-9}{2}}).(\color{green}{x}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{-9}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{2})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{8}{5}x-\frac{9}{2}x-\frac{9}{2}.\frac{8}{5}& \text{Uitwerken } \\ & =x^2+(\frac{8}{5}+(\frac{-9}{2}))x-(\frac{-72}{10}) & \text{Neem samen} \\ &=x^2-\frac{29}{10}x-(\frac{-72}{10}) & \text{Maak de som} \\ &=x^2-\frac{29}{10}x+\frac{36}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-7}{14})(\frac{-16}{8}-p)& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{-p}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(-2)} + \color{orange}{(\frac{1}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -ap-2a-\frac{1}{2}p-\frac{1}{2}.2& \text{Uitwerken } \\ & =-ap-2a-\frac{1}{2}p-\frac{2}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-2a-\frac{1}{2}p-1 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-9}{5}+a)(a-17)& =(\color{red}{a}+\color{orange}{\frac{-9}{5}}).(\color{green}{a}+\color{blue}{(-17)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(-17)} + \color{orange}{(\frac{-9}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(-17)}& \text{Boogjes en uitschrijven} \\ & = aa-17a-\frac{9}{5}a+\frac{9}{5}.17& \text{Uitwerken } \\ & =a^2+((-17)+(\frac{-9}{5}))a+\frac{153}{5} & \text{Neem samen} \\ &=a^2-\frac{94}{5}a+\frac{153}{5} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(p+\frac{-8}{18})(q+\frac{-13}{15})& =(\color{red}{p}+\color{orange}{\frac{-4}{9}}).(\color{green}{q}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{13}{15}p-\frac{4}{9}q+\frac{4}{9}.\frac{13}{15}& \text{Uitwerken } \\ & =pq-\frac{13}{15}p-\frac{4}{9}q+\frac{52}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(b-\frac{10}{6})(\frac{4}{20}-p)& =(\color{red}{b}+\color{orange}{\frac{-5}{3}}).(\color{green}{-p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{5}b+\frac{5}{3}p-\frac{5}{3}.\frac{1}{5}& \text{Uitwerken } \\ & =-bp+\frac{1}{5}b+\frac{5}{3}p-\frac{5}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{1}{5}b+\frac{5}{3}p-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(q+\frac{8}{15})(a-\frac{-18}{6})& =(\color{red}{q}+\color{orange}{\frac{8}{15}}).(\color{green}{a}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{8}{15})} . \color{green}{(a)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = aq+3q+\frac{8}{15}a+\frac{8}{15}.3& \text{Uitwerken } \\ & =aq+3q+\frac{8}{15}a+\frac{24}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+3q+\frac{8}{15}a+\frac{8}{5} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-19}{16}+b)(b+\frac{7}{9})& =(\color{red}{b}+\color{orange}{\frac{-19}{16}}).(\color{green}{b}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-19}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{16})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{7}{9}b-\frac{19}{16}b-\frac{19}{16}.\frac{7}{9}& \text{Uitwerken } \\ & =b^2+(\frac{7}{9}+(\frac{-19}{16}))b-(\frac{-133}{144}) & \text{Neem samen} \\ &=b^2-\frac{59}{144}b-(\frac{-133}{144}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{16}{19}-b)(\frac{13}{2}-p)& =(\color{red}{-b}+\color{orange}{\frac{16}{19}}).(\color{green}{-p}+\color{blue}{\frac{13}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{13}{2})} + \color{orange}{(\frac{16}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(\frac{13}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{13}{2}b-\frac{16}{19}p+\frac{16}{19}.\frac{13}{2}& \text{Uitwerken } \\ & =bp-\frac{13}{2}b-\frac{16}{19}p+\frac{208}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{13}{2}b-\frac{16}{19}p+\frac{104}{19} & \text{Vereenvoudig} \\\end{align}\)
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