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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-18}{15}-q)(\frac{-11}{16}-q)& =(\color{red}{-q}+\color{orange}{\frac{-6}{5}}).(\color{green}{-q}+\color{blue}{\frac{-11}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{-11}{16})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{-11}{16})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{11}{16}q+\frac{6}{5}q+\frac{6}{5}.\frac{11}{16}& \text{Uitwerken } \\ & =q^2+(\frac{11}{16}+\frac{6}{5})q+\frac{66}{80} & \text{Neem samen} \\ &=q^2+\frac{151}{80}q+\frac{66}{80} & \text{Maak de som} \\ &=q^2+\frac{151}{80}q+\frac{33}{40} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  2. \(\begin{align}(b-\frac{13}{11})(\frac{4}{8}+x)& =(\color{red}{b}+\color{orange}{\frac{-13}{11}}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-13}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{11})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{2}b-\frac{13}{11}x-\frac{13}{11}.\frac{1}{2}& \text{Uitwerken } \\ & =bx+\frac{1}{2}b-\frac{13}{11}x-\frac{13}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{-19}{2}-a)(q-\frac{12}{13})& =(\color{red}{-a}+\color{orange}{\frac{-19}{2}}).(\color{green}{q}+\color{blue}{\frac{-12}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-12}{13})} + \color{orange}{(\frac{-19}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(\frac{-12}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{12}{13}a-\frac{19}{2}q+\frac{19}{2}.\frac{12}{13}& \text{Uitwerken } \\ & =-aq+\frac{12}{13}a-\frac{19}{2}q+\frac{228}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{12}{13}a-\frac{19}{2}q+\frac{114}{13} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-18}{5}-x)(p+\frac{16}{10})& =(\color{red}{-x}+\color{orange}{\frac{-18}{5}}).(\color{green}{p}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{-18}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-18}{5})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{8}{5}x-\frac{18}{5}p-\frac{18}{5}.\frac{8}{5}& \text{Uitwerken } \\ & =-px-\frac{8}{5}x-\frac{18}{5}p-\frac{144}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{16}{2}-p)(p-\frac{6}{3})& =(\color{red}{-p}+\color{orange}{8}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(-2)} + \color{orange}{(8)} . \color{green}{(p)} + \color{orange}{(8)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -pp+2p+8p-8.2& \text{Uitwerken } \\ & =-p^2+(2+8)p-16 & \text{Neem samen} \\ &=-p^2+10p-16 & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(\frac{6}{3}-b)((-3)+p)& =(\color{red}{-b}+\color{orange}{2}).(\color{green}{p}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(-3)} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -bp+3b+2p-2.3& \text{Uitwerken } \\ & =-bp+3b+2p-6 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a+\frac{-4}{6})(p+(-7))& =(\color{red}{a}+\color{orange}{\frac{-2}{3}}).(\color{green}{p}+\color{blue}{(-7)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-7)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = ap-7a-\frac{2}{3}p+\frac{2}{3}.7& \text{Uitwerken } \\ & =ap-7a-\frac{2}{3}p+\frac{14}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(p-\frac{-19}{15})(\frac{-1}{19}-p)& =(\color{red}{p}+\color{orange}{\frac{19}{15}}).(\color{green}{-p}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{19}{15})} . \color{green}{(-p)} + \color{orange}{(\frac{19}{15})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{1}{19}p-\frac{19}{15}p-\frac{19}{15}.\frac{1}{19}& \text{Uitwerken } \\ & =-p^2+((\frac{-1}{19})+(\frac{-19}{15}))p-\frac{19}{285} & \text{Neem samen} \\ &=-p^2-\frac{376}{285}p-\frac{19}{285} & \text{Maak de som} \\ &=-p^2-\frac{376}{285}p-\frac{1}{15} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  9. \(\begin{align}(\frac{-12}{5}+x)(b+\frac{-1}{18})& =(\color{red}{x}+\color{orange}{\frac{-12}{5}}).(\color{green}{b}+\color{blue}{\frac{-1}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{18})} + \color{orange}{(\frac{-12}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-12}{5})} . \color{blue}{(\frac{-1}{18})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{18}x-\frac{12}{5}b+\frac{12}{5}.\frac{1}{18}& \text{Uitwerken } \\ & =bx-\frac{1}{18}x-\frac{12}{5}b+\frac{12}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{1}{18}x-\frac{12}{5}b+\frac{2}{15} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(20+q)(\frac{-8}{19}+x)& =(\color{red}{q}+\color{orange}{20}).(\color{green}{x}+\color{blue}{\frac{-8}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{19})} + \color{orange}{(20)} . \color{green}{(x)} + \color{orange}{(20)} . \color{blue}{(\frac{-8}{19})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{8}{19}q+20x-20.\frac{8}{19}& \text{Uitwerken } \\ & =qx-\frac{8}{19}q+20x-\frac{160}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{4}{12}-q)(17+q)& =(\color{red}{-q}+\color{orange}{\frac{1}{3}}).(\color{green}{q}+\color{blue}{17})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(17)} + \color{orange}{(\frac{1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(17)}& \text{Boogjes en uitschrijven} \\ & = -qq-17q+\frac{1}{3}q+\frac{1}{3}.17& \text{Uitwerken } \\ & =-q^2+((-17)+\frac{1}{3})q+(\frac{-17}{3}) & \text{Neem samen} \\ &=-q^2-\frac{50}{3}q+(\frac{-17}{3}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{19}{20}+q)(\frac{-9}{9}+a)& =(\color{red}{q}+\color{orange}{\frac{19}{20}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{19}{20})} . \color{green}{(a)} + \color{orange}{(\frac{19}{20})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aq-1q+\frac{19}{20}a-\frac{19}{20}.1& \text{Uitwerken } \\ & =aq-1q+\frac{19}{20}a-\frac{19}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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