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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a+\frac{17}{10})(a-\frac{-1}{13})& =(\color{red}{a}+\color{orange}{\frac{17}{10}}).(\color{green}{a}+\color{blue}{\frac{1}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{13})} + \color{orange}{(\frac{17}{10})} . \color{green}{(a)} + \color{orange}{(\frac{17}{10})} . \color{blue}{(\frac{1}{13})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{13}a+\frac{17}{10}a+\frac{17}{10}.\frac{1}{13}& \text{Uitwerken } \\ & =a^2+(\frac{1}{13}+\frac{17}{10})a+\frac{17}{130} & \text{Neem samen} \\ &=a^2+\frac{231}{130}a+\frac{17}{130} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(b-\frac{-9}{4})(\frac{-16}{11}+a)& =(\color{red}{b}+\color{orange}{\frac{9}{4}}).(\color{green}{a}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(\frac{9}{4})} . \color{green}{(a)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{16}{11}b+\frac{9}{4}a-\frac{9}{4}.\frac{16}{11}& \text{Uitwerken } \\ & =ab-\frac{16}{11}b+\frac{9}{4}a-\frac{144}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{16}{11}b+\frac{9}{4}a-\frac{36}{11} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b-\frac{1}{16})(\frac{6}{18}-b)& =(\color{red}{b}+\color{orange}{\frac{-1}{16}}).(\color{green}{-b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-1}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{16})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{1}{3}b+\frac{1}{16}b-\frac{1}{16}.\frac{1}{3}& \text{Uitwerken } \\ & =-b^2+(\frac{1}{3}+\frac{1}{16})b-\frac{1}{48} & \text{Neem samen} \\ &=-b^2+\frac{19}{48}b-\frac{1}{48} & \text{Maak de som} \\\end{align}\)
  4. \(\begin{align}(x-\frac{-9}{6})(\frac{8}{6}-x)& =(\color{red}{x}+\color{orange}{\frac{3}{2}}).(\color{green}{-x}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{4}{3}x-\frac{3}{2}x+\frac{3}{2}.\frac{4}{3}& \text{Uitwerken } \\ & =-x^2+(\frac{4}{3}+(\frac{-3}{2}))x+(\frac{-12}{6}) & \text{Neem samen} \\ &=-x^2-\frac{1}{6}x+(\frac{-12}{6}) & \text{Maak de som} \\ &=-x^2-\frac{1}{6}x+(-2) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{-18}{2}+q)(x+\frac{4}{16})& =(\color{red}{q}+\color{orange}{(-9)}).(\color{green}{x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(-9)} . \color{green}{(x)} + \color{orange}{(-9)} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{4}q-9x-9.\frac{1}{4}& \text{Uitwerken } \\ & =qx+\frac{1}{4}q-9x-\frac{9}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{9}{3}+b)(p+\frac{-5}{4})& =(\color{red}{b}+\color{orange}{3}).(\color{green}{p}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{4}b+3p-3.\frac{5}{4}& \text{Uitwerken } \\ & =bp-\frac{5}{4}b+3p-\frac{15}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x+\frac{-5}{12})(\frac{-13}{2}+b)& =(\color{red}{x}+\color{orange}{\frac{-5}{12}}).(\color{green}{b}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(\frac{-5}{12})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{12})} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{13}{2}x-\frac{5}{12}b+\frac{5}{12}.\frac{13}{2}& \text{Uitwerken } \\ & =bx-\frac{13}{2}x-\frac{5}{12}b+\frac{65}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(a+\frac{6}{12})(a-\frac{1}{12})& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{12}a+\frac{1}{2}a-\frac{1}{2}.\frac{1}{12}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{12})+\frac{1}{2})a-(\frac{-1}{24}) & \text{Neem samen} \\ &=a^2+\frac{5}{12}a-(\frac{-1}{24}) & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(a+\frac{12}{20})(a+\frac{4}{14})& =(\color{red}{a}+\color{orange}{\frac{3}{5}}).(\color{green}{a}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{3}{5})} . \color{green}{(a)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{2}{7}a+\frac{3}{5}a+\frac{3}{5}.\frac{2}{7}& \text{Uitwerken } \\ & =a^2+(\frac{2}{7}+\frac{3}{5})a+\frac{6}{35} & \text{Neem samen} \\ &=a^2+\frac{31}{35}a+\frac{6}{35} & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(p-\frac{18}{8})(\frac{-15}{9}-q)& =(\color{red}{p}+\color{orange}{\frac{-9}{4}}).(\color{green}{-q}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{5}{3}p+\frac{9}{4}q+\frac{9}{4}.\frac{5}{3}& \text{Uitwerken } \\ & =-pq-\frac{5}{3}p+\frac{9}{4}q+\frac{45}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{5}{3}p+\frac{9}{4}q+\frac{15}{4} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(q+\frac{9}{16})(x-\frac{-5}{19})& =(\color{red}{q}+\color{orange}{\frac{9}{16}}).(\color{green}{x}+\color{blue}{\frac{5}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{5}{19})} + \color{orange}{(\frac{9}{16})} . \color{green}{(x)} + \color{orange}{(\frac{9}{16})} . \color{blue}{(\frac{5}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{19}q+\frac{9}{16}x+\frac{9}{16}.\frac{5}{19}& \text{Uitwerken } \\ & =qx+\frac{5}{19}q+\frac{9}{16}x+\frac{45}{304} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{1}{5}+q)(\frac{-15}{12}-a)& =(\color{red}{q}+\color{orange}{\frac{1}{5}}).(\color{green}{-a}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{1}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{5}{4}q-\frac{1}{5}a-\frac{1}{5}.\frac{5}{4}& \text{Uitwerken } \\ & =-aq-\frac{5}{4}q-\frac{1}{5}a-\frac{5}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{5}{4}q-\frac{1}{5}a-\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
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