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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-15}{16}-q)(a+\frac{-9}{8})& =(\color{red}{-q}+\color{orange}{\frac{-15}{16}}).(\color{green}{a}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{-15}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{9}{8}q-\frac{15}{16}a+\frac{15}{16}.\frac{9}{8}& \text{Uitwerken } \\ & =-aq+\frac{9}{8}q-\frac{15}{16}a+\frac{135}{128} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(x+6)(\frac{5}{9}+x)& =(\color{red}{x}+\color{orange}{6}).(\color{green}{x}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(6)} . \color{green}{(x)} + \color{orange}{(6)} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{5}{9}x+6x+6.\frac{5}{9}& \text{Uitwerken } \\ & =x^2+(\frac{5}{9}+6)x+\frac{30}{9} & \text{Neem samen} \\ &=x^2+\frac{59}{9}x+\frac{30}{9} & \text{Maak de som} \\ &=x^2+\frac{59}{9}x+\frac{10}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(x-\frac{7}{15})(\frac{10}{15}+p)& =(\color{red}{x}+\color{orange}{\frac{-7}{15}}).(\color{green}{p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-7}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{2}{3}x-\frac{7}{15}p-\frac{7}{15}.\frac{2}{3}& \text{Uitwerken } \\ & =px+\frac{2}{3}x-\frac{7}{15}p-\frac{14}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q-\frac{12}{6})(\frac{13}{10}+p)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{13}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{13}{10})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{13}{10})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{13}{10}q-2p-2.\frac{13}{10}& \text{Uitwerken } \\ & =pq+\frac{13}{10}q-2p-\frac{26}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{13}{10}q-2p-\frac{13}{5} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-6}{18}-x)(\frac{10}{16}+q)& =(\color{red}{-x}+\color{orange}{\frac{-1}{3}}).(\color{green}{q}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{5}{8}x-\frac{1}{3}q-\frac{1}{3}.\frac{5}{8}& \text{Uitwerken } \\ & =-qx-\frac{5}{8}x-\frac{1}{3}q-\frac{5}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{14}{17}-q)(q-\frac{-16}{13})& =(\color{red}{-q}+\color{orange}{\frac{14}{17}}).(\color{green}{q}+\color{blue}{\frac{16}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{16}{13})} + \color{orange}{(\frac{14}{17})} . \color{green}{(q)} + \color{orange}{(\frac{14}{17})} . \color{blue}{(\frac{16}{13})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{16}{13}q+\frac{14}{17}q+\frac{14}{17}.\frac{16}{13}& \text{Uitwerken } \\ & =-q^2+((\frac{-16}{13})+\frac{14}{17})q+(\frac{-224}{221}) & \text{Neem samen} \\ &=-q^2-\frac{90}{221}q+(\frac{-224}{221}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(\frac{-3}{10}-x)(p-\frac{-9}{13})& =(\color{red}{-x}+\color{orange}{\frac{-3}{10}}).(\color{green}{p}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{9}{13}x-\frac{3}{10}p-\frac{3}{10}.\frac{9}{13}& \text{Uitwerken } \\ & =-px-\frac{9}{13}x-\frac{3}{10}p-\frac{27}{130} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{8}{11}-b)(a+\frac{-12}{20})& =(\color{red}{-b}+\color{orange}{\frac{8}{11}}).(\color{green}{a}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{8}{11})} . \color{green}{(a)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{3}{5}b+\frac{8}{11}a-\frac{8}{11}.\frac{3}{5}& \text{Uitwerken } \\ & =-ab+\frac{3}{5}b+\frac{8}{11}a-\frac{24}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q+\frac{1}{11})(\frac{15}{5}+a)& =(\color{red}{q}+\color{orange}{\frac{1}{11}}).(\color{green}{a}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{1}{11})} . \color{green}{(a)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = aq+3q+\frac{1}{11}a+\frac{1}{11}.3& \text{Uitwerken } \\ & =aq+3q+\frac{1}{11}a+\frac{3}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q-\frac{-18}{19})(\frac{18}{13}+a)& =(\color{red}{q}+\color{orange}{\frac{18}{19}}).(\color{green}{a}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{18}{19})} . \color{green}{(a)} + \color{orange}{(\frac{18}{19})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{18}{13}q+\frac{18}{19}a+\frac{18}{19}.\frac{18}{13}& \text{Uitwerken } \\ & =aq+\frac{18}{13}q+\frac{18}{19}a+\frac{324}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q-\frac{-20}{13})(5+p)& =(\color{red}{q}+\color{orange}{\frac{20}{13}}).(\color{green}{p}+\color{blue}{5})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(5)} + \color{orange}{(\frac{20}{13})} . \color{green}{(p)} + \color{orange}{(\frac{20}{13})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = pq+5q+\frac{20}{13}p+\frac{20}{13}.5& \text{Uitwerken } \\ & =pq+5q+\frac{20}{13}p+\frac{100}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q-\frac{-10}{3})(x-\frac{-9}{6})& =(\color{red}{q}+\color{orange}{\frac{10}{3}}).(\color{green}{x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{10}{3})} . \color{green}{(x)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{2}q+\frac{10}{3}x+\frac{10}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =qx+\frac{3}{2}q+\frac{10}{3}x+\frac{30}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{3}{2}q+\frac{10}{3}x+5 & \text{Vereenvoudig} \\\end{align}\)
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