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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-\frac{-16}{15})(q+\frac{-20}{19})& =(\color{red}{q}+\color{orange}{\frac{16}{15}}).(\color{green}{q}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{16}{15})} . \color{green}{(q)} + \color{orange}{(\frac{16}{15})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{20}{19}q+\frac{16}{15}q-\frac{16}{15}.\frac{20}{19}& \text{Uitwerken } \\ & =q^2+((\frac{-20}{19})+\frac{16}{15})q-(\frac{-320}{285}) & \text{Neem samen} \\ &=q^2+\frac{4}{285}q-(\frac{-320}{285}) & \text{Maak de som} \\ &=q^2+\frac{4}{285}q+\frac{64}{57} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  2. \(\begin{align}(\frac{-9}{7}-q)(q-\frac{6}{16})& =(\color{red}{-q}+\color{orange}{\frac{-9}{7}}).(\color{green}{q}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{3}{8}q-\frac{9}{7}q+\frac{9}{7}.\frac{3}{8}& \text{Uitwerken } \\ & =-q^2+(\frac{3}{8}+(\frac{-9}{7}))q+(\frac{-27}{56}) & \text{Neem samen} \\ &=-q^2-\frac{51}{56}q+(\frac{-27}{56}) & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(\frac{2}{18}-p)(q-\frac{9}{17})& =(\color{red}{-p}+\color{orange}{\frac{1}{9}}).(\color{green}{q}+\color{blue}{\frac{-9}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-9}{17})} + \color{orange}{(\frac{1}{9})} . \color{green}{(q)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{-9}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{9}{17}p+\frac{1}{9}q-\frac{1}{9}.\frac{9}{17}& \text{Uitwerken } \\ & =-pq+\frac{9}{17}p+\frac{1}{9}q-\frac{9}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{9}{17}p+\frac{1}{9}q-\frac{1}{17} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x+\frac{-8}{9})(b+\frac{2}{17})& =(\color{red}{x}+\color{orange}{\frac{-8}{9}}).(\color{green}{b}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{2}{17}x-\frac{8}{9}b-\frac{8}{9}.\frac{2}{17}& \text{Uitwerken } \\ & =bx+\frac{2}{17}x-\frac{8}{9}b-\frac{16}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-10}{19}+b)(p+\frac{4}{8})& =(\color{red}{b}+\color{orange}{\frac{-10}{19}}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-10}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{19})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{2}b-\frac{10}{19}p-\frac{10}{19}.\frac{1}{2}& \text{Uitwerken } \\ & =bp+\frac{1}{2}b-\frac{10}{19}p-\frac{10}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{1}{2}b-\frac{10}{19}p-\frac{5}{19} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-6}{13})(q+\frac{2}{19})& =(\color{red}{x}+\color{orange}{\frac{-6}{13}}).(\color{green}{q}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(\frac{-6}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{13})} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{2}{19}x-\frac{6}{13}q-\frac{6}{13}.\frac{2}{19}& \text{Uitwerken } \\ & =qx+\frac{2}{19}x-\frac{6}{13}q-\frac{12}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(a-\frac{-8}{4})(\frac{-12}{20}+x)& =(\color{red}{a}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{5}a+2x-2.\frac{3}{5}& \text{Uitwerken } \\ & =ax-\frac{3}{5}a+2x-\frac{6}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q+\frac{11}{20})(p-\frac{13}{19})& =(\color{red}{q}+\color{orange}{\frac{11}{20}}).(\color{green}{p}+\color{blue}{\frac{-13}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{19})} + \color{orange}{(\frac{11}{20})} . \color{green}{(p)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(\frac{-13}{19})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{13}{19}q+\frac{11}{20}p-\frac{11}{20}.\frac{13}{19}& \text{Uitwerken } \\ & =pq-\frac{13}{19}q+\frac{11}{20}p-\frac{143}{380} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-7}{9}-b)(\frac{16}{7}+p)& =(\color{red}{-b}+\color{orange}{\frac{-7}{9}}).(\color{green}{p}+\color{blue}{\frac{16}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{16}{7})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{16}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{16}{7}b-\frac{7}{9}p-\frac{7}{9}.\frac{16}{7}& \text{Uitwerken } \\ & =-bp-\frac{16}{7}b-\frac{7}{9}p-\frac{112}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{16}{7}b-\frac{7}{9}p-\frac{16}{9} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-15}{4}-b)(16-a)& =(\color{red}{-b}+\color{orange}{\frac{-15}{4}}).(\color{green}{-a}+\color{blue}{16})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(16)} + \color{orange}{(\frac{-15}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(16)}& \text{Boogjes en uitschrijven} \\ & = ab-16b+\frac{15}{4}a-\frac{15}{4}.16& \text{Uitwerken } \\ & =ab-16b+\frac{15}{4}a-\frac{240}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-16b+\frac{15}{4}a-60 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(x+\frac{12}{11})(a-\frac{-10}{2})& =(\color{red}{x}+\color{orange}{\frac{12}{11}}).(\color{green}{a}+\color{blue}{5})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(5)} + \color{orange}{(\frac{12}{11})} . \color{green}{(a)} + \color{orange}{(\frac{12}{11})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = ax+5x+\frac{12}{11}a+\frac{12}{11}.5& \text{Uitwerken } \\ & =ax+5x+\frac{12}{11}a+\frac{60}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{12}{18})(\frac{-3}{18}-a)& =(\color{red}{a}+\color{orange}{\frac{2}{3}}).(\color{green}{-a}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{2}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{1}{6}a-\frac{2}{3}a-\frac{2}{3}.\frac{1}{6}& \text{Uitwerken } \\ & =-a^2+((\frac{-1}{6})+(\frac{-2}{3}))a-\frac{2}{18} & \text{Neem samen} \\ &=-a^2-\frac{5}{6}a-\frac{2}{18} & \text{Maak de som} \\ &=-a^2-\frac{5}{6}a-\frac{1}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
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