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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-19}{16}-a)(a+\frac{15}{10})& =(\color{red}{-a}+\color{orange}{\frac{-19}{16}}).(\color{green}{a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-19}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{16})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{3}{2}a-\frac{19}{16}a-\frac{19}{16}.\frac{3}{2}& \text{Uitwerken } \\ & =-a^2+((\frac{-3}{2})+(\frac{-19}{16}))a-\frac{57}{32} & \text{Neem samen} \\ &=-a^2-\frac{43}{16}a-\frac{57}{32} & \text{Maak de som} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-11}{2})(\frac{5}{12}-b)& =(\color{red}{p}+\color{orange}{\frac{-11}{2}}).(\color{green}{-b}+\color{blue}{\frac{5}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{5}{12})} + \color{orange}{(\frac{-11}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{2})} . \color{blue}{(\frac{5}{12})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{5}{12}p+\frac{11}{2}b-\frac{11}{2}.\frac{5}{12}& \text{Uitwerken } \\ & =-bp+\frac{5}{12}p+\frac{11}{2}b-\frac{55}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{16}{12}+x)(\frac{-6}{6}+p)& =(\color{red}{x}+\color{orange}{\frac{4}{3}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1x+\frac{4}{3}p-\frac{4}{3}.1& \text{Uitwerken } \\ & =px-1x+\frac{4}{3}p-\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(b+\frac{6}{19})(\frac{-9}{4}-x)& =(\color{red}{b}+\color{orange}{\frac{6}{19}}).(\color{green}{-x}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(\frac{6}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{9}{4}b-\frac{6}{19}x-\frac{6}{19}.\frac{9}{4}& \text{Uitwerken } \\ & =-bx-\frac{9}{4}b-\frac{6}{19}x-\frac{54}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{9}{4}b-\frac{6}{19}x-\frac{27}{38} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{13}{2}+b)(p+\frac{-8}{20})& =(\color{red}{b}+\color{orange}{\frac{13}{2}}).(\color{green}{p}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{13}{2})} . \color{green}{(p)} + \color{orange}{(\frac{13}{2})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{2}{5}b+\frac{13}{2}p-\frac{13}{2}.\frac{2}{5}& \text{Uitwerken } \\ & =bp-\frac{2}{5}b+\frac{13}{2}p-\frac{26}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{2}{5}b+\frac{13}{2}p-\frac{13}{5} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-11}{6}+a)(q-\frac{17}{13})& =(\color{red}{a}+\color{orange}{\frac{-11}{6}}).(\color{green}{q}+\color{blue}{\frac{-17}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{13})} + \color{orange}{(\frac{-11}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{6})} . \color{blue}{(\frac{-17}{13})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{17}{13}a-\frac{11}{6}q+\frac{11}{6}.\frac{17}{13}& \text{Uitwerken } \\ & =aq-\frac{17}{13}a-\frac{11}{6}q+\frac{187}{78} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{-3}{16}-q)(\frac{12}{19}-q)& =(\color{red}{-q}+\color{orange}{\frac{-3}{16}}).(\color{green}{-q}+\color{blue}{\frac{12}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{12}{19})} + \color{orange}{(\frac{-3}{16})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{16})} . \color{blue}{(\frac{12}{19})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{12}{19}q+\frac{3}{16}q-\frac{3}{16}.\frac{12}{19}& \text{Uitwerken } \\ & =q^2+((\frac{-12}{19})+\frac{3}{16})q-(\frac{-36}{304}) & \text{Neem samen} \\ &=q^2-\frac{135}{304}q-(\frac{-36}{304}) & \text{Maak de som} \\ &=q^2-\frac{135}{304}q+\frac{9}{76} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  8. \(\begin{align}(\frac{11}{8}+x)(p+\frac{-14}{13})& =(\color{red}{x}+\color{orange}{\frac{11}{8}}).(\color{green}{p}+\color{blue}{\frac{-14}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-14}{13})} + \color{orange}{(\frac{11}{8})} . \color{green}{(p)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{-14}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{14}{13}x+\frac{11}{8}p-\frac{11}{8}.\frac{14}{13}& \text{Uitwerken } \\ & =px-\frac{14}{13}x+\frac{11}{8}p-\frac{154}{104} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{14}{13}x+\frac{11}{8}p-\frac{77}{52} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(\frac{3}{10}-b)(b-\frac{-6}{7})& =(\color{red}{-b}+\color{orange}{\frac{3}{10}}).(\color{green}{b}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{3}{10})} . \color{green}{(b)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{6}{7}b+\frac{3}{10}b+\frac{3}{10}.\frac{6}{7}& \text{Uitwerken } \\ & =-b^2+((\frac{-6}{7})+\frac{3}{10})b+(\frac{-18}{70}) & \text{Neem samen} \\ &=-b^2-\frac{39}{70}b+(\frac{-18}{70}) & \text{Maak de som} \\ &=-b^2-\frac{39}{70}b+(\frac{-9}{35}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(\frac{-20}{7}+p)(\frac{-3}{13}-p)& =(\color{red}{p}+\color{orange}{\frac{-20}{7}}).(\color{green}{-p}+\color{blue}{\frac{-3}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{13})} + \color{orange}{(\frac{-20}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-20}{7})} . \color{blue}{(\frac{-3}{13})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{3}{13}p+\frac{20}{7}p+\frac{20}{7}.\frac{3}{13}& \text{Uitwerken } \\ & =-p^2+((\frac{-3}{13})+\frac{20}{7})p+(\frac{-60}{91}) & \text{Neem samen} \\ &=-p^2+\frac{239}{91}p+(\frac{-60}{91}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(p-\frac{-17}{13})(b+\frac{13}{16})& =(\color{red}{p}+\color{orange}{\frac{17}{13}}).(\color{green}{b}+\color{blue}{\frac{13}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{13}{16})} + \color{orange}{(\frac{17}{13})} . \color{green}{(b)} + \color{orange}{(\frac{17}{13})} . \color{blue}{(\frac{13}{16})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{16}p+\frac{17}{13}b+\frac{17}{13}.\frac{13}{16}& \text{Uitwerken } \\ & =bp+\frac{13}{16}p+\frac{17}{13}b+\frac{221}{208} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{13}{16}p+\frac{17}{13}b+\frac{17}{16} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{5}{10}-q)(x-\frac{-8}{6})& =(\color{red}{-q}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{4}{3}q+\frac{1}{2}x+\frac{1}{2}.\frac{4}{3}& \text{Uitwerken } \\ & =-qx-\frac{4}{3}q+\frac{1}{2}x+\frac{4}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{4}{3}q+\frac{1}{2}x+\frac{2}{3} & \text{Vereenvoudig} \\\end{align}\)
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