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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{9}{14})(b+\frac{-6}{16})& =(\color{red}{x}+\color{orange}{\frac{-9}{14}}).(\color{green}{b}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{8}x-\frac{9}{14}b+\frac{9}{14}.\frac{3}{8}& \text{Uitwerken } \\ & =bx-\frac{3}{8}x-\frac{9}{14}b+\frac{27}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(17+a)(\frac{15}{9}+q)& =(\color{red}{a}+\color{orange}{17}).(\color{green}{q}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(17)} . \color{green}{(q)} + \color{orange}{(17)} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{5}{3}a+17q+17.\frac{5}{3}& \text{Uitwerken } \\ & =aq+\frac{5}{3}a+17q+\frac{85}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p+\frac{8}{13})(\frac{-15}{3}-x)& =(\color{red}{p}+\color{orange}{\frac{8}{13}}).(\color{green}{-x}+\color{blue}{(-5)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(-5)} + \color{orange}{(\frac{8}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = -px-5p-\frac{8}{13}x-\frac{8}{13}.5& \text{Uitwerken } \\ & =-px-5p-\frac{8}{13}x-\frac{40}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{9}{2}-q)(q-\frac{-10}{9})& =(\color{red}{-q}+\color{orange}{\frac{9}{2}}).(\color{green}{q}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{9}{2})} . \color{green}{(q)} + \color{orange}{(\frac{9}{2})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{10}{9}q+\frac{9}{2}q+\frac{9}{2}.\frac{10}{9}& \text{Uitwerken } \\ & =-q^2+((\frac{-10}{9})+\frac{9}{2})q+(\frac{-90}{18}) & \text{Neem samen} \\ &=-q^2+\frac{61}{18}q+(\frac{-90}{18}) & \text{Maak de som} \\ &=-q^2+\frac{61}{18}q+(-5) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(q+\frac{7}{16})(a+\frac{-1}{12})& =(\color{red}{q}+\color{orange}{\frac{7}{16}}).(\color{green}{a}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(\frac{7}{16})} . \color{green}{(a)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{12}q+\frac{7}{16}a-\frac{7}{16}.\frac{1}{12}& \text{Uitwerken } \\ & =aq-\frac{1}{12}q+\frac{7}{16}a-\frac{7}{192} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-14}{3}+b)(a+\frac{-14}{2})& =(\color{red}{b}+\color{orange}{\frac{-14}{3}}).(\color{green}{a}+\color{blue}{(-7)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-7)} + \color{orange}{(\frac{-14}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-14}{3})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = ab-7b-\frac{14}{3}a+\frac{14}{3}.7& \text{Uitwerken } \\ & =ab-7b-\frac{14}{3}a+\frac{98}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(b-8)(q-\frac{-18}{14})& =(\color{red}{b}+\color{orange}{(-8)}).(\color{green}{q}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(-8)} . \color{green}{(q)} + \color{orange}{(-8)} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{9}{7}b-8q-8.\frac{9}{7}& \text{Uitwerken } \\ & =bq+\frac{9}{7}b-8q-\frac{72}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(x-\frac{-16}{14})(a+\frac{-20}{14})& =(\color{red}{x}+\color{orange}{\frac{8}{7}}).(\color{green}{a}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{8}{7})} . \color{green}{(a)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{10}{7}x+\frac{8}{7}a-\frac{8}{7}.\frac{10}{7}& \text{Uitwerken } \\ & =ax-\frac{10}{7}x+\frac{8}{7}a-\frac{80}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{4}{19}+x)(p+\frac{-11}{15})& =(\color{red}{x}+\color{orange}{\frac{4}{19}}).(\color{green}{p}+\color{blue}{\frac{-11}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{15})} + \color{orange}{(\frac{4}{19})} . \color{green}{(p)} + \color{orange}{(\frac{4}{19})} . \color{blue}{(\frac{-11}{15})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{11}{15}x+\frac{4}{19}p-\frac{4}{19}.\frac{11}{15}& \text{Uitwerken } \\ & =px-\frac{11}{15}x+\frac{4}{19}p-\frac{44}{285} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(b+\frac{4}{17})(p-\frac{2}{13})& =(\color{red}{b}+\color{orange}{\frac{4}{17}}).(\color{green}{p}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(\frac{4}{17})} . \color{green}{(p)} + \color{orange}{(\frac{4}{17})} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{2}{13}b+\frac{4}{17}p-\frac{4}{17}.\frac{2}{13}& \text{Uitwerken } \\ & =bp-\frac{2}{13}b+\frac{4}{17}p-\frac{8}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-1}{13}+q)(q-\frac{-14}{5})& =(\color{red}{q}+\color{orange}{\frac{-1}{13}}).(\color{green}{q}+\color{blue}{\frac{14}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{14}{5})} + \color{orange}{(\frac{-1}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{13})} . \color{blue}{(\frac{14}{5})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{14}{5}q-\frac{1}{13}q-\frac{1}{13}.\frac{14}{5}& \text{Uitwerken } \\ & =q^2+(\frac{14}{5}+(\frac{-1}{13}))q-(\frac{-14}{65}) & \text{Neem samen} \\ &=q^2+\frac{177}{65}q-(\frac{-14}{65}) & \text{Maak de som} \\\end{align}\)
  12. \(\begin{align}(\frac{17}{9}+x)(x+\frac{9}{18})& =(\color{red}{x}+\color{orange}{\frac{17}{9}}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{17}{9})} . \color{green}{(x)} + \color{orange}{(\frac{17}{9})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{1}{2}x+\frac{17}{9}x+\frac{17}{9}.\frac{1}{2}& \text{Uitwerken } \\ & =x^2+(\frac{1}{2}+\frac{17}{9})x+\frac{17}{18} & \text{Neem samen} \\ &=x^2+\frac{43}{18}x+\frac{17}{18} & \text{Maak de som} \\\end{align}\)
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