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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{-7}{3}+a)(x+(-4))& =(\color{red}{a}+\color{orange}{\frac{-7}{3}}).(\color{green}{x}+\color{blue}{(-4)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-4)} + \color{orange}{(\frac{-7}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = ax-4a-\frac{7}{3}x+\frac{7}{3}.4& \text{Uitwerken } \\ & =ax-4a-\frac{7}{3}x+\frac{28}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{19}{16}-q)(\frac{3}{7}+x)& =(\color{red}{-q}+\color{orange}{\frac{19}{16}}).(\color{green}{x}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{19}{16})} . \color{green}{(x)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{3}{7}q+\frac{19}{16}x+\frac{19}{16}.\frac{3}{7}& \text{Uitwerken } \\ & =-qx-\frac{3}{7}q+\frac{19}{16}x+\frac{57}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(b-\frac{-7}{5})(\frac{-6}{17}+p)& =(\color{red}{b}+\color{orange}{\frac{7}{5}}).(\color{green}{p}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(\frac{7}{5})} . \color{green}{(p)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{6}{17}b+\frac{7}{5}p-\frac{7}{5}.\frac{6}{17}& \text{Uitwerken } \\ & =bp-\frac{6}{17}b+\frac{7}{5}p-\frac{42}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-2}{17}+x)(p-\frac{17}{13})& =(\color{red}{x}+\color{orange}{\frac{-2}{17}}).(\color{green}{p}+\color{blue}{\frac{-17}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{13})} + \color{orange}{(\frac{-2}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{17})} . \color{blue}{(\frac{-17}{13})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{13}x-\frac{2}{17}p+\frac{2}{17}.\frac{17}{13}& \text{Uitwerken } \\ & =px-\frac{17}{13}x-\frac{2}{17}p+\frac{34}{221} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{17}{13}x-\frac{2}{17}p+\frac{2}{13} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(17-b)(\frac{-13}{5}-p)& =(\color{red}{-b}+\color{orange}{17}).(\color{green}{-p}+\color{blue}{\frac{-13}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{-13}{5})} + \color{orange}{(17)} . \color{green}{(-p)} + \color{orange}{(17)} . \color{blue}{(\frac{-13}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{5}b-17p-17.\frac{13}{5}& \text{Uitwerken } \\ & =bp+\frac{13}{5}b-17p-\frac{221}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{15}{17})(\frac{20}{7}-x)& =(\color{red}{a}+\color{orange}{\frac{-15}{17}}).(\color{green}{-x}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(\frac{-15}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-15}{17})} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{20}{7}a+\frac{15}{17}x-\frac{15}{17}.\frac{20}{7}& \text{Uitwerken } \\ & =-ax+\frac{20}{7}a+\frac{15}{17}x-\frac{300}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{16}{11}-x)((-11)+p)& =(\color{red}{-x}+\color{orange}{\frac{16}{11}}).(\color{green}{p}+\color{blue}{(-11)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(-11)} + \color{orange}{(\frac{16}{11})} . \color{green}{(p)} + \color{orange}{(\frac{16}{11})} . \color{blue}{(-11)}& \text{Boogjes en uitschrijven} \\ & = -px+11x+\frac{16}{11}p-\frac{16}{11}.11& \text{Uitwerken } \\ & =-px+11x+\frac{16}{11}p-\frac{176}{11} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+11x+\frac{16}{11}p-16 & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{8}{2}-a)(x+\frac{-11}{10})& =(\color{red}{-a}+\color{orange}{4}).(\color{green}{x}+\color{blue}{\frac{-11}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{-11}{10})} + \color{orange}{(4)} . \color{green}{(x)} + \color{orange}{(4)} . \color{blue}{(\frac{-11}{10})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{11}{10}a+4x-4.\frac{11}{10}& \text{Uitwerken } \\ & =-ax+\frac{11}{10}a+4x-\frac{44}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{11}{10}a+4x-\frac{22}{5} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(x-\frac{-13}{3})(a+\frac{-14}{2})& =(\color{red}{x}+\color{orange}{\frac{13}{3}}).(\color{green}{a}+\color{blue}{(-7)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-7)} + \color{orange}{(\frac{13}{3})} . \color{green}{(a)} + \color{orange}{(\frac{13}{3})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = ax-7x+\frac{13}{3}a-\frac{13}{3}.7& \text{Uitwerken } \\ & =ax-7x+\frac{13}{3}a-\frac{91}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{14}{12}+b)((-6)-p)& =(\color{red}{b}+\color{orange}{\frac{7}{6}}).(\color{green}{-p}+\color{blue}{(-6)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(-6)} + \color{orange}{(\frac{7}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = -bp-6b-\frac{7}{6}p-\frac{7}{6}.6& \text{Uitwerken } \\ & =-bp-6b-\frac{7}{6}p-\frac{42}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-6b-\frac{7}{6}p-7 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(a+\frac{2}{20})(q-\frac{11}{4})& =(\color{red}{a}+\color{orange}{\frac{1}{10}}).(\color{green}{q}+\color{blue}{\frac{-11}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{4})} + \color{orange}{(\frac{1}{10})} . \color{green}{(q)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{-11}{4})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{11}{4}a+\frac{1}{10}q-\frac{1}{10}.\frac{11}{4}& \text{Uitwerken } \\ & =aq-\frac{11}{4}a+\frac{1}{10}q-\frac{11}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q+\frac{-2}{3})(p+\frac{7}{19})& =(\color{red}{q}+\color{orange}{\frac{-2}{3}}).(\color{green}{p}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{7}{19}q-\frac{2}{3}p-\frac{2}{3}.\frac{7}{19}& \text{Uitwerken } \\ & =pq+\frac{7}{19}q-\frac{2}{3}p-\frac{14}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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