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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{1}{3}-b)(x-\frac{13}{17})& =(\color{red}{-b}+\color{orange}{\frac{1}{3}}).(\color{green}{x}+\color{blue}{\frac{-13}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-13}{17})} + \color{orange}{(\frac{1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-13}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{13}{17}b+\frac{1}{3}x-\frac{1}{3}.\frac{13}{17}& \text{Uitwerken } \\ & =-bx+\frac{13}{17}b+\frac{1}{3}x-\frac{13}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p+\frac{-4}{3})(\frac{5}{6}-x)& =(\color{red}{p}+\color{orange}{\frac{-4}{3}}).(\color{green}{-x}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{5}{6}p+\frac{4}{3}x-\frac{4}{3}.\frac{5}{6}& \text{Uitwerken } \\ & =-px+\frac{5}{6}p+\frac{4}{3}x-\frac{20}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{5}{6}p+\frac{4}{3}x-\frac{10}{9} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{15}{13}-q)(\frac{20}{6}+a)& =(\color{red}{-q}+\color{orange}{\frac{15}{13}}).(\color{green}{a}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{15}{13})} . \color{green}{(a)} + \color{orange}{(\frac{15}{13})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{10}{3}q+\frac{15}{13}a+\frac{15}{13}.\frac{10}{3}& \text{Uitwerken } \\ & =-aq-\frac{10}{3}q+\frac{15}{13}a+\frac{150}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{10}{3}q+\frac{15}{13}a+\frac{50}{13} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(x+\frac{15}{7})(\frac{-9}{15}+a)& =(\color{red}{x}+\color{orange}{\frac{15}{7}}).(\color{green}{a}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{15}{7})} . \color{green}{(a)} + \color{orange}{(\frac{15}{7})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{3}{5}x+\frac{15}{7}a-\frac{15}{7}.\frac{3}{5}& \text{Uitwerken } \\ & =ax-\frac{3}{5}x+\frac{15}{7}a-\frac{45}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{3}{5}x+\frac{15}{7}a-\frac{9}{7} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-6}{8}-b)(a+\frac{6}{15})& =(\color{red}{-b}+\color{orange}{\frac{-3}{4}}).(\color{green}{a}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{2}{5}b-\frac{3}{4}a-\frac{3}{4}.\frac{2}{5}& \text{Uitwerken } \\ & =-ab-\frac{2}{5}b-\frac{3}{4}a-\frac{6}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{2}{5}b-\frac{3}{4}a-\frac{3}{10} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(a-\frac{6}{3})(\frac{7}{2}-p)& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{-p}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(-2)} . \color{green}{(-p)} + \color{orange}{(-2)} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{7}{2}a+2p-2.\frac{7}{2}& \text{Uitwerken } \\ & =-ap+\frac{7}{2}a+2p-\frac{14}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{7}{2}a+2p-7 & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{6}{15}+p)(q-\frac{10}{5})& =(\color{red}{p}+\color{orange}{\frac{2}{5}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{2}{5})} . \color{green}{(q)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pq-2p+\frac{2}{5}q-\frac{2}{5}.2& \text{Uitwerken } \\ & =pq-2p+\frac{2}{5}q-\frac{4}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{14}{20}-a)(b-\frac{3}{4})& =(\color{red}{-a}+\color{orange}{\frac{7}{10}}).(\color{green}{b}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{7}{10})} . \color{green}{(b)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{3}{4}a+\frac{7}{10}b-\frac{7}{10}.\frac{3}{4}& \text{Uitwerken } \\ & =-ab+\frac{3}{4}a+\frac{7}{10}b-\frac{21}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(a+\frac{1}{2})(\frac{7}{19}-b)& =(\color{red}{a}+\color{orange}{\frac{1}{2}}).(\color{green}{-b}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{7}{19}a-\frac{1}{2}b+\frac{1}{2}.\frac{7}{19}& \text{Uitwerken } \\ & =-ab+\frac{7}{19}a-\frac{1}{2}b+\frac{7}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x+(-18))(q-\frac{-4}{11})& =(\color{red}{x}+\color{orange}{(-18)}).(\color{green}{q}+\color{blue}{\frac{4}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{4}{11})} + \color{orange}{(-18)} . \color{green}{(q)} + \color{orange}{(-18)} . \color{blue}{(\frac{4}{11})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{4}{11}x-18q-18.\frac{4}{11}& \text{Uitwerken } \\ & =qx+\frac{4}{11}x-18q-\frac{72}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p-\frac{14}{18})(\frac{6}{5}+p)& =(\color{red}{p}+\color{orange}{\frac{-7}{9}}).(\color{green}{p}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{6}{5}p-\frac{7}{9}p-\frac{7}{9}.\frac{6}{5}& \text{Uitwerken } \\ & =p^2+(\frac{6}{5}+(\frac{-7}{9}))p-(\frac{-42}{45}) & \text{Neem samen} \\ &=p^2+\frac{19}{45}p-(\frac{-42}{45}) & \text{Maak de som} \\ &=p^2+\frac{19}{45}p+\frac{14}{15} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{-12}{11}+p)(\frac{8}{16}+a)& =(\color{red}{p}+\color{orange}{\frac{-12}{11}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-12}{11})} . \color{green}{(a)} + \color{orange}{(\frac{-12}{11})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{2}p-\frac{12}{11}a-\frac{12}{11}.\frac{1}{2}& \text{Uitwerken } \\ & =ap+\frac{1}{2}p-\frac{12}{11}a-\frac{12}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{1}{2}p-\frac{12}{11}a-\frac{6}{11} & \text{Vereenvoudig} \\\end{align}\)
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