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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{15}{5}-b)(a+\frac{19}{19})& =(\color{red}{-b}+\color{orange}{3}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(1)} + \color{orange}{(3)} . \color{green}{(a)} + \color{orange}{(3)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -ab-1b+3a+3.1& \text{Uitwerken } \\ & =-ab-1b+3a+3 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{4}{17})(p-\frac{13}{8})& =(\color{red}{p}+\color{orange}{\frac{-4}{17}}).(\color{green}{p}+\color{blue}{\frac{-13}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{8})} + \color{orange}{(\frac{-4}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{17})} . \color{blue}{(\frac{-13}{8})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{13}{8}p-\frac{4}{17}p+\frac{4}{17}.\frac{13}{8}& \text{Uitwerken } \\ & =p^2+((\frac{-13}{8})+(\frac{-4}{17}))p+\frac{52}{136} & \text{Neem samen} \\ &=p^2-\frac{253}{136}p+\frac{52}{136} & \text{Maak de som} \\ &=p^2-\frac{253}{136}p+\frac{13}{34} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{2}{6}-b)(\frac{-18}{17}+a)& =(\color{red}{-b}+\color{orange}{\frac{1}{3}}).(\color{green}{a}+\color{blue}{\frac{-18}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-18}{17})} + \color{orange}{(\frac{1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-18}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{18}{17}b+\frac{1}{3}a-\frac{1}{3}.\frac{18}{17}& \text{Uitwerken } \\ & =-ab+\frac{18}{17}b+\frac{1}{3}a-\frac{18}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{18}{17}b+\frac{1}{3}a-\frac{6}{17} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(\frac{-9}{17}+p)(\frac{-13}{16}-x)& =(\color{red}{p}+\color{orange}{\frac{-9}{17}}).(\color{green}{-x}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(\frac{-9}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-9}{17})} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{13}{16}p+\frac{9}{17}x+\frac{9}{17}.\frac{13}{16}& \text{Uitwerken } \\ & =-px-\frac{13}{16}p+\frac{9}{17}x+\frac{117}{272} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{-2}{15}-q)(\frac{-3}{5}+p)& =(\color{red}{-q}+\color{orange}{\frac{-2}{15}}).(\color{green}{p}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-2}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{15})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{3}{5}q-\frac{2}{15}p+\frac{2}{15}.\frac{3}{5}& \text{Uitwerken } \\ & =-pq+\frac{3}{5}q-\frac{2}{15}p+\frac{6}{75} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{3}{5}q-\frac{2}{15}p+\frac{2}{25} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-6}{3}-b)(b-\frac{14}{6})& =(\color{red}{-b}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{7}{3}b-2b+2.\frac{7}{3}& \text{Uitwerken } \\ & =-b^2+(\frac{7}{3}+(-2))b+(\frac{-14}{3}) & \text{Neem samen} \\ &=-b^2+\frac{1}{3}b+(\frac{-14}{3}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(b-\frac{15}{19})(\frac{6}{19}+x)& =(\color{red}{b}+\color{orange}{\frac{-15}{19}}).(\color{green}{x}+\color{blue}{\frac{6}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{6}{19})} + \color{orange}{(\frac{-15}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{19})} . \color{blue}{(\frac{6}{19})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{6}{19}b-\frac{15}{19}x-\frac{15}{19}.\frac{6}{19}& \text{Uitwerken } \\ & =bx+\frac{6}{19}b-\frac{15}{19}x-\frac{90}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(b-\frac{4}{7})(\frac{2}{2}+p)& =(\color{red}{b}+\color{orange}{\frac{-4}{7}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-4}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp+1b-\frac{4}{7}p-\frac{4}{7}.1& \text{Uitwerken } \\ & =bp+1b-\frac{4}{7}p-\frac{4}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(q+\frac{7}{16})(\frac{-1}{17}-a)& =(\color{red}{q}+\color{orange}{\frac{7}{16}}).(\color{green}{-a}+\color{blue}{\frac{-1}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{17})} + \color{orange}{(\frac{7}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(\frac{-1}{17})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{17}q-\frac{7}{16}a-\frac{7}{16}.\frac{1}{17}& \text{Uitwerken } \\ & =-aq-\frac{1}{17}q-\frac{7}{16}a-\frac{7}{272} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{11}{12}-x)(\frac{2}{16}-p)& =(\color{red}{-x}+\color{orange}{\frac{11}{12}}).(\color{green}{-p}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{11}{12})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{12})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{8}x-\frac{11}{12}p+\frac{11}{12}.\frac{1}{8}& \text{Uitwerken } \\ & =px-\frac{1}{8}x-\frac{11}{12}p+\frac{11}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{-2}{4}-p)(a-\frac{-9}{19})& =(\color{red}{-p}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{9}{19}p-\frac{1}{2}a-\frac{1}{2}.\frac{9}{19}& \text{Uitwerken } \\ & =-ap-\frac{9}{19}p-\frac{1}{2}a-\frac{9}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(a+\frac{12}{10})(\frac{-20}{16}-x)& =(\color{red}{a}+\color{orange}{\frac{6}{5}}).(\color{green}{-x}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{6}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{5}{4}a-\frac{6}{5}x-\frac{6}{5}.\frac{5}{4}& \text{Uitwerken } \\ & =-ax-\frac{5}{4}a-\frac{6}{5}x-\frac{30}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{5}{4}a-\frac{6}{5}x-\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
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