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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{7}{14}+x)(p-\frac{-5}{4})& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{4}x+\frac{1}{2}p+\frac{1}{2}.\frac{5}{4}& \text{Uitwerken } \\ & =px+\frac{5}{4}x+\frac{1}{2}p+\frac{5}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{-6}{7})(\frac{6}{17}-x)& =(\color{red}{p}+\color{orange}{\frac{6}{7}}).(\color{green}{-x}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(\frac{6}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{6}{17}p-\frac{6}{7}x+\frac{6}{7}.\frac{6}{17}& \text{Uitwerken } \\ & =-px+\frac{6}{17}p-\frac{6}{7}x+\frac{36}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{5}{15}-b)(\frac{-20}{14}-x)& =(\color{red}{-b}+\color{orange}{\frac{1}{3}}).(\color{green}{-x}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{10}{7}b-\frac{1}{3}x-\frac{1}{3}.\frac{10}{7}& \text{Uitwerken } \\ & =bx+\frac{10}{7}b-\frac{1}{3}x-\frac{10}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{2}{5})(b-\frac{-8}{9})& =(\color{red}{q}+\color{orange}{\frac{2}{5}}).(\color{green}{b}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{8}{9}q+\frac{2}{5}b+\frac{2}{5}.\frac{8}{9}& \text{Uitwerken } \\ & =bq+\frac{8}{9}q+\frac{2}{5}b+\frac{16}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{10}{11}+b)(\frac{12}{4}-p)& =(\color{red}{b}+\color{orange}{\frac{10}{11}}).(\color{green}{-p}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(3)} + \color{orange}{(\frac{10}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{10}{11})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -bp+3b-\frac{10}{11}p+\frac{10}{11}.3& \text{Uitwerken } \\ & =-bp+3b-\frac{10}{11}p+\frac{30}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-10}{19}-a)(\frac{-16}{15}-p)& =(\color{red}{-a}+\color{orange}{\frac{-10}{19}}).(\color{green}{-p}+\color{blue}{\frac{-16}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-p)} + \color{red}{(-a)} . \color{blue}{(\frac{-16}{15})} + \color{orange}{(\frac{-10}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{-10}{19})} . \color{blue}{(\frac{-16}{15})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{16}{15}a+\frac{10}{19}p+\frac{10}{19}.\frac{16}{15}& \text{Uitwerken } \\ & =ap+\frac{16}{15}a+\frac{10}{19}p+\frac{160}{285} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{16}{15}a+\frac{10}{19}p+\frac{32}{57} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}(\frac{-9}{8}-b)(x+\frac{-15}{2})& =(\color{red}{-b}+\color{orange}{\frac{-9}{8}}).(\color{green}{x}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{15}{2}b-\frac{9}{8}x+\frac{9}{8}.\frac{15}{2}& \text{Uitwerken } \\ & =-bx+\frac{15}{2}b-\frac{9}{8}x+\frac{135}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{15}{20}-x)(11-x)& =(\color{red}{-x}+\color{orange}{\frac{3}{4}}).(\color{green}{-x}+\color{blue}{11})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(11)} + \color{orange}{(\frac{3}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = xx-11x-\frac{3}{4}x+\frac{3}{4}.11& \text{Uitwerken } \\ & =x^2+((-11)+(\frac{-3}{4}))x+\frac{33}{4} & \text{Neem samen} \\ &=x^2-\frac{47}{4}x+\frac{33}{4} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(\frac{-2}{17}+a)(a-\frac{20}{16})& =(\color{red}{a}+\color{orange}{\frac{-2}{17}}).(\color{green}{a}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-2}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{17})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{5}{4}a-\frac{2}{17}a+\frac{2}{17}.\frac{5}{4}& \text{Uitwerken } \\ & =a^2+((\frac{-5}{4})+(\frac{-2}{17}))a+\frac{10}{68} & \text{Neem samen} \\ &=a^2-\frac{93}{68}a+\frac{10}{68} & \text{Maak de som} \\ &=a^2-\frac{93}{68}a+\frac{5}{34} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  10. \(\begin{align}(q+\frac{3}{19})(p-\frac{-18}{17})& =(\color{red}{q}+\color{orange}{\frac{3}{19}}).(\color{green}{p}+\color{blue}{\frac{18}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{18}{17})} + \color{orange}{(\frac{3}{19})} . \color{green}{(p)} + \color{orange}{(\frac{3}{19})} . \color{blue}{(\frac{18}{17})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{18}{17}q+\frac{3}{19}p+\frac{3}{19}.\frac{18}{17}& \text{Uitwerken } \\ & =pq+\frac{18}{17}q+\frac{3}{19}p+\frac{54}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(\frac{10}{16}+a)(\frac{-16}{15}+a)& =(\color{red}{a}+\color{orange}{\frac{5}{8}}).(\color{green}{a}+\color{blue}{\frac{-16}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{15})} + \color{orange}{(\frac{5}{8})} . \color{green}{(a)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(\frac{-16}{15})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{16}{15}a+\frac{5}{8}a-\frac{5}{8}.\frac{16}{15}& \text{Uitwerken } \\ & =a^2+((\frac{-16}{15})+\frac{5}{8})a-(\frac{-80}{120}) & \text{Neem samen} \\ &=a^2-\frac{53}{120}a-(\frac{-80}{120}) & \text{Maak de som} \\ &=a^2-\frac{53}{120}a+\frac{2}{3} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  12. \(\begin{align}(\frac{-18}{15}-b)(\frac{-15}{20}-p)& =(\color{red}{-b}+\color{orange}{\frac{-6}{5}}).(\color{green}{-p}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{4}b+\frac{6}{5}p+\frac{6}{5}.\frac{3}{4}& \text{Uitwerken } \\ & =bp+\frac{3}{4}b+\frac{6}{5}p+\frac{18}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{3}{4}b+\frac{6}{5}p+\frac{9}{10} & \text{Vereenvoudig} \\\end{align}\)
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