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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{5}{14})(\frac{11}{16}-a)& =(\color{red}{p}+\color{orange}{\frac{5}{14}}).(\color{green}{-a}+\color{blue}{\frac{11}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{11}{16})} + \color{orange}{(\frac{5}{14})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(\frac{11}{16})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{11}{16}p-\frac{5}{14}a+\frac{5}{14}.\frac{11}{16}& \text{Uitwerken } \\ & =-ap+\frac{11}{16}p-\frac{5}{14}a+\frac{55}{224} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(p-\frac{6}{9})(\frac{16}{12}+a)& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{4}{3}p-\frac{2}{3}a-\frac{2}{3}.\frac{4}{3}& \text{Uitwerken } \\ & =ap+\frac{4}{3}p-\frac{2}{3}a-\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(p-\frac{18}{9})(\frac{-2}{14}+x)& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{7}p-2x+2.\frac{1}{7}& \text{Uitwerken } \\ & =px-\frac{1}{7}p-2x+\frac{2}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(a+\frac{13}{18})(x+(-1))& =(\color{red}{a}+\color{orange}{\frac{13}{18}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{13}{18})} . \color{green}{(x)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1a+\frac{13}{18}x-\frac{13}{18}.1& \text{Uitwerken } \\ & =ax-1a+\frac{13}{18}x-\frac{13}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(a+\frac{12}{14})(\frac{-13}{18}-x)& =(\color{red}{a}+\color{orange}{\frac{6}{7}}).(\color{green}{-x}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(\frac{6}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{13}{18}a-\frac{6}{7}x-\frac{6}{7}.\frac{13}{18}& \text{Uitwerken } \\ & =-ax-\frac{13}{18}a-\frac{6}{7}x-\frac{78}{126} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{13}{18}a-\frac{6}{7}x-\frac{13}{21} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(x+\frac{-13}{14})(12+x)& =(\color{red}{x}+\color{orange}{\frac{-13}{14}}).(\color{green}{x}+\color{blue}{12})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(12)} + \color{orange}{(\frac{-13}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = xx+12x-\frac{13}{14}x-\frac{13}{14}.12& \text{Uitwerken } \\ & =x^2+(12+(\frac{-13}{14}))x-(\frac{-156}{14}) & \text{Neem samen} \\ &=x^2+\frac{155}{14}x-(\frac{-156}{14}) & \text{Maak de som} \\ &=x^2+\frac{155}{14}x+\frac{78}{7} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  7. \(\begin{align}(q+\frac{-18}{9})(\frac{1}{3}-p)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{-p}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(-2)} . \color{green}{(-p)} + \color{orange}{(-2)} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{3}q+2p-2.\frac{1}{3}& \text{Uitwerken } \\ & =-pq+\frac{1}{3}q+2p-\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-8}{19}+a)(\frac{6}{5}-q)& =(\color{red}{a}+\color{orange}{\frac{-8}{19}}).(\color{green}{-q}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-8}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-8}{19})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{6}{5}a+\frac{8}{19}q-\frac{8}{19}.\frac{6}{5}& \text{Uitwerken } \\ & =-aq+\frac{6}{5}a+\frac{8}{19}q-\frac{48}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(x+\frac{13}{13})(b-\frac{-13}{12})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{13}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{13}{12})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{13}{12})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{13}{12}x+1b+1.\frac{13}{12}& \text{Uitwerken } \\ & =bx+\frac{13}{12}x+1b+\frac{13}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{18}{20}+b)(b-\frac{20}{3})& =(\color{red}{b}+\color{orange}{\frac{9}{10}}).(\color{green}{b}+\color{blue}{\frac{-20}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{3})} + \color{orange}{(\frac{9}{10})} . \color{green}{(b)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{-20}{3})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{20}{3}b+\frac{9}{10}b-\frac{9}{10}.\frac{20}{3}& \text{Uitwerken } \\ & =b^2+((\frac{-20}{3})+\frac{9}{10})b-(\frac{-180}{30}) & \text{Neem samen} \\ &=b^2-\frac{173}{30}b-(\frac{-180}{30}) & \text{Maak de som} \\ &=b^2-\frac{173}{30}b+6 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
  11. \(\begin{align}(p+\frac{-8}{19})(a+\frac{-15}{17})& =(\color{red}{p}+\color{orange}{\frac{-8}{19}}).(\color{green}{a}+\color{blue}{\frac{-15}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{17})} + \color{orange}{(\frac{-8}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{19})} . \color{blue}{(\frac{-15}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{15}{17}p-\frac{8}{19}a+\frac{8}{19}.\frac{15}{17}& \text{Uitwerken } \\ & =ap-\frac{15}{17}p-\frac{8}{19}a+\frac{120}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{13}{16}+x)(q+\frac{6}{17})& =(\color{red}{x}+\color{orange}{\frac{13}{16}}).(\color{green}{q}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(\frac{13}{16})} . \color{green}{(q)} + \color{orange}{(\frac{13}{16})} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{6}{17}x+\frac{13}{16}q+\frac{13}{16}.\frac{6}{17}& \text{Uitwerken } \\ & =qx+\frac{6}{17}x+\frac{13}{16}q+\frac{78}{272} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{6}{17}x+\frac{13}{16}q+\frac{39}{136} & \text{Vereenvoudig} \\\end{align}\)
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