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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{19}{18}-a)(\frac{-13}{2}-b)& =(\color{red}{-a}+\color{orange}{\frac{19}{18}}).(\color{green}{-b}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(\frac{19}{18})} . \color{green}{(-b)} + \color{orange}{(\frac{19}{18})} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{13}{2}a-\frac{19}{18}b-\frac{19}{18}.\frac{13}{2}& \text{Uitwerken } \\ & =ab+\frac{13}{2}a-\frac{19}{18}b-\frac{247}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{13}{15}-p)(a+\frac{-6}{16})& =(\color{red}{-p}+\color{orange}{\frac{13}{15}}).(\color{green}{a}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{13}{15})} . \color{green}{(a)} + \color{orange}{(\frac{13}{15})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{3}{8}p+\frac{13}{15}a-\frac{13}{15}.\frac{3}{8}& \text{Uitwerken } \\ & =-ap+\frac{3}{8}p+\frac{13}{15}a-\frac{39}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{3}{8}p+\frac{13}{15}a-\frac{13}{40} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(\frac{-4}{7}-x)(x-\frac{14}{4})& =(\color{red}{-x}+\color{orange}{\frac{-4}{7}}).(\color{green}{x}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{7}{2}x-\frac{4}{7}x+\frac{4}{7}.\frac{7}{2}& \text{Uitwerken } \\ & =-x^2+(\frac{7}{2}+(\frac{-4}{7}))x+(\frac{-28}{14}) & \text{Neem samen} \\ &=-x^2+\frac{41}{14}x+(\frac{-28}{14}) & \text{Maak de som} \\ &=-x^2+\frac{41}{14}x+(-2) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(p+\frac{-15}{4})(b-\frac{-10}{15})& =(\color{red}{p}+\color{orange}{\frac{-15}{4}}).(\color{green}{b}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{3}p-\frac{15}{4}b-\frac{15}{4}.\frac{2}{3}& \text{Uitwerken } \\ & =bp+\frac{2}{3}p-\frac{15}{4}b-\frac{30}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{2}{3}p-\frac{15}{4}b-\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(p-\frac{5}{3})(\frac{19}{12}-q)& =(\color{red}{p}+\color{orange}{\frac{-5}{3}}).(\color{green}{-q}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{19}{12}p+\frac{5}{3}q-\frac{5}{3}.\frac{19}{12}& \text{Uitwerken } \\ & =-pq+\frac{19}{12}p+\frac{5}{3}q-\frac{95}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{6}{2}-b)(\frac{1}{4}-a)& =(\color{red}{-b}+\color{orange}{3}).(\color{green}{-a}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(3)} . \color{green}{(-a)} + \color{orange}{(3)} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{4}b-3a+3.\frac{1}{4}& \text{Uitwerken } \\ & =ab-\frac{1}{4}b-3a+\frac{3}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(x-\frac{-8}{2})(\frac{-5}{14}+q)& =(\color{red}{x}+\color{orange}{4}).(\color{green}{q}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(4)} . \color{green}{(q)} + \color{orange}{(4)} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{14}x+4q-4.\frac{5}{14}& \text{Uitwerken } \\ & =qx-\frac{5}{14}x+4q-\frac{20}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{5}{14}x+4q-\frac{10}{7} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{15}{15}-a)(\frac{11}{9}+p)& =(\color{red}{-a}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{11}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{9})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{11}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{11}{9}a+1p+1.\frac{11}{9}& \text{Uitwerken } \\ & =-ap-\frac{11}{9}a+1p+\frac{11}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{14}{19}-x)(\frac{14}{6}-b)& =(\color{red}{-x}+\color{orange}{\frac{14}{19}}).(\color{green}{-b}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{14}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{14}{19})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{7}{3}x-\frac{14}{19}b+\frac{14}{19}.\frac{7}{3}& \text{Uitwerken } \\ & =bx-\frac{7}{3}x-\frac{14}{19}b+\frac{98}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(x+\frac{-15}{11})(\frac{-14}{10}+x)& =(\color{red}{x}+\color{orange}{\frac{-15}{11}}).(\color{green}{x}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{7}{5}x-\frac{15}{11}x+\frac{15}{11}.\frac{7}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-7}{5})+(\frac{-15}{11}))x+\frac{105}{55} & \text{Neem samen} \\ &=x^2-\frac{152}{55}x+\frac{105}{55} & \text{Maak de som} \\ &=x^2-\frac{152}{55}x+\frac{21}{11} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  11. \(\begin{align}(p+\frac{13}{20})(a+\frac{-9}{15})& =(\color{red}{p}+\color{orange}{\frac{13}{20}}).(\color{green}{a}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{13}{20})} . \color{green}{(a)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{5}p+\frac{13}{20}a-\frac{13}{20}.\frac{3}{5}& \text{Uitwerken } \\ & =ap-\frac{3}{5}p+\frac{13}{20}a-\frac{39}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{4}{19}+q)(q+\frac{-14}{5})& =(\color{red}{q}+\color{orange}{\frac{4}{19}}).(\color{green}{q}+\color{blue}{\frac{-14}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-14}{5})} + \color{orange}{(\frac{4}{19})} . \color{green}{(q)} + \color{orange}{(\frac{4}{19})} . \color{blue}{(\frac{-14}{5})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{14}{5}q+\frac{4}{19}q-\frac{4}{19}.\frac{14}{5}& \text{Uitwerken } \\ & =q^2+((\frac{-14}{5})+\frac{4}{19})q-(\frac{-56}{95}) & \text{Neem samen} \\ &=q^2-\frac{246}{95}q-(\frac{-56}{95}) & \text{Maak de som} \\\end{align}\)
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