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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{-1}{19})(b+\frac{12}{4})& =(\color{red}{p}+\color{orange}{\frac{1}{19}}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(\frac{1}{19})} . \color{green}{(b)} + \color{orange}{(\frac{1}{19})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bp+3p+\frac{1}{19}b+\frac{1}{19}.3& \text{Uitwerken } \\ & =bp+3p+\frac{1}{19}b+\frac{3}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{15}+b)(x-\frac{-15}{14})& =(\color{red}{b}+\color{orange}{\frac{8}{15}}).(\color{green}{x}+\color{blue}{\frac{15}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{15}{14})} + \color{orange}{(\frac{8}{15})} . \color{green}{(x)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(\frac{15}{14})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{15}{14}b+\frac{8}{15}x+\frac{8}{15}.\frac{15}{14}& \text{Uitwerken } \\ & =bx+\frac{15}{14}b+\frac{8}{15}x+\frac{120}{210} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{15}{14}b+\frac{8}{15}x+\frac{4}{7} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(b+10)(\frac{-16}{15}-x)& =(\color{red}{b}+\color{orange}{10}).(\color{green}{-x}+\color{blue}{\frac{-16}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{15})} + \color{orange}{(10)} . \color{green}{(-x)} + \color{orange}{(10)} . \color{blue}{(\frac{-16}{15})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{16}{15}b-10x-10.\frac{16}{15}& \text{Uitwerken } \\ & =-bx-\frac{16}{15}b-10x-\frac{160}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{16}{15}b-10x-\frac{32}{3} & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(b-\frac{13}{7})(x-\frac{5}{16})& =(\color{red}{b}+\color{orange}{\frac{-13}{7}}).(\color{green}{x}+\color{blue}{\frac{-5}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{16})} + \color{orange}{(\frac{-13}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{7})} . \color{blue}{(\frac{-5}{16})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{5}{16}b-\frac{13}{7}x+\frac{13}{7}.\frac{5}{16}& \text{Uitwerken } \\ & =bx-\frac{5}{16}b-\frac{13}{7}x+\frac{65}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{9}{15}-x)(x+\frac{-12}{16})& =(\color{red}{-x}+\color{orange}{\frac{3}{5}}).(\color{green}{x}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{3}{5})} . \color{green}{(x)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{3}{4}x+\frac{3}{5}x-\frac{3}{5}.\frac{3}{4}& \text{Uitwerken } \\ & =-x^2+(\frac{3}{4}+\frac{3}{5})x-\frac{9}{20} & \text{Neem samen} \\ &=-x^2+\frac{27}{20}x-\frac{9}{20} & \text{Maak de som} \\\end{align}\)
  6. \(\begin{align}(q+\frac{-8}{18})(\frac{20}{14}+p)& =(\color{red}{q}+\color{orange}{\frac{-4}{9}}).(\color{green}{p}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{10}{7}q-\frac{4}{9}p-\frac{4}{9}.\frac{10}{7}& \text{Uitwerken } \\ & =pq+\frac{10}{7}q-\frac{4}{9}p-\frac{40}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{4}{7}-p)(\frac{3}{19}+x)& =(\color{red}{-p}+\color{orange}{\frac{4}{7}}).(\color{green}{x}+\color{blue}{\frac{3}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{3}{19})} + \color{orange}{(\frac{4}{7})} . \color{green}{(x)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{3}{19})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{3}{19}p+\frac{4}{7}x+\frac{4}{7}.\frac{3}{19}& \text{Uitwerken } \\ & =-px-\frac{3}{19}p+\frac{4}{7}x+\frac{12}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{-14}{10}-b)(a+\frac{-4}{8})& =(\color{red}{-b}+\color{orange}{\frac{-7}{5}}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{2}b-\frac{7}{5}a+\frac{7}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =-ab+\frac{1}{2}b-\frac{7}{5}a+\frac{7}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-16}{18}-q)(\frac{-19}{18}+x)& =(\color{red}{-q}+\color{orange}{\frac{-8}{9}}).(\color{green}{x}+\color{blue}{\frac{-19}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-19}{18})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{-19}{18})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{19}{18}q-\frac{8}{9}x+\frac{8}{9}.\frac{19}{18}& \text{Uitwerken } \\ & =-qx+\frac{19}{18}q-\frac{8}{9}x+\frac{152}{162} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx+\frac{19}{18}q-\frac{8}{9}x+\frac{76}{81} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(\frac{-20}{18}-b)(\frac{20}{2}-b)& =(\color{red}{-b}+\color{orange}{\frac{-10}{9}}).(\color{green}{-b}+\color{blue}{10})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(10)} + \color{orange}{(\frac{-10}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = bb-10b+\frac{10}{9}b-\frac{10}{9}.10& \text{Uitwerken } \\ & =b^2+((-10)+\frac{10}{9})b-(\frac{-100}{9}) & \text{Neem samen} \\ &=b^2-\frac{80}{9}b-(\frac{-100}{9}) & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(b-\frac{-15}{10})(a-\frac{9}{2})& =(\color{red}{b}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{9}{2}b+\frac{3}{2}a-\frac{3}{2}.\frac{9}{2}& \text{Uitwerken } \\ & =ab-\frac{9}{2}b+\frac{3}{2}a-\frac{27}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(b+\frac{-18}{6})(a-\frac{-12}{20})& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{a}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(-3)} . \color{green}{(a)} + \color{orange}{(-3)} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{5}b-3a-3.\frac{3}{5}& \text{Uitwerken } \\ & =ab+\frac{3}{5}b-3a-\frac{9}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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