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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(x-\frac{4}{6})(a-19)& =(\color{red}{x}+\color{orange}{\frac{-2}{3}}).(\color{green}{a}+\color{blue}{(-19)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-19)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = ax-19x-\frac{2}{3}a+\frac{2}{3}.19& \text{Uitwerken } \\ & =ax-19x-\frac{2}{3}a+\frac{38}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{15}{9}-a)(\frac{-9}{5}+p)& =(\color{red}{-a}+\color{orange}{\frac{5}{3}}).(\color{green}{p}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{9}{5}a+\frac{5}{3}p-\frac{5}{3}.\frac{9}{5}& \text{Uitwerken } \\ & =-ap+\frac{9}{5}a+\frac{5}{3}p-\frac{45}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{9}{5}a+\frac{5}{3}p-3 & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(a+\frac{-8}{9})(\frac{9}{4}-q)& =(\color{red}{a}+\color{orange}{\frac{-8}{9}}).(\color{green}{-q}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{9}{4}a+\frac{8}{9}q-\frac{8}{9}.\frac{9}{4}& \text{Uitwerken } \\ & =-aq+\frac{9}{4}a+\frac{8}{9}q-\frac{72}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{9}{4}a+\frac{8}{9}q-2 & \text{Vereenvoudig} \\\end{align}\)
  4. \(\begin{align}(a-\frac{20}{6})(p+\frac{-15}{20})& =(\color{red}{a}+\color{orange}{\frac{-10}{3}}).(\color{green}{p}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{4}a-\frac{10}{3}p+\frac{10}{3}.\frac{3}{4}& \text{Uitwerken } \\ & =ap-\frac{3}{4}a-\frac{10}{3}p+\frac{30}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{3}{4}a-\frac{10}{3}p+\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-7}{6}+a)(b+\frac{18}{4})& =(\color{red}{a}+\color{orange}{\frac{-7}{6}}).(\color{green}{b}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{9}{2}a-\frac{7}{6}b-\frac{7}{6}.\frac{9}{2}& \text{Uitwerken } \\ & =ab+\frac{9}{2}a-\frac{7}{6}b-\frac{63}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{9}{2}a-\frac{7}{6}b-\frac{21}{4} & \text{Vereenvoudig} \\\end{align}\)
  6. \(\begin{align}(\frac{-17}{4}-b)(b-\frac{-14}{6})& =(\color{red}{-b}+\color{orange}{\frac{-17}{4}}).(\color{green}{b}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{-17}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{4})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{7}{3}b-\frac{17}{4}b-\frac{17}{4}.\frac{7}{3}& \text{Uitwerken } \\ & =-b^2+((\frac{-7}{3})+(\frac{-17}{4}))b-\frac{119}{12} & \text{Neem samen} \\ &=-b^2-\frac{79}{12}b-\frac{119}{12} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(q-\frac{-10}{12})(\frac{16}{7}+p)& =(\color{red}{q}+\color{orange}{\frac{5}{6}}).(\color{green}{p}+\color{blue}{\frac{16}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{16}{7})} + \color{orange}{(\frac{5}{6})} . \color{green}{(p)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{16}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{16}{7}q+\frac{5}{6}p+\frac{5}{6}.\frac{16}{7}& \text{Uitwerken } \\ & =pq+\frac{16}{7}q+\frac{5}{6}p+\frac{80}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{16}{7}q+\frac{5}{6}p+\frac{40}{21} & \text{Vereenvoudig} \\\end{align}\)
  8. \(\begin{align}(\frac{-19}{19}+q)(\frac{-13}{2}-a)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{-a}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(-1)} . \color{green}{(-a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{13}{2}q+1a+1.\frac{13}{2}& \text{Uitwerken } \\ & =-aq-\frac{13}{2}q+1a+\frac{13}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p-\frac{2}{2})(x-\frac{3}{3})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1p-1x+1.1& \text{Uitwerken } \\ & =px-1p-1x+1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{15}{5}-x)(b-\frac{13}{2})& =(\color{red}{-x}+\color{orange}{3}).(\color{green}{b}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{13}{2}x+3b-3.\frac{13}{2}& \text{Uitwerken } \\ & =-bx+\frac{13}{2}x+3b-\frac{39}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(p+\frac{12}{17})(\frac{4}{9}-q)& =(\color{red}{p}+\color{orange}{\frac{12}{17}}).(\color{green}{-q}+\color{blue}{\frac{4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{4}{9})} + \color{orange}{(\frac{12}{17})} . \color{green}{(-q)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{4}{9})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{4}{9}p-\frac{12}{17}q+\frac{12}{17}.\frac{4}{9}& \text{Uitwerken } \\ & =-pq+\frac{4}{9}p-\frac{12}{17}q+\frac{48}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{4}{9}p-\frac{12}{17}q+\frac{16}{51} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(x-\frac{-9}{3})(a-\frac{8}{17})& =(\color{red}{x}+\color{orange}{3}).(\color{green}{a}+\color{blue}{\frac{-8}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{17})} + \color{orange}{(3)} . \color{green}{(a)} + \color{orange}{(3)} . \color{blue}{(\frac{-8}{17})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{8}{17}x+3a-3.\frac{8}{17}& \text{Uitwerken } \\ & =ax-\frac{8}{17}x+3a-\frac{24}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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