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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p+\frac{3}{10})(\frac{-1}{16}+a)& =(\color{red}{p}+\color{orange}{\frac{3}{10}}).(\color{green}{a}+\color{blue}{\frac{-1}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{16})} + \color{orange}{(\frac{3}{10})} . \color{green}{(a)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-1}{16})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{16}p+\frac{3}{10}a-\frac{3}{10}.\frac{1}{16}& \text{Uitwerken } \\ & =ap-\frac{1}{16}p+\frac{3}{10}a-\frac{3}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  2. \(\begin{align}(\frac{11}{12}-x)(x+\frac{-10}{11})& =(\color{red}{-x}+\color{orange}{\frac{11}{12}}).(\color{green}{x}+\color{blue}{\frac{-10}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-10}{11})} + \color{orange}{(\frac{11}{12})} . \color{green}{(x)} + \color{orange}{(\frac{11}{12})} . \color{blue}{(\frac{-10}{11})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{10}{11}x+\frac{11}{12}x-\frac{11}{12}.\frac{10}{11}& \text{Uitwerken } \\ & =-x^2+(\frac{10}{11}+\frac{11}{12})x-\frac{110}{132} & \text{Neem samen} \\ &=-x^2+\frac{241}{132}x-\frac{110}{132} & \text{Maak de som} \\ &=-x^2+\frac{241}{132}x-\frac{5}{6} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(\frac{18}{6}+p)(b-\frac{-2}{10})& =(\color{red}{p}+\color{orange}{3}).(\color{green}{b}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{5}p+3b+3.\frac{1}{5}& \text{Uitwerken } \\ & =bp+\frac{1}{5}p+3b+\frac{3}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-18}{8}+a)(p-1)& =(\color{red}{a}+\color{orange}{\frac{-9}{4}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-9}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ap-1a-\frac{9}{4}p+\frac{9}{4}.1& \text{Uitwerken } \\ & =ap-1a-\frac{9}{4}p+\frac{9}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{5}{11}+p)(\frac{-2}{2}+q)& =(\color{red}{p}+\color{orange}{\frac{5}{11}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{5}{11})} . \color{green}{(q)} + \color{orange}{(\frac{5}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq-1p+\frac{5}{11}q-\frac{5}{11}.1& \text{Uitwerken } \\ & =pq-1p+\frac{5}{11}q-\frac{5}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(a-\frac{-20}{14})(a+\frac{-20}{7})& =(\color{red}{a}+\color{orange}{\frac{10}{7}}).(\color{green}{a}+\color{blue}{\frac{-20}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{7})} + \color{orange}{(\frac{10}{7})} . \color{green}{(a)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{-20}{7})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{20}{7}a+\frac{10}{7}a-\frac{10}{7}.\frac{20}{7}& \text{Uitwerken } \\ & =a^2+((\frac{-20}{7})+\frac{10}{7})a-(\frac{-200}{49}) & \text{Neem samen} \\ &=a^2-\frac{10}{7}a-(\frac{-200}{49}) & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(x-\frac{3}{6})(\frac{9}{20}-b)& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{-b}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{9}{20}x+\frac{1}{2}b-\frac{1}{2}.\frac{9}{20}& \text{Uitwerken } \\ & =-bx+\frac{9}{20}x+\frac{1}{2}b-\frac{9}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{16}{9}+b)(\frac{-12}{20}+p)& =(\color{red}{b}+\color{orange}{\frac{16}{9}}).(\color{green}{p}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{16}{9})} . \color{green}{(p)} + \color{orange}{(\frac{16}{9})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{5}b+\frac{16}{9}p-\frac{16}{9}.\frac{3}{5}& \text{Uitwerken } \\ & =bp-\frac{3}{5}b+\frac{16}{9}p-\frac{48}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{3}{5}b+\frac{16}{9}p-\frac{16}{15} & \text{Vereenvoudig} \\\end{align}\)
  9. \(\begin{align}(b+\frac{-1}{17})(b-\frac{-3}{9})& =(\color{red}{b}+\color{orange}{\frac{-1}{17}}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-1}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{3}b-\frac{1}{17}b-\frac{1}{17}.\frac{1}{3}& \text{Uitwerken } \\ & =b^2+(\frac{1}{3}+(\frac{-1}{17}))b-(\frac{-1}{51}) & \text{Neem samen} \\ &=b^2+\frac{14}{51}b-(\frac{-1}{51}) & \text{Maak de som} \\\end{align}\)
  10. \(\begin{align}(p-\frac{14}{6})(q-\frac{-20}{11})& =(\color{red}{p}+\color{orange}{\frac{-7}{3}}).(\color{green}{q}+\color{blue}{\frac{20}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{20}{11})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{20}{11})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{20}{11}p-\frac{7}{3}q-\frac{7}{3}.\frac{20}{11}& \text{Uitwerken } \\ & =pq+\frac{20}{11}p-\frac{7}{3}q-\frac{140}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  11. \(\begin{align}(q+\frac{12}{3})(x+\frac{15}{10})& =(\color{red}{q}+\color{orange}{4}).(\color{green}{x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(4)} . \color{green}{(x)} + \color{orange}{(4)} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{2}q+4x+4.\frac{3}{2}& \text{Uitwerken } \\ & =qx+\frac{3}{2}q+4x+\frac{12}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{3}{2}q+4x+6 & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-14}{8}-b)(\frac{15}{8}+b)& =(\color{red}{-b}+\color{orange}{\frac{-7}{4}}).(\color{green}{b}+\color{blue}{\frac{15}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{15}{8})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{15}{8})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{15}{8}b-\frac{7}{4}b-\frac{7}{4}.\frac{15}{8}& \text{Uitwerken } \\ & =-b^2+((\frac{-15}{8})+(\frac{-7}{4}))b-\frac{105}{32} & \text{Neem samen} \\ &=-b^2-\frac{29}{8}b-\frac{105}{32} & \text{Maak de som} \\\end{align}\)
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