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

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Werk uit en vereenvoudig

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(p-\frac{11}{18})(x+10)& =(\color{red}{p}+\color{orange}{\frac{-11}{18}}).(\color{green}{x}+\color{blue}{10})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(10)} + \color{orange}{(\frac{-11}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{18})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = px+10p-\frac{11}{18}x-\frac{11}{18}.10& \text{Uitwerken } \\ & =px+10p-\frac{11}{18}x-\frac{110}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+10p-\frac{11}{18}x-\frac{55}{9} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-3}{2}+a)(\frac{-11}{15}-a)& =(\color{red}{a}+\color{orange}{\frac{-3}{2}}).(\color{green}{-a}+\color{blue}{\frac{-11}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{15})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-11}{15})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{11}{15}a+\frac{3}{2}a+\frac{3}{2}.\frac{11}{15}& \text{Uitwerken } \\ & =-a^2+((\frac{-11}{15})+\frac{3}{2})a+(\frac{-33}{30}) & \text{Neem samen} \\ &=-a^2+\frac{23}{30}a+(\frac{-33}{30}) & \text{Maak de som} \\ &=-a^2+\frac{23}{30}a+(\frac{-11}{10}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  3. \(\begin{align}(p-\frac{-1}{20})(x+\frac{-11}{4})& =(\color{red}{p}+\color{orange}{\frac{1}{20}}).(\color{green}{x}+\color{blue}{\frac{-11}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{4})} + \color{orange}{(\frac{1}{20})} . \color{green}{(x)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(\frac{-11}{4})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{11}{4}p+\frac{1}{20}x-\frac{1}{20}.\frac{11}{4}& \text{Uitwerken } \\ & =px-\frac{11}{4}p+\frac{1}{20}x-\frac{11}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(p-\frac{3}{9})(\frac{-6}{14}+p)& =(\color{red}{p}+\color{orange}{\frac{-1}{3}}).(\color{green}{p}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{3}{7}p-\frac{1}{3}p+\frac{1}{3}.\frac{3}{7}& \text{Uitwerken } \\ & =p^2+((\frac{-3}{7})+(\frac{-1}{3}))p+\frac{3}{21} & \text{Neem samen} \\ &=p^2-\frac{16}{21}p+\frac{3}{21} & \text{Maak de som} \\ &=p^2-\frac{16}{21}p+\frac{1}{7} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  5. \(\begin{align}(\frac{-1}{14}+p)(\frac{12}{4}-q)& =(\color{red}{p}+\color{orange}{\frac{-1}{14}}).(\color{green}{-q}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(\frac{-1}{14})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{14})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -pq+3p+\frac{1}{14}q-\frac{1}{14}.3& \text{Uitwerken } \\ & =-pq+3p+\frac{1}{14}q-\frac{3}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(\frac{-9}{10}+q)(b-\frac{-1}{6})& =(\color{red}{q}+\color{orange}{\frac{-9}{10}}).(\color{green}{b}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{6}q-\frac{9}{10}b-\frac{9}{10}.\frac{1}{6}& \text{Uitwerken } \\ & =bq+\frac{1}{6}q-\frac{9}{10}b-\frac{9}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{1}{6}q-\frac{9}{10}b-\frac{3}{20} & \text{Vereenvoudig} \\\end{align}\)
  7. \(\begin{align}((-7)+x)(\frac{4}{16}-x)& =(\color{red}{x}+\color{orange}{(-7)}).(\color{green}{-x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(-7)} . \color{green}{(-x)} + \color{orange}{(-7)} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{1}{4}x+7x-7.\frac{1}{4}& \text{Uitwerken } \\ & =-x^2+(\frac{1}{4}+7)x-\frac{7}{4} & \text{Neem samen} \\ &=-x^2+\frac{29}{4}x-\frac{7}{4} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(a+\frac{-10}{10})(p-\frac{-11}{9})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{11}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{11}{9})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{11}{9})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{11}{9}a-1p-1.\frac{11}{9}& \text{Uitwerken } \\ & =ap+\frac{11}{9}a-1p-\frac{11}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{-3}{19}+q)(\frac{-17}{18}+x)& =(\color{red}{q}+\color{orange}{\frac{-3}{19}}).(\color{green}{x}+\color{blue}{\frac{-17}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{18})} + \color{orange}{(\frac{-3}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{19})} . \color{blue}{(\frac{-17}{18})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{17}{18}q-\frac{3}{19}x+\frac{3}{19}.\frac{17}{18}& \text{Uitwerken } \\ & =qx-\frac{17}{18}q-\frac{3}{19}x+\frac{51}{342} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{17}{18}q-\frac{3}{19}x+\frac{17}{114} & \text{Vereenvoudig} \\\end{align}\)
  10. \(\begin{align}(p-\frac{-6}{2})(\frac{20}{6}+b)& =(\color{red}{p}+\color{orange}{3}).(\color{green}{b}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{10}{3}p+3b+3.\frac{10}{3}& \text{Uitwerken } \\ & =bp+\frac{10}{3}p+3b+\frac{30}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{10}{3}p+3b+10 & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{3}{3}-x)(b+\frac{-20}{11})& =(\color{red}{-x}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{-20}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-20}{11})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{-20}{11})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{20}{11}x+1b-1.\frac{20}{11}& \text{Uitwerken } \\ & =-bx+\frac{20}{11}x+1b-\frac{20}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(q-\frac{-5}{13})(q-\frac{-8}{9})& =(\color{red}{q}+\color{orange}{\frac{5}{13}}).(\color{green}{q}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{5}{13})} . \color{green}{(q)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{8}{9}q+\frac{5}{13}q+\frac{5}{13}.\frac{8}{9}& \text{Uitwerken } \\ & =q^2+(\frac{8}{9}+\frac{5}{13})q+\frac{40}{117} & \text{Neem samen} \\ &=q^2+\frac{149}{117}q+\frac{40}{117} & \text{Maak de som} \\\end{align}\)
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