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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(\frac{11}{20}-a)(b+14)& =(\color{red}{-a}+\color{orange}{\frac{11}{20}}).(\color{green}{b}+\color{blue}{14})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(14)} + \color{orange}{(\frac{11}{20})} . \color{green}{(b)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(14)}& \text{Boogjes en uitschrijven} \\ & = -ab-14a+\frac{11}{20}b+\frac{11}{20}.14& \text{Uitwerken } \\ & =-ab-14a+\frac{11}{20}b+\frac{154}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-14a+\frac{11}{20}b+\frac{77}{10} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{8}{18}-b)(p-\frac{-19}{18})& =(\color{red}{-b}+\color{orange}{\frac{4}{9}}).(\color{green}{p}+\color{blue}{\frac{19}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{18})} + \color{orange}{(\frac{4}{9})} . \color{green}{(p)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{19}{18})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{19}{18}b+\frac{4}{9}p+\frac{4}{9}.\frac{19}{18}& \text{Uitwerken } \\ & =-bp-\frac{19}{18}b+\frac{4}{9}p+\frac{76}{162} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{19}{18}b+\frac{4}{9}p+\frac{38}{81} & \text{Vereenvoudig} \\\end{align}\)
  3. \(\begin{align}(x+\frac{-13}{13})(a-\frac{18}{3})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{(-6)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-6)} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = ax-6x-1a+1.6& \text{Uitwerken } \\ & =ax-6x-1a+6 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(q+\frac{7}{7})(a+\frac{16}{4})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{a}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(4)} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = aq+4q+1a+1.4& \text{Uitwerken } \\ & =aq+4q+1a+4 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{18}{8}+q)(p+\frac{19}{19})& =(\color{red}{q}+\color{orange}{\frac{9}{4}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{9}{4})} . \color{green}{(p)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pq+1q+\frac{9}{4}p+\frac{9}{4}.1& \text{Uitwerken } \\ & =pq+1q+\frac{9}{4}p+\frac{9}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q+\frac{13}{5})(q-\frac{-3}{2})& =(\color{red}{q}+\color{orange}{\frac{13}{5}}).(\color{green}{q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{13}{5})} . \color{green}{(q)} + \color{orange}{(\frac{13}{5})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{3}{2}q+\frac{13}{5}q+\frac{13}{5}.\frac{3}{2}& \text{Uitwerken } \\ & =q^2+(\frac{3}{2}+\frac{13}{5})q+\frac{39}{10} & \text{Neem samen} \\ &=q^2+\frac{41}{10}q+\frac{39}{10} & \text{Maak de som} \\\end{align}\)
  7. \(\begin{align}(x-\frac{-11}{9})(x-\frac{-12}{15})& =(\color{red}{x}+\color{orange}{\frac{11}{9}}).(\color{green}{x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{11}{9})} . \color{green}{(x)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{4}{5}x+\frac{11}{9}x+\frac{11}{9}.\frac{4}{5}& \text{Uitwerken } \\ & =x^2+(\frac{4}{5}+\frac{11}{9})x+\frac{44}{45} & \text{Neem samen} \\ &=x^2+\frac{91}{45}x+\frac{44}{45} & \text{Maak de som} \\\end{align}\)
  8. \(\begin{align}(\frac{-18}{9}-a)(\frac{-6}{14}-q)& =(\color{red}{-a}+\color{orange}{(-2)}).(\color{green}{-q}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(-2)} . \color{green}{(-q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{7}a+2q+2.\frac{3}{7}& \text{Uitwerken } \\ & =aq+\frac{3}{7}a+2q+\frac{6}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(\frac{13}{13}+p)(\frac{9}{8}+b)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{8}p+1b+1.\frac{9}{8}& \text{Uitwerken } \\ & =bp+\frac{9}{8}p+1b+\frac{9}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(q+\frac{10}{14})(q-\frac{-3}{11})& =(\color{red}{q}+\color{orange}{\frac{5}{7}}).(\color{green}{q}+\color{blue}{\frac{3}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{3}{11})} + \color{orange}{(\frac{5}{7})} . \color{green}{(q)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(\frac{3}{11})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{3}{11}q+\frac{5}{7}q+\frac{5}{7}.\frac{3}{11}& \text{Uitwerken } \\ & =q^2+(\frac{3}{11}+\frac{5}{7})q+\frac{15}{77} & \text{Neem samen} \\ &=q^2+\frac{76}{77}q+\frac{15}{77} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(a-\frac{-8}{18})(\frac{-20}{19}-q)& =(\color{red}{a}+\color{orange}{\frac{4}{9}}).(\color{green}{-q}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{4}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{20}{19}a-\frac{4}{9}q-\frac{4}{9}.\frac{20}{19}& \text{Uitwerken } \\ & =-aq-\frac{20}{19}a-\frac{4}{9}q-\frac{80}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(15-q)(q-\frac{9}{8})& =(\color{red}{-q}+\color{orange}{15}).(\color{green}{q}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(15)} . \color{green}{(q)} + \color{orange}{(15)} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{9}{8}q+15q-15.\frac{9}{8}& \text{Uitwerken } \\ & =-q^2+(\frac{9}{8}+15)q-\frac{135}{8} & \text{Neem samen} \\ &=-q^2+\frac{129}{8}q-\frac{135}{8} & \text{Maak de som} \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-28 22:28:48
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