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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(a-\frac{1}{2})(\frac{-8}{2}+b)& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-4)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = ab-4a-\frac{1}{2}b+\frac{1}{2}.4& \text{Uitwerken } \\ & =ab-4a-\frac{1}{2}b+\frac{4}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-4a-\frac{1}{2}b+2 & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(p-\frac{7}{11})(p-\frac{3}{17})& =(\color{red}{p}+\color{orange}{\frac{-7}{11}}).(\color{green}{p}+\color{blue}{\frac{-3}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{17})} + \color{orange}{(\frac{-7}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(\frac{-3}{17})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{3}{17}p-\frac{7}{11}p+\frac{7}{11}.\frac{3}{17}& \text{Uitwerken } \\ & =p^2+((\frac{-3}{17})+(\frac{-7}{11}))p+\frac{21}{187} & \text{Neem samen} \\ &=p^2-\frac{152}{187}p+\frac{21}{187} & \text{Maak de som} \\\end{align}\)
  3. \(\begin{align}(x-4)(a-\frac{-9}{15})& =(\color{red}{x}+\color{orange}{(-4)}).(\color{green}{a}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(-4)} . \color{green}{(a)} + \color{orange}{(-4)} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{5}x-4a-4.\frac{3}{5}& \text{Uitwerken } \\ & =ax+\frac{3}{5}x-4a-\frac{12}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  4. \(\begin{align}(\frac{-9}{20}-b)(\frac{-9}{19}-q)& =(\color{red}{-b}+\color{orange}{\frac{-9}{20}}).(\color{green}{-q}+\color{blue}{\frac{-9}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{-9}{19})} + \color{orange}{(\frac{-9}{20})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{20})} . \color{blue}{(\frac{-9}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{9}{19}b+\frac{9}{20}q+\frac{9}{20}.\frac{9}{19}& \text{Uitwerken } \\ & =bq+\frac{9}{19}b+\frac{9}{20}q+\frac{81}{380} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  5. \(\begin{align}(\frac{7}{16}+q)(q+\frac{10}{13})& =(\color{red}{q}+\color{orange}{\frac{7}{16}}).(\color{green}{q}+\color{blue}{\frac{10}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{10}{13})} + \color{orange}{(\frac{7}{16})} . \color{green}{(q)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(\frac{10}{13})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{10}{13}q+\frac{7}{16}q+\frac{7}{16}.\frac{10}{13}& \text{Uitwerken } \\ & =q^2+(\frac{10}{13}+\frac{7}{16})q+\frac{70}{208} & \text{Neem samen} \\ &=q^2+\frac{251}{208}q+\frac{70}{208} & \text{Maak de som} \\ &=q^2+\frac{251}{208}q+\frac{35}{104} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  6. \(\begin{align}(\frac{-13}{11}-b)(x-\frac{16}{12})& =(\color{red}{-b}+\color{orange}{\frac{-13}{11}}).(\color{green}{x}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-13}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{11})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{4}{3}b-\frac{13}{11}x+\frac{13}{11}.\frac{4}{3}& \text{Uitwerken } \\ & =-bx+\frac{4}{3}b-\frac{13}{11}x+\frac{52}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{3}{10}+a)(\frac{2}{20}-q)& =(\color{red}{a}+\color{orange}{\frac{3}{10}}).(\color{green}{-q}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{3}{10})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{10}a-\frac{3}{10}q+\frac{3}{10}.\frac{1}{10}& \text{Uitwerken } \\ & =-aq+\frac{1}{10}a-\frac{3}{10}q+\frac{3}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(q-\frac{10}{14})(b-\frac{11}{18})& =(\color{red}{q}+\color{orange}{\frac{-5}{7}}).(\color{green}{b}+\color{blue}{\frac{-11}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{18})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{-11}{18})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{11}{18}q-\frac{5}{7}b+\frac{5}{7}.\frac{11}{18}& \text{Uitwerken } \\ & =bq-\frac{11}{18}q-\frac{5}{7}b+\frac{55}{126} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  9. \(\begin{align}(p+\frac{14}{14})(a-\frac{20}{16})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{5}{4}p+1a-1.\frac{5}{4}& \text{Uitwerken } \\ & =ap-\frac{5}{4}p+1a-\frac{5}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(a+\frac{12}{2})(b-\frac{-17}{18})& =(\color{red}{a}+\color{orange}{6}).(\color{green}{b}+\color{blue}{\frac{17}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{17}{18})} + \color{orange}{(6)} . \color{green}{(b)} + \color{orange}{(6)} . \color{blue}{(\frac{17}{18})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{17}{18}a+6b+6.\frac{17}{18}& \text{Uitwerken } \\ & =ab+\frac{17}{18}a+6b+\frac{102}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{17}{18}a+6b+\frac{17}{3} & \text{Vereenvoudig} \\\end{align}\)
  11. \(\begin{align}(\frac{-3}{16}+q)(p-\frac{-15}{16})& =(\color{red}{q}+\color{orange}{\frac{-3}{16}}).(\color{green}{p}+\color{blue}{\frac{15}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{15}{16})} + \color{orange}{(\frac{-3}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{16})} . \color{blue}{(\frac{15}{16})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{15}{16}q-\frac{3}{16}p-\frac{3}{16}.\frac{15}{16}& \text{Uitwerken } \\ & =pq+\frac{15}{16}q-\frac{3}{16}p-\frac{45}{256} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  12. \(\begin{align}(\frac{-13}{5}-q)(\frac{-6}{13}-p)& =(\color{red}{-q}+\color{orange}{\frac{-13}{5}}).(\color{green}{-p}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(\frac{-13}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{-13}{5})} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{6}{13}q+\frac{13}{5}p+\frac{13}{5}.\frac{6}{13}& \text{Uitwerken } \\ & =pq+\frac{6}{13}q+\frac{13}{5}p+\frac{78}{65} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{6}{13}q+\frac{13}{5}p+\frac{6}{5} & \text{Vereenvoudig} \\\end{align}\)
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