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

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

Werk uit en vereenvoudig

Verbetersleutel

  1. \(\begin{align}(q-(-6))(\frac{-7}{20}+a)& =(\color{red}{q}+\color{orange}{6}).(\color{green}{a}+\color{blue}{\frac{-7}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{20})} + \color{orange}{(6)} . \color{green}{(a)} + \color{orange}{(6)} . \color{blue}{(\frac{-7}{20})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{7}{20}q+6a-6.\frac{7}{20}& \text{Uitwerken } \\ & =aq-\frac{7}{20}q+6a-\frac{42}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{7}{20}q+6a-\frac{21}{10} & \text{Vereenvoudig} \\\end{align}\)
  2. \(\begin{align}(\frac{-17}{3}-x)(a+\frac{20}{16})& =(\color{red}{-x}+\color{orange}{\frac{-17}{3}}).(\color{green}{a}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{5}{4}x-\frac{17}{3}a-\frac{17}{3}.\frac{5}{4}& \text{Uitwerken } \\ & =-ax-\frac{5}{4}x-\frac{17}{3}a-\frac{85}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  3. \(\begin{align}(\frac{7}{6}+q)(q+\frac{12}{9})& =(\color{red}{q}+\color{orange}{\frac{7}{6}}).(\color{green}{q}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{7}{6})} . \color{green}{(q)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{4}{3}q+\frac{7}{6}q+\frac{7}{6}.\frac{4}{3}& \text{Uitwerken } \\ & =q^2+(\frac{4}{3}+\frac{7}{6})q+\frac{28}{18} & \text{Neem samen} \\ &=q^2+\frac{15}{6}q+\frac{28}{18} & \text{Maak de som} \\ &=q^2+\frac{5}{2}q+\frac{14}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
  4. \(\begin{align}(\frac{12}{17}+b)(\frac{-3}{10}+q)& =(\color{red}{b}+\color{orange}{\frac{12}{17}}).(\color{green}{q}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{12}{17})} . \color{green}{(q)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{10}b+\frac{12}{17}q-\frac{12}{17}.\frac{3}{10}& \text{Uitwerken } \\ & =bq-\frac{3}{10}b+\frac{12}{17}q-\frac{36}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{3}{10}b+\frac{12}{17}q-\frac{18}{85} & \text{Vereenvoudig} \\\end{align}\)
  5. \(\begin{align}(\frac{-9}{17}+a)(b+\frac{3}{13})& =(\color{red}{a}+\color{orange}{\frac{-9}{17}}).(\color{green}{b}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(\frac{-9}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{17})} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{13}a-\frac{9}{17}b-\frac{9}{17}.\frac{3}{13}& \text{Uitwerken } \\ & =ab+\frac{3}{13}a-\frac{9}{17}b-\frac{27}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  6. \(\begin{align}(q+\frac{-10}{14})(a-\frac{-2}{9})& =(\color{red}{q}+\color{orange}{\frac{-5}{7}}).(\color{green}{a}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{2}{9}q-\frac{5}{7}a-\frac{5}{7}.\frac{2}{9}& \text{Uitwerken } \\ & =aq+\frac{2}{9}q-\frac{5}{7}a-\frac{10}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  7. \(\begin{align}(\frac{19}{6}-q)(\frac{17}{3}-a)& =(\color{red}{-q}+\color{orange}{\frac{19}{6}}).(\color{green}{-a}+\color{blue}{\frac{17}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{17}{3})} + \color{orange}{(\frac{19}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{19}{6})} . \color{blue}{(\frac{17}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{17}{3}q-\frac{19}{6}a+\frac{19}{6}.\frac{17}{3}& \text{Uitwerken } \\ & =aq-\frac{17}{3}q-\frac{19}{6}a+\frac{323}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  8. \(\begin{align}(\frac{14}{8}-x)(\frac{19}{8}-x)& =(\color{red}{-x}+\color{orange}{\frac{7}{4}}).(\color{green}{-x}+\color{blue}{\frac{19}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-x)} + \color{red}{(-x)} . \color{blue}{(\frac{19}{8})} + \color{orange}{(\frac{7}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{19}{8})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{19}{8}x-\frac{7}{4}x+\frac{7}{4}.\frac{19}{8}& \text{Uitwerken } \\ & =x^2+((\frac{-19}{8})+(\frac{-7}{4}))x+\frac{133}{32} & \text{Neem samen} \\ &=x^2-\frac{33}{8}x+\frac{133}{32} & \text{Maak de som} \\\end{align}\)
  9. \(\begin{align}(q-\frac{10}{20})(p+\frac{-3}{3})& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq-1q-\frac{1}{2}p+\frac{1}{2}.1& \text{Uitwerken } \\ & =pq-1q-\frac{1}{2}p+\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
  10. \(\begin{align}(\frac{15}{19}+q)(\frac{7}{13}+q)& =(\color{red}{q}+\color{orange}{\frac{15}{19}}).(\color{green}{q}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{15}{19})} . \color{green}{(q)} + \color{orange}{(\frac{15}{19})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{7}{13}q+\frac{15}{19}q+\frac{15}{19}.\frac{7}{13}& \text{Uitwerken } \\ & =q^2+(\frac{7}{13}+\frac{15}{19})q+\frac{105}{247} & \text{Neem samen} \\ &=q^2+\frac{328}{247}q+\frac{105}{247} & \text{Maak de som} \\\end{align}\)
  11. \(\begin{align}(b+\frac{-6}{4})(\frac{-4}{7}+p)& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{p}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{7}b-\frac{3}{2}p+\frac{3}{2}.\frac{4}{7}& \text{Uitwerken } \\ & =bp-\frac{4}{7}b-\frac{3}{2}p+\frac{12}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{4}{7}b-\frac{3}{2}p+\frac{6}{7} & \text{Vereenvoudig} \\\end{align}\)
  12. \(\begin{align}(\frac{-18}{8}+x)(\frac{7}{7}-b)& =(\color{red}{x}+\color{orange}{\frac{-9}{4}}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-9}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bx+1x+\frac{9}{4}b-\frac{9}{4}.1& \text{Uitwerken } \\ & =-bx+1x+\frac{9}{4}b-\frac{9}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
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