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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{19}{13}+b)(\frac{2}{8}+q)& =(\color{red}{b}+\color{orange}{\frac{19}{13}}).(\color{green}{q}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{19}{13})} . \color{green}{(q)} + \color{orange}{(\frac{19}{13})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{4}b+\frac{19}{13}q+\frac{19}{13}.\frac{1}{4}& \text{Uitwerken } \\ & =bq+\frac{1}{4}b+\frac{19}{13}q+\frac{19}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-7}{2}-q)(\frac{3}{5}-q)& =(\color{red}{-q}+\color{orange}{\frac{-7}{2}}).(\color{green}{-q}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{3}{5}q+\frac{7}{2}q-\frac{7}{2}.\frac{3}{5}& \text{Uitwerken } \\ & =q^2+((\frac{-3}{5})+\frac{7}{2})q-(\frac{-21}{10}) & \text{Neem samen} \\ &=q^2+\frac{29}{10}q-(\frac{-21}{10}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(b-\frac{3}{10})(x-\frac{-17}{9})& =(\color{red}{b}+\color{orange}{\frac{-3}{10}}).(\color{green}{x}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{17}{9}b-\frac{3}{10}x-\frac{3}{10}.\frac{17}{9}& \text{Uitwerken } \\ & =bx+\frac{17}{9}b-\frac{3}{10}x-\frac{51}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{17}{9}b-\frac{3}{10}x-\frac{17}{30} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(q+\frac{20}{12})(\frac{3}{14}+p)& =(\color{red}{q}+\color{orange}{\frac{5}{3}}).(\color{green}{p}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(\frac{5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{3}{14}q+\frac{5}{3}p+\frac{5}{3}.\frac{3}{14}& \text{Uitwerken } \\ & =pq+\frac{3}{14}q+\frac{5}{3}p+\frac{15}{42} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{3}{14}q+\frac{5}{3}p+\frac{5}{14} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{10}{2}+x)(x-\frac{3}{3})& =(\color{red}{x}+\color{orange}{5}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(5)} . \color{green}{(x)} + \color{orange}{(5)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = xx-1x+5x-5.1& \text{Uitwerken } \\ & =x^2+((-1)+5)x-(-5) & \text{Neem samen} \\ &=x^2+4x-(-5) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{-4}{10}+x)(b-\frac{-7}{7})& =(\color{red}{x}+\color{orange}{\frac{-2}{5}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx+1x-\frac{2}{5}b-\frac{2}{5}.1& \text{Uitwerken } \\ & =bx+1x-\frac{2}{5}b-\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p-\frac{-9}{19})(\frac{-11}{20}-x)& =(\color{red}{p}+\color{orange}{\frac{9}{19}}).(\color{green}{-x}+\color{blue}{\frac{-11}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{20})} + \color{orange}{(\frac{9}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{-11}{20})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{11}{20}p-\frac{9}{19}x-\frac{9}{19}.\frac{11}{20}& \text{Uitwerken } \\ & =-px-\frac{11}{20}p-\frac{9}{19}x-\frac{99}{380} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-18}{18}+q)(x-\frac{17}{10})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{-17}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{10})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{-17}{10})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{17}{10}q-1x+1.\frac{17}{10}& \text{Uitwerken } \\ & =qx-\frac{17}{10}q-1x+\frac{17}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x-\frac{3}{3})(\frac{18}{14}-b)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{-b}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(-1)} . \color{green}{(-b)} + \color{orange}{(-1)} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{9}{7}x+1b-1.\frac{9}{7}& \text{Uitwerken } \\ & =-bx+\frac{9}{7}x+1b-\frac{9}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-5}{11}+b)(\frac{16}{10}-p)& =(\color{red}{b}+\color{orange}{\frac{-5}{11}}).(\color{green}{-p}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{-5}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{8}{5}b+\frac{5}{11}p-\frac{5}{11}.\frac{8}{5}& \text{Uitwerken } \\ & =-bp+\frac{8}{5}b+\frac{5}{11}p-\frac{40}{55} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{8}{5}b+\frac{5}{11}p-\frac{8}{11} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-16}{7}+p)(b+\frac{-19}{14})& =(\color{red}{p}+\color{orange}{\frac{-16}{7}}).(\color{green}{b}+\color{blue}{\frac{-19}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{14})} + \color{orange}{(\frac{-16}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{7})} . \color{blue}{(\frac{-19}{14})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{14}p-\frac{16}{7}b+\frac{16}{7}.\frac{19}{14}& \text{Uitwerken } \\ & =bp-\frac{19}{14}p-\frac{16}{7}b+\frac{304}{98} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{19}{14}p-\frac{16}{7}b+\frac{152}{49} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{18}{11}+p)(q+\frac{-4}{5})& =(\color{red}{p}+\color{orange}{\frac{18}{11}}).(\color{green}{q}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{18}{11})} . \color{green}{(q)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{4}{5}p+\frac{18}{11}q-\frac{18}{11}.\frac{4}{5}& \text{Uitwerken } \\ & =pq-\frac{4}{5}p+\frac{18}{11}q-\frac{72}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)