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

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

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Verbetersleutel

1. \(\begin{align}(b+\frac{13}{8})(\frac{11}{3}+a)& =(\color{red}{b}+\color{orange}{\frac{13}{8}}).(\color{green}{a}+\color{blue}{\frac{11}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{11}{3})} + \color{orange}{(\frac{13}{8})} . \color{green}{(a)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(\frac{11}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{11}{3}b+\frac{13}{8}a+\frac{13}{8}.\frac{11}{3}& \text{Uitwerken } \\ & =ab+\frac{11}{3}b+\frac{13}{8}a+\frac{143}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{16}{19}+q)(\frac{-19}{13}+x)& =(\color{red}{q}+\color{orange}{\frac{16}{19}}).(\color{green}{x}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{16}{19})} . \color{green}{(x)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{19}{13}q+\frac{16}{19}x-\frac{16}{19}.\frac{19}{13}& \text{Uitwerken } \\ & =qx-\frac{19}{13}q+\frac{16}{19}x-\frac{304}{247} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{19}{13}q+\frac{16}{19}x-\frac{16}{13} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(q-\frac{-3}{9})(a+\frac{-13}{10})& =(\color{red}{q}+\color{orange}{\frac{1}{3}}).(\color{green}{a}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(\frac{1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{13}{10}q+\frac{1}{3}a-\frac{1}{3}.\frac{13}{10}& \text{Uitwerken } \\ & =aq-\frac{13}{10}q+\frac{1}{3}a-\frac{13}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p-\frac{13}{9})(\frac{-18}{7}-q)& =(\color{red}{p}+\color{orange}{\frac{-13}{9}}).(\color{green}{-q}+\color{blue}{\frac{-18}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-18}{7})} + \color{orange}{(\frac{-13}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{-13}{9})} . \color{blue}{(\frac{-18}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{18}{7}p+\frac{13}{9}q+\frac{13}{9}.\frac{18}{7}& \text{Uitwerken } \\ & =-pq-\frac{18}{7}p+\frac{13}{9}q+\frac{234}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{18}{7}p+\frac{13}{9}q+\frac{26}{7} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-7}{13}-b)(x+\frac{-7}{6})& =(\color{red}{-b}+\color{orange}{\frac{-7}{13}}).(\color{green}{x}+\color{blue}{\frac{-7}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{6})} + \color{orange}{(\frac{-7}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{13})} . \color{blue}{(\frac{-7}{6})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{7}{6}b-\frac{7}{13}x+\frac{7}{13}.\frac{7}{6}& \text{Uitwerken } \\ & =-bx+\frac{7}{6}b-\frac{7}{13}x+\frac{49}{78} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{16}{20}+p)(15+b)& =(\color{red}{p}+\color{orange}{\frac{4}{5}}).(\color{green}{b}+\color{blue}{15})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(15)} + \color{orange}{(\frac{4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(15)}& \text{Boogjes en uitschrijven} \\ & = bp+15p+\frac{4}{5}b+\frac{4}{5}.15& \text{Uitwerken } \\ & =bp+15p+\frac{4}{5}b+\frac{60}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+15p+\frac{4}{5}b+12 & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(b-\frac{19}{11})(x+\frac{11}{20})& =(\color{red}{b}+\color{orange}{\frac{-19}{11}}).(\color{green}{x}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{20}b-\frac{19}{11}x-\frac{19}{11}.\frac{11}{20}& \text{Uitwerken } \\ & =bx+\frac{11}{20}b-\frac{19}{11}x-\frac{209}{220} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{11}{20}b-\frac{19}{11}x-\frac{19}{20} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{8}{20}-x)(\frac{-2}{10}+b)& =(\color{red}{-x}+\color{orange}{\frac{2}{5}}).(\color{green}{b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{5}x+\frac{2}{5}b-\frac{2}{5}.\frac{1}{5}& \text{Uitwerken } \\ & =-bx+\frac{1}{5}x+\frac{2}{5}b-\frac{2}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(6+b)(q+\frac{11}{7})& =(\color{red}{b}+\color{orange}{6}).(\color{green}{q}+\color{blue}{\frac{11}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{11}{7})} + \color{orange}{(6)} . \color{green}{(q)} + \color{orange}{(6)} . \color{blue}{(\frac{11}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{11}{7}b+6q+6.\frac{11}{7}& \text{Uitwerken } \\ & =bq+\frac{11}{7}b+6q+\frac{66}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(p-\frac{-11}{5})(p-\frac{-18}{18})& =(\color{red}{p}+\color{orange}{\frac{11}{5}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{11}{5})} . \color{green}{(p)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pp+1p+\frac{11}{5}p+\frac{11}{5}.1& \text{Uitwerken } \\ & =p^2+(1+\frac{11}{5})p+\frac{11}{5} & \text{Neem samen} \\ &=p^2+\frac{16}{5}p+\frac{11}{5} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(q-\frac{-18}{13})(\frac{14}{9}+a)& =(\color{red}{q}+\color{orange}{\frac{18}{13}}).(\color{green}{a}+\color{blue}{\frac{14}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{14}{9})} + \color{orange}{(\frac{18}{13})} . \color{green}{(a)} + \color{orange}{(\frac{18}{13})} . \color{blue}{(\frac{14}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{14}{9}q+\frac{18}{13}a+\frac{18}{13}.\frac{14}{9}& \text{Uitwerken } \\ & =aq+\frac{14}{9}q+\frac{18}{13}a+\frac{252}{117} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{14}{9}q+\frac{18}{13}a+\frac{28}{13} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(x-\frac{-11}{19})(\frac{-20}{10}-a)& =(\color{red}{x}+\color{orange}{\frac{11}{19}}).(\color{green}{-a}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{11}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -ax-2x-\frac{11}{19}a-\frac{11}{19}.2& \text{Uitwerken } \\ & =-ax-2x-\frac{11}{19}a-\frac{22}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)