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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-8}{13}-x)(\frac{2}{14}-q)& =(\color{red}{-x}+\color{orange}{\frac{-8}{13}}).(\color{green}{-q}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-8}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{-8}{13})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{7}x+\frac{8}{13}q-\frac{8}{13}.\frac{1}{7}& \text{Uitwerken } \\ & =qx-\frac{1}{7}x+\frac{8}{13}q-\frac{8}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{11}{11}-q)(\frac{10}{18}+p)& =(\color{red}{-q}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{5}{9}q+1p+1.\frac{5}{9}& \text{Uitwerken } \\ & =-pq-\frac{5}{9}q+1p+\frac{5}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q+11)(\frac{17}{19}+x)& =(\color{red}{q}+\color{orange}{11}).(\color{green}{x}+\color{blue}{\frac{17}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{17}{19})} + \color{orange}{(11)} . \color{green}{(x)} + \color{orange}{(11)} . \color{blue}{(\frac{17}{19})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{17}{19}q+11x+11.\frac{17}{19}& \text{Uitwerken } \\ & =qx+\frac{17}{19}q+11x+\frac{187}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{11}{17}-q)(p+\frac{20}{2})& =(\color{red}{-q}+\color{orange}{\frac{11}{17}}).(\color{green}{p}+\color{blue}{10})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(10)} + \color{orange}{(\frac{11}{17})} . \color{green}{(p)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = -pq-10q+\frac{11}{17}p+\frac{11}{17}.10& \text{Uitwerken } \\ & =-pq-10q+\frac{11}{17}p+\frac{110}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b-\frac{12}{8})(b+\frac{1}{7})& =(\color{red}{b}+\color{orange}{\frac{-3}{2}}).(\color{green}{b}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{7}b-\frac{3}{2}b-\frac{3}{2}.\frac{1}{7}& \text{Uitwerken } \\ & =b^2+(\frac{1}{7}+(\frac{-3}{2}))b-(\frac{-3}{14}) & \text{Neem samen} \\ &=b^2-\frac{19}{14}b-(\frac{-3}{14}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{-9}{16}-b)(\frac{11}{18}+q)& =(\color{red}{-b}+\color{orange}{\frac{-9}{16}}).(\color{green}{q}+\color{blue}{\frac{11}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{18})} + \color{orange}{(\frac{-9}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{16})} . \color{blue}{(\frac{11}{18})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{11}{18}b-\frac{9}{16}q-\frac{9}{16}.\frac{11}{18}& \text{Uitwerken } \\ & =-bq-\frac{11}{18}b-\frac{9}{16}q-\frac{99}{288} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{11}{18}b-\frac{9}{16}q-\frac{11}{32} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{15}{4}+a)(\frac{-19}{6}-q)& =(\color{red}{a}+\color{orange}{\frac{15}{4}}).(\color{green}{-q}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(\frac{15}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{15}{4})} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{19}{6}a-\frac{15}{4}q-\frac{15}{4}.\frac{19}{6}& \text{Uitwerken } \\ & =-aq-\frac{19}{6}a-\frac{15}{4}q-\frac{285}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{19}{6}a-\frac{15}{4}q-\frac{95}{8} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(x-\frac{16}{10})(\frac{-10}{8}+a)& =(\color{red}{x}+\color{orange}{\frac{-8}{5}}).(\color{green}{a}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{4}x-\frac{8}{5}a+\frac{8}{5}.\frac{5}{4}& \text{Uitwerken } \\ & =ax-\frac{5}{4}x-\frac{8}{5}a+\frac{40}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{5}{4}x-\frac{8}{5}a+2 & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(a-\frac{7}{14})(x-\frac{9}{17})& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{-9}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{17})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-9}{17})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{9}{17}a-\frac{1}{2}x+\frac{1}{2}.\frac{9}{17}& \text{Uitwerken } \\ & =ax-\frac{9}{17}a-\frac{1}{2}x+\frac{9}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-11}{14}-b)(p+\frac{13}{4})& =(\color{red}{-b}+\color{orange}{\frac{-11}{14}}).(\color{green}{p}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{13}{4}b-\frac{11}{14}p-\frac{11}{14}.\frac{13}{4}& \text{Uitwerken } \\ & =-bp-\frac{13}{4}b-\frac{11}{14}p-\frac{143}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(b+\frac{-11}{7})(a+\frac{14}{19})& =(\color{red}{b}+\color{orange}{\frac{-11}{7}}).(\color{green}{a}+\color{blue}{\frac{14}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{14}{19})} + \color{orange}{(\frac{-11}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{7})} . \color{blue}{(\frac{14}{19})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{14}{19}b-\frac{11}{7}a-\frac{11}{7}.\frac{14}{19}& \text{Uitwerken } \\ & =ab+\frac{14}{19}b-\frac{11}{7}a-\frac{154}{133} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{14}{19}b-\frac{11}{7}a-\frac{22}{19} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(q+\frac{20}{7})(p+\frac{-20}{5})& =(\color{red}{q}+\color{orange}{\frac{20}{7}}).(\color{green}{p}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-4)} + \color{orange}{(\frac{20}{7})} . \color{green}{(p)} + \color{orange}{(\frac{20}{7})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = pq-4q+\frac{20}{7}p-\frac{20}{7}.4& \text{Uitwerken } \\ & =pq-4q+\frac{20}{7}p-\frac{80}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)