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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{-5}{6})(\frac{2}{18}-q)& =(\color{red}{p}+\color{orange}{\frac{5}{6}}).(\color{green}{-q}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{5}{6})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{9}p-\frac{5}{6}q+\frac{5}{6}.\frac{1}{9}& \text{Uitwerken } \\ & =-pq+\frac{1}{9}p-\frac{5}{6}q+\frac{5}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-5}{17}+b)(p-\frac{-5}{10})& =(\color{red}{b}+\color{orange}{\frac{-5}{17}}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-5}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{17})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{2}b-\frac{5}{17}p-\frac{5}{17}.\frac{1}{2}& \text{Uitwerken } \\ & =bp+\frac{1}{2}b-\frac{5}{17}p-\frac{5}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x-\frac{-9}{7})(x-\frac{6}{5})& =(\color{red}{x}+\color{orange}{\frac{9}{7}}).(\color{green}{x}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{9}{7})} . \color{green}{(x)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{6}{5}x+\frac{9}{7}x-\frac{9}{7}.\frac{6}{5}& \text{Uitwerken } \\ & =x^2+((\frac{-6}{5})+\frac{9}{7})x-(\frac{-54}{35}) & \text{Neem samen} \\ &=x^2+\frac{3}{35}x-(\frac{-54}{35}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{13}{9}+b)(\frac{-13}{4}+a)& =(\color{red}{b}+\color{orange}{\frac{13}{9}}).(\color{green}{a}+\color{blue}{\frac{-13}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{4})} + \color{orange}{(\frac{13}{9})} . \color{green}{(a)} + \color{orange}{(\frac{13}{9})} . \color{blue}{(\frac{-13}{4})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{4}b+\frac{13}{9}a-\frac{13}{9}.\frac{13}{4}& \text{Uitwerken } \\ & =ab-\frac{13}{4}b+\frac{13}{9}a-\frac{169}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-4}{12}+p)(q-\frac{9}{12})& =(\color{red}{p}+\color{orange}{\frac{-1}{3}}).(\color{green}{q}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{4}p-\frac{1}{3}q+\frac{1}{3}.\frac{3}{4}& \text{Uitwerken } \\ & =pq-\frac{3}{4}p-\frac{1}{3}q+\frac{3}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{3}{4}p-\frac{1}{3}q+\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(a+\frac{-14}{11})((-16)+q)& =(\color{red}{a}+\color{orange}{\frac{-14}{11}}).(\color{green}{q}+\color{blue}{(-16)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-16)} + \color{orange}{(\frac{-14}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = aq-16a-\frac{14}{11}q+\frac{14}{11}.16& \text{Uitwerken } \\ & =aq-16a-\frac{14}{11}q+\frac{224}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-3}{10}-x)(p+\frac{-20}{16})& =(\color{red}{-x}+\color{orange}{\frac{-3}{10}}).(\color{green}{p}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{5}{4}x-\frac{3}{10}p+\frac{3}{10}.\frac{5}{4}& \text{Uitwerken } \\ & =-px+\frac{5}{4}x-\frac{3}{10}p+\frac{15}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{5}{4}x-\frac{3}{10}p+\frac{3}{8} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(x-\frac{11}{16})(\frac{-14}{8}+a)& =(\color{red}{x}+\color{orange}{\frac{-11}{16}}).(\color{green}{a}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{4}x-\frac{11}{16}a+\frac{11}{16}.\frac{7}{4}& \text{Uitwerken } \\ & =ax-\frac{7}{4}x-\frac{11}{16}a+\frac{77}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(b-\frac{-6}{11})(\frac{5}{4}+q)& =(\color{red}{b}+\color{orange}{\frac{6}{11}}).(\color{green}{q}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{6}{11})} . \color{green}{(q)} + \color{orange}{(\frac{6}{11})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{4}b+\frac{6}{11}q+\frac{6}{11}.\frac{5}{4}& \text{Uitwerken } \\ & =bq+\frac{5}{4}b+\frac{6}{11}q+\frac{30}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{5}{4}b+\frac{6}{11}q+\frac{15}{22} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{7}{14}-x)(p+\frac{2}{13})& =(\color{red}{-x}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{2}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{2}{13})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{2}{13})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{2}{13}x+\frac{1}{2}p+\frac{1}{2}.\frac{2}{13}& \text{Uitwerken } \\ & =-px-\frac{2}{13}x+\frac{1}{2}p+\frac{2}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{2}{13}x+\frac{1}{2}p+\frac{1}{13} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{17}{6}+p)(b+\frac{-11}{8})& =(\color{red}{p}+\color{orange}{\frac{17}{6}}).(\color{green}{b}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{17}{6})} . \color{green}{(b)} + \color{orange}{(\frac{17}{6})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{11}{8}p+\frac{17}{6}b-\frac{17}{6}.\frac{11}{8}& \text{Uitwerken } \\ & =bp-\frac{11}{8}p+\frac{17}{6}b-\frac{187}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-18}{12}-p)(\frac{15}{9}-b)& =(\color{red}{-p}+\color{orange}{\frac{-3}{2}}).(\color{green}{-b}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{3}p+\frac{3}{2}b-\frac{3}{2}.\frac{5}{3}& \text{Uitwerken } \\ & =bp-\frac{5}{3}p+\frac{3}{2}b-\frac{15}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{5}{3}p+\frac{3}{2}b-\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)