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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{-17}{14})(x-\frac{3}{9})& =(\color{red}{a}+\color{orange}{\frac{-17}{14}}).(\color{green}{x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-17}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{14})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{3}a-\frac{17}{14}x+\frac{17}{14}.\frac{1}{3}& \text{Uitwerken } \\ & =ax-\frac{1}{3}a-\frac{17}{14}x+\frac{17}{42} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}((-6)-p)(\frac{-18}{11}+q)& =(\color{red}{-p}+\color{orange}{(-6)}).(\color{green}{q}+\color{blue}{\frac{-18}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-18}{11})} + \color{orange}{(-6)} . \color{green}{(q)} + \color{orange}{(-6)} . \color{blue}{(\frac{-18}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{18}{11}p-6q+6.\frac{18}{11}& \text{Uitwerken } \\ & =-pq+\frac{18}{11}p-6q+\frac{108}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-10}{13}+a)(\frac{12}{14}+x)& =(\color{red}{a}+\color{orange}{\frac{-10}{13}}).(\color{green}{x}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{-10}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{13})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{6}{7}a-\frac{10}{13}x-\frac{10}{13}.\frac{6}{7}& \text{Uitwerken } \\ & =ax+\frac{6}{7}a-\frac{10}{13}x-\frac{60}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(b-\frac{-19}{10})(\frac{11}{2}-q)& =(\color{red}{b}+\color{orange}{\frac{19}{10}}).(\color{green}{-q}+\color{blue}{\frac{11}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{11}{2})} + \color{orange}{(\frac{19}{10})} . \color{green}{(-q)} + \color{orange}{(\frac{19}{10})} . \color{blue}{(\frac{11}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{11}{2}b-\frac{19}{10}q+\frac{19}{10}.\frac{11}{2}& \text{Uitwerken } \\ & =-bq+\frac{11}{2}b-\frac{19}{10}q+\frac{209}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-5}{5}+b)(a+\frac{-10}{6})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{3}b-1a+1.\frac{5}{3}& \text{Uitwerken } \\ & =ab-\frac{5}{3}b-1a+\frac{5}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p+\frac{-14}{6})(a+\frac{5}{3})& =(\color{red}{p}+\color{orange}{\frac{-7}{3}}).(\color{green}{a}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{5}{3}p-\frac{7}{3}a-\frac{7}{3}.\frac{5}{3}& \text{Uitwerken } \\ & =ap+\frac{5}{3}p-\frac{7}{3}a-\frac{35}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-16}{16}+q)(x+\frac{-10}{2})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{(-5)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-5)} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = qx-5q-1x+1.5& \text{Uitwerken } \\ & =qx-5q-1x+5 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{6}{14}-x)(\frac{-7}{5}+a)& =(\color{red}{-x}+\color{orange}{\frac{3}{7}}).(\color{green}{a}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{3}{7})} . \color{green}{(a)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{7}{5}x+\frac{3}{7}a-\frac{3}{7}.\frac{7}{5}& \text{Uitwerken } \\ & =-ax+\frac{7}{5}x+\frac{3}{7}a-\frac{21}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{7}{5}x+\frac{3}{7}a-\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(a-\frac{19}{9})(19+b)& =(\color{red}{a}+\color{orange}{\frac{-19}{9}}).(\color{green}{b}+\color{blue}{19})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(19)} + \color{orange}{(\frac{-19}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(19)}& \text{Boogjes en uitschrijven} \\ & = ab+19a-\frac{19}{9}b-\frac{19}{9}.19& \text{Uitwerken } \\ & =ab+19a-\frac{19}{9}b-\frac{361}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-4}{6}+b)(\frac{3}{15}-p)& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{-p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{5}b+\frac{2}{3}p-\frac{2}{3}.\frac{1}{5}& \text{Uitwerken } \\ & =-bp+\frac{1}{5}b+\frac{2}{3}p-\frac{2}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-\frac{14}{3})(\frac{-4}{7}+x)& =(\color{red}{a}+\color{orange}{\frac{-14}{3}}).(\color{green}{x}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-14}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{3})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{4}{7}a-\frac{14}{3}x+\frac{14}{3}.\frac{4}{7}& \text{Uitwerken } \\ & =ax-\frac{4}{7}a-\frac{14}{3}x+\frac{56}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{4}{7}a-\frac{14}{3}x+\frac{8}{3} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(a-\frac{-15}{5})(b-\frac{11}{12})& =(\color{red}{a}+\color{orange}{3}).(\color{green}{b}+\color{blue}{\frac{-11}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{12})} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(\frac{-11}{12})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{11}{12}a+3b-3.\frac{11}{12}& \text{Uitwerken } \\ & =ab-\frac{11}{12}a+3b-\frac{33}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{11}{12}a+3b-\frac{11}{4} & \text{Vereenvoudig} \\\end{align}\)