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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{15}{3}+x)(a-\frac{12}{10})& =(\color{red}{x}+\color{orange}{5}).(\color{green}{a}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(5)} . \color{green}{(a)} + \color{orange}{(5)} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{6}{5}x+5a-5.\frac{6}{5}& \text{Uitwerken } \\ & =ax-\frac{6}{5}x+5a-\frac{30}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{6}{5}x+5a-6 & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{4}{9}+q)(a+\frac{-4}{9})& =(\color{red}{q}+\color{orange}{\frac{4}{9}}).(\color{green}{a}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{4}{9})} . \color{green}{(a)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{4}{9}q+\frac{4}{9}a-\frac{4}{9}.\frac{4}{9}& \text{Uitwerken } \\ & =aq-\frac{4}{9}q+\frac{4}{9}a-\frac{16}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-5}{11}-q)(p-\frac{-12}{16})& =(\color{red}{-q}+\color{orange}{\frac{-5}{11}}).(\color{green}{p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-5}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{3}{4}q-\frac{5}{11}p-\frac{5}{11}.\frac{3}{4}& \text{Uitwerken } \\ & =-pq-\frac{3}{4}q-\frac{5}{11}p-\frac{15}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p+\frac{5}{10})(b+\frac{19}{16})& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{19}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{19}{16})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{19}{16})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{16}p+\frac{1}{2}b+\frac{1}{2}.\frac{19}{16}& \text{Uitwerken } \\ & =bp+\frac{19}{16}p+\frac{1}{2}b+\frac{19}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x-\frac{-13}{3})(p-\frac{-16}{4})& =(\color{red}{x}+\color{orange}{\frac{13}{3}}).(\color{green}{p}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(4)} + \color{orange}{(\frac{13}{3})} . \color{green}{(p)} + \color{orange}{(\frac{13}{3})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = px+4x+\frac{13}{3}p+\frac{13}{3}.4& \text{Uitwerken } \\ & =px+4x+\frac{13}{3}p+\frac{52}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-8}{6}-x)(\frac{-10}{4}+b)& =(\color{red}{-x}+\color{orange}{\frac{-4}{3}}).(\color{green}{b}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{5}{2}x-\frac{4}{3}b+\frac{4}{3}.\frac{5}{2}& \text{Uitwerken } \\ & =-bx+\frac{5}{2}x-\frac{4}{3}b+\frac{20}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+\frac{5}{2}x-\frac{4}{3}b+\frac{10}{3} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(p-\frac{-19}{13})(b-\frac{-10}{4})& =(\color{red}{p}+\color{orange}{\frac{19}{13}}).(\color{green}{b}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{19}{13})} . \color{green}{(b)} + \color{orange}{(\frac{19}{13})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{2}p+\frac{19}{13}b+\frac{19}{13}.\frac{5}{2}& \text{Uitwerken } \\ & =bp+\frac{5}{2}p+\frac{19}{13}b+\frac{95}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{12}{16}-x)(\frac{-2}{18}+a)& =(\color{red}{-x}+\color{orange}{\frac{3}{4}}).(\color{green}{a}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{3}{4})} . \color{green}{(a)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{1}{9}x+\frac{3}{4}a-\frac{3}{4}.\frac{1}{9}& \text{Uitwerken } \\ & =-ax+\frac{1}{9}x+\frac{3}{4}a-\frac{3}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{1}{9}x+\frac{3}{4}a-\frac{1}{12} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-12}{6}-x)(q+\frac{3}{14})& =(\color{red}{-x}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{3}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{14})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{3}{14})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{3}{14}x-2q-2.\frac{3}{14}& \text{Uitwerken } \\ & =-qx-\frac{3}{14}x-2q-\frac{6}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{3}{14}x-2q-\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p+\frac{-19}{6})(\frac{9}{10}-x)& =(\color{red}{p}+\color{orange}{\frac{-19}{6}}).(\color{green}{-x}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-19}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{6})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{9}{10}p+\frac{19}{6}x-\frac{19}{6}.\frac{9}{10}& \text{Uitwerken } \\ & =-px+\frac{9}{10}p+\frac{19}{6}x-\frac{171}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{9}{10}p+\frac{19}{6}x-\frac{57}{20} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(p-\frac{2}{14})(\frac{-4}{12}-x)& =(\color{red}{p}+\color{orange}{\frac{-1}{7}}).(\color{green}{-x}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{3}p+\frac{1}{7}x+\frac{1}{7}.\frac{1}{3}& \text{Uitwerken } \\ & =-px-\frac{1}{3}p+\frac{1}{7}x+\frac{1}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q+\frac{-14}{5})(\frac{15}{3}+x)& =(\color{red}{q}+\color{orange}{\frac{-14}{5}}).(\color{green}{x}+\color{blue}{5})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(5)} + \color{orange}{(\frac{-14}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-14}{5})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = qx+5q-\frac{14}{5}x-\frac{14}{5}.5& \text{Uitwerken } \\ & =qx+5q-\frac{14}{5}x-\frac{70}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+5q-\frac{14}{5}x-14 & \text{Vereenvoudig} \\\end{align}\)