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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{-15}{3})(x+\frac{10}{11})& =(\color{red}{p}+\color{orange}{(-5)}).(\color{green}{x}+\color{blue}{\frac{10}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{10}{11})} + \color{orange}{(-5)} . \color{green}{(x)} + \color{orange}{(-5)} . \color{blue}{(\frac{10}{11})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{10}{11}p-5x-5.\frac{10}{11}& \text{Uitwerken } \\ & =px+\frac{10}{11}p-5x-\frac{50}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{19}{6}+p)(q+\frac{9}{16})& =(\color{red}{p}+\color{orange}{\frac{19}{6}}).(\color{green}{q}+\color{blue}{\frac{9}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{9}{16})} + \color{orange}{(\frac{19}{6})} . \color{green}{(q)} + \color{orange}{(\frac{19}{6})} . \color{blue}{(\frac{9}{16})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{9}{16}p+\frac{19}{6}q+\frac{19}{6}.\frac{9}{16}& \text{Uitwerken } \\ & =pq+\frac{9}{16}p+\frac{19}{6}q+\frac{171}{96} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{9}{16}p+\frac{19}{6}q+\frac{57}{32} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{20}{16}+a)(p-\frac{-1}{15})& =(\color{red}{a}+\color{orange}{\frac{5}{4}}).(\color{green}{p}+\color{blue}{\frac{1}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{15})} + \color{orange}{(\frac{5}{4})} . \color{green}{(p)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{1}{15})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{15}a+\frac{5}{4}p+\frac{5}{4}.\frac{1}{15}& \text{Uitwerken } \\ & =ap+\frac{1}{15}a+\frac{5}{4}p+\frac{5}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{1}{15}a+\frac{5}{4}p+\frac{1}{12} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(a-\frac{-15}{7})(\frac{10}{18}-b)& =(\color{red}{a}+\color{orange}{\frac{15}{7}}).(\color{green}{-b}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{15}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{15}{7})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{5}{9}a-\frac{15}{7}b+\frac{15}{7}.\frac{5}{9}& \text{Uitwerken } \\ & =-ab+\frac{5}{9}a-\frac{15}{7}b+\frac{75}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{5}{9}a-\frac{15}{7}b+\frac{25}{21} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(p-\frac{-1}{6})(x+\frac{20}{11})& =(\color{red}{p}+\color{orange}{\frac{1}{6}}).(\color{green}{x}+\color{blue}{\frac{20}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{20}{11})} + \color{orange}{(\frac{1}{6})} . \color{green}{(x)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{20}{11})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{20}{11}p+\frac{1}{6}x+\frac{1}{6}.\frac{20}{11}& \text{Uitwerken } \\ & =px+\frac{20}{11}p+\frac{1}{6}x+\frac{20}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{20}{11}p+\frac{1}{6}x+\frac{10}{33} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{6}{7}-q)(x-\frac{-4}{2})& =(\color{red}{-q}+\color{orange}{\frac{6}{7}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{6}{7})} . \color{green}{(x)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -qx-2q+\frac{6}{7}x+\frac{6}{7}.2& \text{Uitwerken } \\ & =-qx-2q+\frac{6}{7}x+\frac{12}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-18}{10}+b)(x-\frac{13}{20})& =(\color{red}{b}+\color{orange}{\frac{-9}{5}}).(\color{green}{x}+\color{blue}{\frac{-13}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{20})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{-13}{20})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{13}{20}b-\frac{9}{5}x+\frac{9}{5}.\frac{13}{20}& \text{Uitwerken } \\ & =bx-\frac{13}{20}b-\frac{9}{5}x+\frac{117}{100} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-1}{3}+a)(x-\frac{-6}{12})& =(\color{red}{a}+\color{orange}{\frac{-1}{3}}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{2}a-\frac{1}{3}x-\frac{1}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =ax+\frac{1}{2}a-\frac{1}{3}x-\frac{1}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p-\frac{13}{2})(a-\frac{6}{4})& =(\color{red}{p}+\color{orange}{\frac{-13}{2}}).(\color{green}{a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-13}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{2})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{3}{2}p-\frac{13}{2}a+\frac{13}{2}.\frac{3}{2}& \text{Uitwerken } \\ & =ap-\frac{3}{2}p-\frac{13}{2}a+\frac{39}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(q+\frac{-2}{5})(x+\frac{-13}{3})& =(\color{red}{q}+\color{orange}{\frac{-2}{5}}).(\color{green}{x}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{3}q-\frac{2}{5}x+\frac{2}{5}.\frac{13}{3}& \text{Uitwerken } \\ & =qx-\frac{13}{3}q-\frac{2}{5}x+\frac{26}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-10}{15}+a)(q+\frac{-15}{15})& =(\color{red}{a}+\color{orange}{\frac{-2}{3}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aq-1a-\frac{2}{3}q+\frac{2}{3}.1& \text{Uitwerken } \\ & =aq-1a-\frac{2}{3}q+\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-19}{13}+p)(\frac{9}{17}-b)& =(\color{red}{p}+\color{orange}{\frac{-19}{13}}).(\color{green}{-b}+\color{blue}{\frac{9}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{17})} + \color{orange}{(\frac{-19}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{13})} . \color{blue}{(\frac{9}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{9}{17}p+\frac{19}{13}b-\frac{19}{13}.\frac{9}{17}& \text{Uitwerken } \\ & =-bp+\frac{9}{17}p+\frac{19}{13}b-\frac{171}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)