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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{-11}{15})(x+\frac{19}{18})& =(\color{red}{p}+\color{orange}{\frac{11}{15}}).(\color{green}{x}+\color{blue}{\frac{19}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{19}{18})} + \color{orange}{(\frac{11}{15})} . \color{green}{(x)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{19}{18})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{19}{18}p+\frac{11}{15}x+\frac{11}{15}.\frac{19}{18}& \text{Uitwerken } \\ & =px+\frac{19}{18}p+\frac{11}{15}x+\frac{209}{270} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-5}{7}+q)(a+\frac{-4}{14})& =(\color{red}{q}+\color{orange}{\frac{-5}{7}}).(\color{green}{a}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{2}{7}q-\frac{5}{7}a+\frac{5}{7}.\frac{2}{7}& \text{Uitwerken } \\ & =aq-\frac{2}{7}q-\frac{5}{7}a+\frac{10}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-15}{10}-x)(\frac{20}{4}-b)& =(\color{red}{-x}+\color{orange}{\frac{-3}{2}}).(\color{green}{-b}+\color{blue}{5})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(5)} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = bx-5x+\frac{3}{2}b-\frac{3}{2}.5& \text{Uitwerken } \\ & =bx-5x+\frac{3}{2}b-\frac{15}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x-\frac{-19}{16})(a-\frac{5}{9})& =(\color{red}{x}+\color{orange}{\frac{19}{16}}).(\color{green}{a}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{19}{16})} . \color{green}{(a)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{9}x+\frac{19}{16}a-\frac{19}{16}.\frac{5}{9}& \text{Uitwerken } \\ & =ax-\frac{5}{9}x+\frac{19}{16}a-\frac{95}{144} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(q-\frac{-11}{3})(b+\frac{7}{12})& =(\color{red}{q}+\color{orange}{\frac{11}{3}}).(\color{green}{b}+\color{blue}{\frac{7}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{7}{12})} + \color{orange}{(\frac{11}{3})} . \color{green}{(b)} + \color{orange}{(\frac{11}{3})} . \color{blue}{(\frac{7}{12})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{12}q+\frac{11}{3}b+\frac{11}{3}.\frac{7}{12}& \text{Uitwerken } \\ & =bq+\frac{7}{12}q+\frac{11}{3}b+\frac{77}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p-\frac{15}{13})(\frac{-10}{17}+q)& =(\color{red}{p}+\color{orange}{\frac{-15}{13}}).(\color{green}{q}+\color{blue}{\frac{-10}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{17})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{-10}{17})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{10}{17}p-\frac{15}{13}q+\frac{15}{13}.\frac{10}{17}& \text{Uitwerken } \\ & =pq-\frac{10}{17}p-\frac{15}{13}q+\frac{150}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-10}{4}+b)(\frac{8}{8}+a)& =(\color{red}{b}+\color{orange}{\frac{-5}{2}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-5}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ab+1b-\frac{5}{2}a-\frac{5}{2}.1& \text{Uitwerken } \\ & =ab+1b-\frac{5}{2}a-\frac{5}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b+\frac{-4}{4})(\frac{18}{10}+a)& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{9}{5}b-1a-1.\frac{9}{5}& \text{Uitwerken } \\ & =ab+\frac{9}{5}b-1a-\frac{9}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p+\frac{-17}{6})(\frac{8}{12}-a)& =(\color{red}{p}+\color{orange}{\frac{-17}{6}}).(\color{green}{-a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-17}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{-17}{6})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{2}{3}p+\frac{17}{6}a-\frac{17}{6}.\frac{2}{3}& \text{Uitwerken } \\ & =-ap+\frac{2}{3}p+\frac{17}{6}a-\frac{34}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{2}{3}p+\frac{17}{6}a-\frac{17}{9} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(a+\frac{4}{9})(\frac{-15}{12}+x)& =(\color{red}{a}+\color{orange}{\frac{4}{9}}).(\color{green}{x}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{4}{9})} . \color{green}{(x)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{4}a+\frac{4}{9}x-\frac{4}{9}.\frac{5}{4}& \text{Uitwerken } \\ & =ax-\frac{5}{4}a+\frac{4}{9}x-\frac{20}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{5}{4}a+\frac{4}{9}x-\frac{5}{9} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(a-\frac{7}{4})(\frac{17}{17}+b)& =(\color{red}{a}+\color{orange}{\frac{-7}{4}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{-7}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ab+1a-\frac{7}{4}b-\frac{7}{4}.1& \text{Uitwerken } \\ & =ab+1a-\frac{7}{4}b-\frac{7}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p-\frac{18}{15})(\frac{-12}{3}+b)& =(\color{red}{p}+\color{orange}{\frac{-6}{5}}).(\color{green}{b}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-4)} + \color{orange}{(\frac{-6}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = bp-4p-\frac{6}{5}b+\frac{6}{5}.4& \text{Uitwerken } \\ & =bp-4p-\frac{6}{5}b+\frac{24}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)