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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q+\frac{2}{18})(\frac{-19}{17}+p)& =(\color{red}{q}+\color{orange}{\frac{1}{9}}).(\color{green}{p}+\color{blue}{\frac{-19}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{17})} + \color{orange}{(\frac{1}{9})} . \color{green}{(p)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{-19}{17})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{17}q+\frac{1}{9}p-\frac{1}{9}.\frac{19}{17}& \text{Uitwerken } \\ & =pq-\frac{19}{17}q+\frac{1}{9}p-\frac{19}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-10}{11}+b)(x+\frac{6}{8})& =(\color{red}{b}+\color{orange}{\frac{-10}{11}}).(\color{green}{x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-10}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{4}b-\frac{10}{11}x-\frac{10}{11}.\frac{3}{4}& \text{Uitwerken } \\ & =bx+\frac{3}{4}b-\frac{10}{11}x-\frac{30}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{3}{4}b-\frac{10}{11}x-\frac{15}{22} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(p-\frac{14}{12})(\frac{-9}{20}-b)& =(\color{red}{p}+\color{orange}{\frac{-7}{6}}).(\color{green}{-b}+\color{blue}{\frac{-9}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{20})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{-9}{20})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{9}{20}p+\frac{7}{6}b+\frac{7}{6}.\frac{9}{20}& \text{Uitwerken } \\ & =-bp-\frac{9}{20}p+\frac{7}{6}b+\frac{63}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{9}{20}p+\frac{7}{6}b+\frac{21}{40} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(b-\frac{1}{2})(\frac{-13}{3}+x)& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{13}{3}b-\frac{1}{2}x+\frac{1}{2}.\frac{13}{3}& \text{Uitwerken } \\ & =bx-\frac{13}{3}b-\frac{1}{2}x+\frac{13}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}((-3)-x)(b+\frac{6}{12})& =(\color{red}{-x}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{2}x-3b-3.\frac{1}{2}& \text{Uitwerken } \\ & =-bx-\frac{1}{2}x-3b-\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{11}{8})(\frac{-19}{13}+x)& =(\color{red}{a}+\color{orange}{\frac{11}{8}}).(\color{green}{x}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{11}{8})} . \color{green}{(x)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{19}{13}a+\frac{11}{8}x-\frac{11}{8}.\frac{19}{13}& \text{Uitwerken } \\ & =ax-\frac{19}{13}a+\frac{11}{8}x-\frac{209}{104} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-17}{3}-q)(x+\frac{-5}{13})& =(\color{red}{-q}+\color{orange}{\frac{-17}{3}}).(\color{green}{x}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{13})} + \color{orange}{(\frac{-17}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{3})} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{5}{13}q-\frac{17}{3}x+\frac{17}{3}.\frac{5}{13}& \text{Uitwerken } \\ & =-qx+\frac{5}{13}q-\frac{17}{3}x+\frac{85}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{9}{12}-q)(\frac{5}{4}-p)& =(\color{red}{-q}+\color{orange}{\frac{3}{4}}).(\color{green}{-p}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{4}q-\frac{3}{4}p+\frac{3}{4}.\frac{5}{4}& \text{Uitwerken } \\ & =pq-\frac{5}{4}q-\frac{3}{4}p+\frac{15}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(b+\frac{-10}{11})(\frac{15}{17}+q)& =(\color{red}{b}+\color{orange}{\frac{-10}{11}}).(\color{green}{q}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(\frac{-10}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{15}{17}b-\frac{10}{11}q-\frac{10}{11}.\frac{15}{17}& \text{Uitwerken } \\ & =bq+\frac{15}{17}b-\frac{10}{11}q-\frac{150}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{11}{9}-x)(\frac{2}{17}-q)& =(\color{red}{-x}+\color{orange}{\frac{11}{9}}).(\color{green}{-q}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-q)} + \color{red}{(-x)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{11}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{11}{9})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{2}{17}x-\frac{11}{9}q+\frac{11}{9}.\frac{2}{17}& \text{Uitwerken } \\ & =qx-\frac{2}{17}x-\frac{11}{9}q+\frac{22}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-10}{13}+b)(\frac{-20}{8}+a)& =(\color{red}{b}+\color{orange}{\frac{-10}{13}}).(\color{green}{a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-10}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{13})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{2}b-\frac{10}{13}a+\frac{10}{13}.\frac{5}{2}& \text{Uitwerken } \\ & =ab-\frac{5}{2}b-\frac{10}{13}a+\frac{50}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{5}{2}b-\frac{10}{13}a+\frac{25}{13} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{19}{8}+a)(b+\frac{20}{12})& =(\color{red}{a}+\color{orange}{\frac{19}{8}}).(\color{green}{b}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{19}{8})} . \color{green}{(b)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{3}a+\frac{19}{8}b+\frac{19}{8}.\frac{5}{3}& \text{Uitwerken } \\ & =ab+\frac{5}{3}a+\frac{19}{8}b+\frac{95}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)