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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{-14}{19})(b+\frac{16}{8})& =(\color{red}{a}+\color{orange}{\frac{14}{19}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{14}{19})} . \color{green}{(b)} + \color{orange}{(\frac{14}{19})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ab+2a+\frac{14}{19}b+\frac{14}{19}.2& \text{Uitwerken } \\ & =ab+2a+\frac{14}{19}b+\frac{28}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b+\frac{-7}{16})(p-\frac{5}{19})& =(\color{red}{b}+\color{orange}{\frac{-7}{16}}).(\color{green}{p}+\color{blue}{\frac{-5}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{19})} + \color{orange}{(\frac{-7}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{16})} . \color{blue}{(\frac{-5}{19})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{19}b-\frac{7}{16}p+\frac{7}{16}.\frac{5}{19}& \text{Uitwerken } \\ & =bp-\frac{5}{19}b-\frac{7}{16}p+\frac{35}{304} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-3}{2}-a)(\frac{1}{17}+b)& =(\color{red}{-a}+\color{orange}{\frac{-3}{2}}).(\color{green}{b}+\color{blue}{\frac{1}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{17})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{1}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{17}a-\frac{3}{2}b-\frac{3}{2}.\frac{1}{17}& \text{Uitwerken } \\ & =-ab-\frac{1}{17}a-\frac{3}{2}b-\frac{3}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{20}{5}+a)(\frac{-6}{2}-q)& =(\color{red}{a}+\color{orange}{4}).(\color{green}{-q}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(-3)} + \color{orange}{(4)} . \color{green}{(-q)} + \color{orange}{(4)} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -aq-3a-4q-4.3& \text{Uitwerken } \\ & =-aq-3a-4q-12 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{17}{2}+b)(\frac{18}{11}+q)& =(\color{red}{b}+\color{orange}{\frac{17}{2}}).(\color{green}{q}+\color{blue}{\frac{18}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{18}{11})} + \color{orange}{(\frac{17}{2})} . \color{green}{(q)} + \color{orange}{(\frac{17}{2})} . \color{blue}{(\frac{18}{11})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{18}{11}b+\frac{17}{2}q+\frac{17}{2}.\frac{18}{11}& \text{Uitwerken } \\ & =bq+\frac{18}{11}b+\frac{17}{2}q+\frac{306}{22} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{18}{11}b+\frac{17}{2}q+\frac{153}{11} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(p+\frac{11}{8})(q+\frac{-7}{13})& =(\color{red}{p}+\color{orange}{\frac{11}{8}}).(\color{green}{q}+\color{blue}{\frac{-7}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{13})} + \color{orange}{(\frac{11}{8})} . \color{green}{(q)} + \color{orange}{(\frac{11}{8})} . \color{blue}{(\frac{-7}{13})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{7}{13}p+\frac{11}{8}q-\frac{11}{8}.\frac{7}{13}& \text{Uitwerken } \\ & =pq-\frac{7}{13}p+\frac{11}{8}q-\frac{77}{104} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q+\frac{-9}{8})((-9)+x)& =(\color{red}{q}+\color{orange}{\frac{-9}{8}}).(\color{green}{x}+\color{blue}{(-9)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-9)} + \color{orange}{(\frac{-9}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = qx-9q-\frac{9}{8}x+\frac{9}{8}.9& \text{Uitwerken } \\ & =qx-9q-\frac{9}{8}x+\frac{81}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p+\frac{-18}{2})(q+\frac{4}{7})& =(\color{red}{p}+\color{orange}{(-9)}).(\color{green}{q}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(-9)} . \color{green}{(q)} + \color{orange}{(-9)} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{7}p-9q-9.\frac{4}{7}& \text{Uitwerken } \\ & =pq+\frac{4}{7}p-9q-\frac{36}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{7}{8}-a)(x-\frac{-2}{10})& =(\color{red}{-a}+\color{orange}{\frac{7}{8}}).(\color{green}{x}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{7}{8})} . \color{green}{(x)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{5}a+\frac{7}{8}x+\frac{7}{8}.\frac{1}{5}& \text{Uitwerken } \\ & =-ax-\frac{1}{5}a+\frac{7}{8}x+\frac{7}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x+\frac{-14}{12})(\frac{3}{18}-q)& =(\color{red}{x}+\color{orange}{\frac{-7}{6}}).(\color{green}{-q}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{6}x+\frac{7}{6}q-\frac{7}{6}.\frac{1}{6}& \text{Uitwerken } \\ & =-qx+\frac{1}{6}x+\frac{7}{6}q-\frac{7}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{4}{9}-q)(a-\frac{-3}{18})& =(\color{red}{-q}+\color{orange}{\frac{4}{9}}).(\color{green}{a}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{4}{9})} . \color{green}{(a)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{6}q+\frac{4}{9}a+\frac{4}{9}.\frac{1}{6}& \text{Uitwerken } \\ & =-aq-\frac{1}{6}q+\frac{4}{9}a+\frac{4}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{1}{6}q+\frac{4}{9}a+\frac{2}{27} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(x+\frac{-6}{11})(\frac{-10}{19}-q)& =(\color{red}{x}+\color{orange}{\frac{-6}{11}}).(\color{green}{-q}+\color{blue}{\frac{-10}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{19})} + \color{orange}{(\frac{-6}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{-6}{11})} . \color{blue}{(\frac{-10}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{10}{19}x+\frac{6}{11}q+\frac{6}{11}.\frac{10}{19}& \text{Uitwerken } \\ & =-qx-\frac{10}{19}x+\frac{6}{11}q+\frac{60}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)