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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{2}{7})(p-\frac{14}{18})& =(\color{red}{a}+\color{orange}{\frac{2}{7}}).(\color{green}{p}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{2}{7})} . \color{green}{(p)} + \color{orange}{(\frac{2}{7})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{9}a+\frac{2}{7}p-\frac{2}{7}.\frac{7}{9}& \text{Uitwerken } \\ & =ap-\frac{7}{9}a+\frac{2}{7}p-\frac{14}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{7}{9}a+\frac{2}{7}p-\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{20}{19}+b)(p+\frac{8}{9})& =(\color{red}{b}+\color{orange}{\frac{20}{19}}).(\color{green}{p}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{20}{19})} . \color{green}{(p)} + \color{orange}{(\frac{20}{19})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{8}{9}b+\frac{20}{19}p+\frac{20}{19}.\frac{8}{9}& \text{Uitwerken } \\ & =bp+\frac{8}{9}b+\frac{20}{19}p+\frac{160}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(a-\frac{3}{19})(b-\frac{5}{8})& =(\color{red}{a}+\color{orange}{\frac{-3}{19}}).(\color{green}{b}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{-3}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{19})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{8}a-\frac{3}{19}b+\frac{3}{19}.\frac{5}{8}& \text{Uitwerken } \\ & =ab-\frac{5}{8}a-\frac{3}{19}b+\frac{15}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q+\frac{2}{5})(x+\frac{-5}{13})& =(\color{red}{q}+\color{orange}{\frac{2}{5}}).(\color{green}{x}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{13})} + \color{orange}{(\frac{2}{5})} . \color{green}{(x)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{13}q+\frac{2}{5}x-\frac{2}{5}.\frac{5}{13}& \text{Uitwerken } \\ & =qx-\frac{5}{13}q+\frac{2}{5}x-\frac{10}{65} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{5}{13}q+\frac{2}{5}x-\frac{2}{13} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-20}{10}+a)(q-\frac{1}{13})& =(\color{red}{a}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{-1}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{13})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{13})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{1}{13}a-2q+2.\frac{1}{13}& \text{Uitwerken } \\ & =aq-\frac{1}{13}a-2q+\frac{2}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{-7}{15})(x-\frac{1}{11})& =(\color{red}{a}+\color{orange}{\frac{-7}{15}}).(\color{green}{x}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{-7}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{11}a-\frac{7}{15}x+\frac{7}{15}.\frac{1}{11}& \text{Uitwerken } \\ & =ax-\frac{1}{11}a-\frac{7}{15}x+\frac{7}{165} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p+\frac{11}{19})(q+\frac{16}{5})& =(\color{red}{p}+\color{orange}{\frac{11}{19}}).(\color{green}{q}+\color{blue}{\frac{16}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{16}{5})} + \color{orange}{(\frac{11}{19})} . \color{green}{(q)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(\frac{16}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{16}{5}p+\frac{11}{19}q+\frac{11}{19}.\frac{16}{5}& \text{Uitwerken } \\ & =pq+\frac{16}{5}p+\frac{11}{19}q+\frac{176}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-2}{4}-p)(b-\frac{14}{8})& =(\color{red}{-p}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{7}{4}p-\frac{1}{2}b+\frac{1}{2}.\frac{7}{4}& \text{Uitwerken } \\ & =-bp+\frac{7}{4}p-\frac{1}{2}b+\frac{7}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(b-\frac{20}{18})(\frac{2}{11}-a)& =(\color{red}{b}+\color{orange}{\frac{-10}{9}}).(\color{green}{-a}+\color{blue}{\frac{2}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{2}{11})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{2}{11})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{2}{11}b+\frac{10}{9}a-\frac{10}{9}.\frac{2}{11}& \text{Uitwerken } \\ & =-ab+\frac{2}{11}b+\frac{10}{9}a-\frac{20}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{2}{6}-x)(\frac{15}{10}-b)& =(\color{red}{-x}+\color{orange}{\frac{1}{3}}).(\color{green}{-b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{1}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{2}x-\frac{1}{3}b+\frac{1}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =bx-\frac{3}{2}x-\frac{1}{3}b+\frac{3}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{3}{2}x-\frac{1}{3}b+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(b+\frac{15}{2})(q+\frac{15}{20})& =(\color{red}{b}+\color{orange}{\frac{15}{2}}).(\color{green}{q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{15}{2})} . \color{green}{(q)} + \color{orange}{(\frac{15}{2})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{4}b+\frac{15}{2}q+\frac{15}{2}.\frac{3}{4}& \text{Uitwerken } \\ & =bq+\frac{3}{4}b+\frac{15}{2}q+\frac{45}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b+\frac{-20}{15})(\frac{1}{6}-q)& =(\color{red}{b}+\color{orange}{\frac{-4}{3}}).(\color{green}{-q}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{6}b+\frac{4}{3}q-\frac{4}{3}.\frac{1}{6}& \text{Uitwerken } \\ & =-bq+\frac{1}{6}b+\frac{4}{3}q-\frac{4}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{1}{6}b+\frac{4}{3}q-\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)