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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{-14}{17})(b-\frac{-9}{18})& =(\color{red}{a}+\color{orange}{\frac{-14}{17}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-14}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{17})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{2}a-\frac{14}{17}b-\frac{14}{17}.\frac{1}{2}& \text{Uitwerken } \\ & =ab+\frac{1}{2}a-\frac{14}{17}b-\frac{14}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{1}{2}a-\frac{14}{17}b-\frac{7}{17} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-8}{14}+q)(\frac{13}{19}+b)& =(\color{red}{q}+\color{orange}{\frac{-4}{7}}).(\color{green}{b}+\color{blue}{\frac{13}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{13}{19})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{13}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{13}{19}q-\frac{4}{7}b-\frac{4}{7}.\frac{13}{19}& \text{Uitwerken } \\ & =bq+\frac{13}{19}q-\frac{4}{7}b-\frac{52}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{1}{14}-p)(\frac{-17}{7}-q)& =(\color{red}{-p}+\color{orange}{\frac{1}{14}}).(\color{green}{-q}+\color{blue}{\frac{-17}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{-17}{7})} + \color{orange}{(\frac{1}{14})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(\frac{-17}{7})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{17}{7}p-\frac{1}{14}q-\frac{1}{14}.\frac{17}{7}& \text{Uitwerken } \\ & =pq+\frac{17}{7}p-\frac{1}{14}q-\frac{17}{98} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{3}{5}+p)(b+\frac{-11}{5})& =(\color{red}{p}+\color{orange}{\frac{3}{5}}).(\color{green}{b}+\color{blue}{\frac{-11}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{5})} + \color{orange}{(\frac{3}{5})} . \color{green}{(b)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-11}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{11}{5}p+\frac{3}{5}b-\frac{3}{5}.\frac{11}{5}& \text{Uitwerken } \\ & =bp-\frac{11}{5}p+\frac{3}{5}b-\frac{33}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-8}{2}-p)(q+\frac{-8}{14})& =(\color{red}{-p}+\color{orange}{(-4)}).(\color{green}{q}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(-4)} . \color{green}{(q)} + \color{orange}{(-4)} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{4}{7}p-4q+4.\frac{4}{7}& \text{Uitwerken } \\ & =-pq+\frac{4}{7}p-4q+\frac{16}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-7}{18}-b)(p-\frac{-4}{15})& =(\color{red}{-b}+\color{orange}{\frac{-7}{18}}).(\color{green}{p}+\color{blue}{\frac{4}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{4}{15})} + \color{orange}{(\frac{-7}{18})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{18})} . \color{blue}{(\frac{4}{15})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{4}{15}b-\frac{7}{18}p-\frac{7}{18}.\frac{4}{15}& \text{Uitwerken } \\ & =-bp-\frac{4}{15}b-\frac{7}{18}p-\frac{28}{270} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{4}{15}b-\frac{7}{18}p-\frac{14}{135} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-10}{10}-x)(q+\frac{16}{17})& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{16}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{16}{17})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{16}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{16}{17}x-1q-1.\frac{16}{17}& \text{Uitwerken } \\ & =-qx-\frac{16}{17}x-1q-\frac{16}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a+\frac{13}{2})(b+\frac{-12}{6})& =(\color{red}{a}+\color{orange}{\frac{13}{2}}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-2)} + \color{orange}{(\frac{13}{2})} . \color{green}{(b)} + \color{orange}{(\frac{13}{2})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ab-2a+\frac{13}{2}b-\frac{13}{2}.2& \text{Uitwerken } \\ & =ab-2a+\frac{13}{2}b-\frac{26}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-2a+\frac{13}{2}b-13 & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{5}{14}+p)((-15)+q)& =(\color{red}{p}+\color{orange}{\frac{5}{14}}).(\color{green}{q}+\color{blue}{(-15)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-15)} + \color{orange}{(\frac{5}{14})} . \color{green}{(q)} + \color{orange}{(\frac{5}{14})} . \color{blue}{(-15)}& \text{Boogjes en uitschrijven} \\ & = pq-15p+\frac{5}{14}q-\frac{5}{14}.15& \text{Uitwerken } \\ & =pq-15p+\frac{5}{14}q-\frac{75}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{1}{18}+q)(\frac{-8}{11}+x)& =(\color{red}{q}+\color{orange}{\frac{1}{18}}).(\color{green}{x}+\color{blue}{\frac{-8}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{11})} + \color{orange}{(\frac{1}{18})} . \color{green}{(x)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{-8}{11})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{8}{11}q+\frac{1}{18}x-\frac{1}{18}.\frac{8}{11}& \text{Uitwerken } \\ & =qx-\frac{8}{11}q+\frac{1}{18}x-\frac{8}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{8}{11}q+\frac{1}{18}x-\frac{4}{99} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(q+\frac{14}{13})(a+\frac{-14}{7})& =(\color{red}{q}+\color{orange}{\frac{14}{13}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{14}{13})} . \color{green}{(a)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = aq-2q+\frac{14}{13}a-\frac{14}{13}.2& \text{Uitwerken } \\ & =aq-2q+\frac{14}{13}a-\frac{28}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x+\frac{8}{15})(\frac{20}{11}+a)& =(\color{red}{x}+\color{orange}{\frac{8}{15}}).(\color{green}{a}+\color{blue}{\frac{20}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{20}{11})} + \color{orange}{(\frac{8}{15})} . \color{green}{(a)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(\frac{20}{11})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{20}{11}x+\frac{8}{15}a+\frac{8}{15}.\frac{20}{11}& \text{Uitwerken } \\ & =ax+\frac{20}{11}x+\frac{8}{15}a+\frac{160}{165} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{20}{11}x+\frac{8}{15}a+\frac{32}{33} & \text{Vereenvoudig} \\\end{align}\)