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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{-1}{11})(p-\frac{3}{2})& =(\color{red}{p}+\color{orange}{\frac{-1}{11}}).(\color{green}{p}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-1}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{11})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{3}{2}p-\frac{1}{11}p+\frac{1}{11}.\frac{3}{2}& \text{Uitwerken } \\ & =p^2+((\frac{-3}{2})+(\frac{-1}{11}))p+\frac{3}{22} & \text{Neem samen} \\ &=p^2-\frac{35}{22}p+\frac{3}{22} & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(q-\frac{1}{15})(p-\frac{-16}{20})& =(\color{red}{q}+\color{orange}{\frac{-1}{15}}).(\color{green}{p}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{4}{5}q-\frac{1}{15}p-\frac{1}{15}.\frac{4}{5}& \text{Uitwerken } \\ & =pq+\frac{4}{5}q-\frac{1}{15}p-\frac{4}{75} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{20}{19}+x)(q-\frac{17}{4})& =(\color{red}{x}+\color{orange}{\frac{20}{19}}).(\color{green}{q}+\color{blue}{\frac{-17}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{4})} + \color{orange}{(\frac{20}{19})} . \color{green}{(q)} + \color{orange}{(\frac{20}{19})} . \color{blue}{(\frac{-17}{4})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{17}{4}x+\frac{20}{19}q-\frac{20}{19}.\frac{17}{4}& \text{Uitwerken } \\ & =qx-\frac{17}{4}x+\frac{20}{19}q-\frac{340}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{17}{4}x+\frac{20}{19}q-\frac{85}{19} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(p+\frac{-4}{2})(\frac{7}{8}+q)& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{7}{8}p-2q-2.\frac{7}{8}& \text{Uitwerken } \\ & =pq+\frac{7}{8}p-2q-\frac{14}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{7}{8}p-2q-\frac{7}{4} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(p+\frac{-11}{13})(b-\frac{4}{8})& =(\color{red}{p}+\color{orange}{\frac{-11}{13}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{2}p-\frac{11}{13}b+\frac{11}{13}.\frac{1}{2}& \text{Uitwerken } \\ & =bp-\frac{1}{2}p-\frac{11}{13}b+\frac{11}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q-(-15))(\frac{-19}{15}+p)& =(\color{red}{q}+\color{orange}{15}).(\color{green}{p}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(15)} . \color{green}{(p)} + \color{orange}{(15)} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{15}q+15p-15.\frac{19}{15}& \text{Uitwerken } \\ & =pq-\frac{19}{15}q+15p-\frac{285}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{19}{15}q+15p-19 & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-9}{6}+a)(p+\frac{11}{13})& =(\color{red}{a}+\color{orange}{\frac{-3}{2}}).(\color{green}{p}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{11}{13}a-\frac{3}{2}p-\frac{3}{2}.\frac{11}{13}& \text{Uitwerken } \\ & =ap+\frac{11}{13}a-\frac{3}{2}p-\frac{33}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q+\frac{2}{4})(a-\frac{8}{14})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{4}{7}q+\frac{1}{2}a-\frac{1}{2}.\frac{4}{7}& \text{Uitwerken } \\ & =aq-\frac{4}{7}q+\frac{1}{2}a-\frac{4}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{4}{7}q+\frac{1}{2}a-\frac{2}{7} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-5}{16}-p)(b+\frac{-15}{8})& =(\color{red}{-p}+\color{orange}{\frac{-5}{16}}).(\color{green}{b}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{-5}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{16})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{15}{8}p-\frac{5}{16}b+\frac{5}{16}.\frac{15}{8}& \text{Uitwerken } \\ & =-bp+\frac{15}{8}p-\frac{5}{16}b+\frac{75}{128} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(p-\frac{13}{9})(b+\frac{-16}{6})& =(\color{red}{p}+\color{orange}{\frac{-13}{9}}).(\color{green}{b}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-13}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{9})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{8}{3}p-\frac{13}{9}b+\frac{13}{9}.\frac{8}{3}& \text{Uitwerken } \\ & =bp-\frac{8}{3}p-\frac{13}{9}b+\frac{104}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(q-\frac{-2}{16})(\frac{17}{12}+a)& =(\color{red}{q}+\color{orange}{\frac{1}{8}}).(\color{green}{a}+\color{blue}{\frac{17}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{17}{12})} + \color{orange}{(\frac{1}{8})} . \color{green}{(a)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{17}{12})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{17}{12}q+\frac{1}{8}a+\frac{1}{8}.\frac{17}{12}& \text{Uitwerken } \\ & =aq+\frac{17}{12}q+\frac{1}{8}a+\frac{17}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b-\frac{-1}{10})(a-\frac{13}{7})& =(\color{red}{b}+\color{orange}{\frac{1}{10}}).(\color{green}{a}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(\frac{1}{10})} . \color{green}{(a)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{7}b+\frac{1}{10}a-\frac{1}{10}.\frac{13}{7}& \text{Uitwerken } \\ & =ab-\frac{13}{7}b+\frac{1}{10}a-\frac{13}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)