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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-15}{11}-b)(\frac{1}{14}+p)& =(\color{red}{-b}+\color{orange}{\frac{-15}{11}}).(\color{green}{p}+\color{blue}{\frac{1}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{14})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{1}{14})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{14}b-\frac{15}{11}p-\frac{15}{11}.\frac{1}{14}& \text{Uitwerken } \\ & =-bp-\frac{1}{14}b-\frac{15}{11}p-\frac{15}{154} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-1}{10}+x)(a-3)& =(\color{red}{x}+\color{orange}{\frac{-1}{10}}).(\color{green}{a}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-3)} + \color{orange}{(\frac{-1}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = ax-3x-\frac{1}{10}a+\frac{1}{10}.3& \text{Uitwerken } \\ & =ax-3x-\frac{1}{10}a+\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x-\frac{2}{16})(\frac{10}{2}-q)& =(\color{red}{x}+\color{orange}{\frac{-1}{8}}).(\color{green}{-q}+\color{blue}{5})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(5)} + \color{orange}{(\frac{-1}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = -qx+5x+\frac{1}{8}q-\frac{1}{8}.5& \text{Uitwerken } \\ & =-qx+5x+\frac{1}{8}q-\frac{5}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x-\frac{8}{9})(\frac{4}{17}+q)& =(\color{red}{x}+\color{orange}{\frac{-8}{9}}).(\color{green}{q}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{4}{17}x-\frac{8}{9}q-\frac{8}{9}.\frac{4}{17}& \text{Uitwerken } \\ & =qx+\frac{4}{17}x-\frac{8}{9}q-\frac{32}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(q-\frac{19}{12})(\frac{19}{11}+a)& =(\color{red}{q}+\color{orange}{\frac{-19}{12}}).(\color{green}{a}+\color{blue}{\frac{19}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{19}{11})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{19}{11})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{19}{11}q-\frac{19}{12}a-\frac{19}{12}.\frac{19}{11}& \text{Uitwerken } \\ & =aq+\frac{19}{11}q-\frac{19}{12}a-\frac{361}{132} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p+\frac{18}{16})(p-\frac{-10}{20})& =(\color{red}{p}+\color{orange}{\frac{9}{8}}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{9}{8})} . \color{green}{(p)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{1}{2}p+\frac{9}{8}p+\frac{9}{8}.\frac{1}{2}& \text{Uitwerken } \\ & =p^2+(\frac{1}{2}+\frac{9}{8})p+\frac{9}{16} & \text{Neem samen} \\ &=p^2+\frac{13}{8}p+\frac{9}{16} & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{7}{9}+a)(\frac{11}{5}-a)& =(\color{red}{a}+\color{orange}{\frac{7}{9}}).(\color{green}{-a}+\color{blue}{\frac{11}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{11}{5})} + \color{orange}{(\frac{7}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{11}{5})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{11}{5}a-\frac{7}{9}a+\frac{7}{9}.\frac{11}{5}& \text{Uitwerken } \\ & =-a^2+(\frac{11}{5}+(\frac{-7}{9}))a+(\frac{-77}{45}) & \text{Neem samen} \\ &=-a^2+\frac{64}{45}a+(\frac{-77}{45}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(\frac{7}{2}-q)(p+\frac{5}{16})& =(\color{red}{-q}+\color{orange}{\frac{7}{2}}).(\color{green}{p}+\color{blue}{\frac{5}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{16})} + \color{orange}{(\frac{7}{2})} . \color{green}{(p)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{5}{16})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{5}{16}q+\frac{7}{2}p+\frac{7}{2}.\frac{5}{16}& \text{Uitwerken } \\ & =-pq-\frac{5}{16}q+\frac{7}{2}p+\frac{35}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p-\frac{-18}{18})(p+\frac{-20}{15})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{4}{3}p+1p-1.\frac{4}{3}& \text{Uitwerken } \\ & =p^2+((\frac{-4}{3})+1)p-(\frac{-4}{3}) & \text{Neem samen} \\ &=p^2-\frac{1}{3}p-(\frac{-4}{3}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(q+\frac{5}{12})(\frac{-14}{6}+b)& =(\color{red}{q}+\color{orange}{\frac{5}{12}}).(\color{green}{b}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{5}{12})} . \color{green}{(b)} + \color{orange}{(\frac{5}{12})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{7}{3}q+\frac{5}{12}b-\frac{5}{12}.\frac{7}{3}& \text{Uitwerken } \\ & =bq-\frac{7}{3}q+\frac{5}{12}b-\frac{35}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(b+\frac{-2}{13})(p+\frac{19}{12})& =(\color{red}{b}+\color{orange}{\frac{-2}{13}}).(\color{green}{p}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{-2}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{12}b-\frac{2}{13}p-\frac{2}{13}.\frac{19}{12}& \text{Uitwerken } \\ & =bp+\frac{19}{12}b-\frac{2}{13}p-\frac{38}{156} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{19}{12}b-\frac{2}{13}p-\frac{19}{78} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-3}{8}-a)(q+\frac{-12}{18})& =(\color{red}{-a}+\color{orange}{\frac{-3}{8}}).(\color{green}{q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{2}{3}a-\frac{3}{8}q+\frac{3}{8}.\frac{2}{3}& \text{Uitwerken } \\ & =-aq+\frac{2}{3}a-\frac{3}{8}q+\frac{6}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{2}{3}a-\frac{3}{8}q+\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)