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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{-18}{9})(\frac{-4}{19}+a)& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{4}{19}p-2a+2.\frac{4}{19}& \text{Uitwerken } \\ & =ap-\frac{4}{19}p-2a+\frac{8}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q+\frac{-5}{6})(a+\frac{1}{7})& =(\color{red}{q}+\color{orange}{\frac{-5}{6}}).(\color{green}{a}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{7}q-\frac{5}{6}a-\frac{5}{6}.\frac{1}{7}& \text{Uitwerken } \\ & =aq+\frac{1}{7}q-\frac{5}{6}a-\frac{5}{42} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-6}{7}+p)(\frac{20}{19}-b)& =(\color{red}{p}+\color{orange}{\frac{-6}{7}}).(\color{green}{-b}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{20}{19}p+\frac{6}{7}b-\frac{6}{7}.\frac{20}{19}& \text{Uitwerken } \\ & =-bp+\frac{20}{19}p+\frac{6}{7}b-\frac{120}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{10}{17}+q)(\frac{-14}{2}+p)& =(\color{red}{q}+\color{orange}{\frac{10}{17}}).(\color{green}{p}+\color{blue}{(-7)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-7)} + \color{orange}{(\frac{10}{17})} . \color{green}{(p)} + \color{orange}{(\frac{10}{17})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = pq-7q+\frac{10}{17}p-\frac{10}{17}.7& \text{Uitwerken } \\ & =pq-7q+\frac{10}{17}p-\frac{70}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(q-\frac{7}{14})(\frac{13}{3}-x)& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{-x}+\color{blue}{\frac{13}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{13}{3})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{13}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{13}{3}q+\frac{1}{2}x-\frac{1}{2}.\frac{13}{3}& \text{Uitwerken } \\ & =-qx+\frac{13}{3}q+\frac{1}{2}x-\frac{13}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x+\frac{-1}{14})(\frac{1}{2}+x)& =(\color{red}{x}+\color{orange}{\frac{-1}{14}}).(\color{green}{x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-1}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{14})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{1}{2}x-\frac{1}{14}x-\frac{1}{14}.\frac{1}{2}& \text{Uitwerken } \\ & =x^2+(\frac{1}{2}+(\frac{-1}{14}))x-(\frac{-1}{28}) & \text{Neem samen} \\ &=x^2+\frac{6}{14}x-(\frac{-1}{28}) & \text{Maak de som} \\ &=x^2+\frac{3}{7}x+\frac{1}{28} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
7. \(\begin{align}(b+\frac{1}{9})(p+\frac{17}{8})& =(\color{red}{b}+\color{orange}{\frac{1}{9}}).(\color{green}{p}+\color{blue}{\frac{17}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{17}{8})} + \color{orange}{(\frac{1}{9})} . \color{green}{(p)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{17}{8})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{17}{8}b+\frac{1}{9}p+\frac{1}{9}.\frac{17}{8}& \text{Uitwerken } \\ & =bp+\frac{17}{8}b+\frac{1}{9}p+\frac{17}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{6}{12}+x)(\frac{-3}{6}+b)& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{2}x+\frac{1}{2}b-\frac{1}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =bx-\frac{1}{2}x+\frac{1}{2}b-\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{12}{18}-p)(\frac{-12}{18}-b)& =(\color{red}{-p}+\color{orange}{\frac{2}{3}}).(\color{green}{-b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{2}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{3}p-\frac{2}{3}b-\frac{2}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =bp+\frac{2}{3}p-\frac{2}{3}b-\frac{4}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(p+\frac{5}{10})(\frac{8}{15}-a)& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{-a}+\color{blue}{\frac{8}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{8}{15})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{8}{15})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{8}{15}p-\frac{1}{2}a+\frac{1}{2}.\frac{8}{15}& \text{Uitwerken } \\ & =-ap+\frac{8}{15}p-\frac{1}{2}a+\frac{8}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{8}{15}p-\frac{1}{2}a+\frac{4}{15} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-20}{18}-q)(\frac{16}{14}-b)& =(\color{red}{-q}+\color{orange}{\frac{-10}{9}}).(\color{green}{-b}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{8}{7}q+\frac{10}{9}b-\frac{10}{9}.\frac{8}{7}& \text{Uitwerken } \\ & =bq-\frac{8}{7}q+\frac{10}{9}b-\frac{80}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{15}{18}-p)(\frac{19}{12}-p)& =(\color{red}{-p}+\color{orange}{\frac{5}{6}}).(\color{green}{-p}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{5}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{19}{12}p-\frac{5}{6}p+\frac{5}{6}.\frac{19}{12}& \text{Uitwerken } \\ & =p^2+((\frac{-19}{12})+(\frac{-5}{6}))p+\frac{95}{72} & \text{Neem samen} \\ &=p^2-\frac{29}{12}p+\frac{95}{72} & \text{Maak de som} \\\end{align}\)