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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{14}{12}+b)(\frac{6}{9}-a)& =(\color{red}{b}+\color{orange}{\frac{7}{6}}).(\color{green}{-a}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{7}{6})} . \color{green}{(-a)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{2}{3}b-\frac{7}{6}a+\frac{7}{6}.\frac{2}{3}& \text{Uitwerken } \\ & =-ab+\frac{2}{3}b-\frac{7}{6}a+\frac{14}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{2}{3}b-\frac{7}{6}a+\frac{7}{9} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-2}{7}-p)(\frac{-19}{11}+a)& =(\color{red}{-p}+\color{orange}{\frac{-2}{7}}).(\color{green}{a}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{19}{11}p-\frac{2}{7}a+\frac{2}{7}.\frac{19}{11}& \text{Uitwerken } \\ & =-ap+\frac{19}{11}p-\frac{2}{7}a+\frac{38}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p+\frac{-14}{8})(\frac{-13}{7}+b)& =(\color{red}{p}+\color{orange}{\frac{-7}{4}}).(\color{green}{b}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{13}{7}p-\frac{7}{4}b+\frac{7}{4}.\frac{13}{7}& \text{Uitwerken } \\ & =bp-\frac{13}{7}p-\frac{7}{4}b+\frac{91}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{13}{7}p-\frac{7}{4}b+\frac{13}{4} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-2}{3}-p)(\frac{-9}{8}+b)& =(\color{red}{-p}+\color{orange}{\frac{-2}{3}}).(\color{green}{b}+\color{blue}{\frac{-9}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-9}{8})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-9}{8})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{9}{8}p-\frac{2}{3}b+\frac{2}{3}.\frac{9}{8}& \text{Uitwerken } \\ & =-bp+\frac{9}{8}p-\frac{2}{3}b+\frac{18}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{9}{8}p-\frac{2}{3}b+\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(x+\frac{-13}{10})(q+\frac{-13}{12})& =(\color{red}{x}+\color{orange}{\frac{-13}{10}}).(\color{green}{q}+\color{blue}{\frac{-13}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{12})} + \color{orange}{(\frac{-13}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(\frac{-13}{12})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{12}x-\frac{13}{10}q+\frac{13}{10}.\frac{13}{12}& \text{Uitwerken } \\ & =qx-\frac{13}{12}x-\frac{13}{10}q+\frac{169}{120} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p-\frac{-7}{2})(\frac{-2}{18}-b)& =(\color{red}{p}+\color{orange}{\frac{7}{2}}).(\color{green}{-b}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{7}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{9}p-\frac{7}{2}b-\frac{7}{2}.\frac{1}{9}& \text{Uitwerken } \\ & =-bp-\frac{1}{9}p-\frac{7}{2}b-\frac{7}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{12}{18}+x)(\frac{-2}{14}-a)& =(\color{red}{x}+\color{orange}{\frac{2}{3}}).(\color{green}{-a}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{2}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{7}x-\frac{2}{3}a-\frac{2}{3}.\frac{1}{7}& \text{Uitwerken } \\ & =-ax-\frac{1}{7}x-\frac{2}{3}a-\frac{2}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p-\frac{-9}{12})(\frac{-9}{6}-q)& =(\color{red}{p}+\color{orange}{\frac{3}{4}}).(\color{green}{-q}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{3}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{3}{2}p-\frac{3}{4}q-\frac{3}{4}.\frac{3}{2}& \text{Uitwerken } \\ & =-pq-\frac{3}{2}p-\frac{3}{4}q-\frac{9}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a-\frac{19}{17})(\frac{-10}{4}-a)& =(\color{red}{a}+\color{orange}{\frac{-19}{17}}).(\color{green}{-a}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-19}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{17})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{5}{2}a+\frac{19}{17}a+\frac{19}{17}.\frac{5}{2}& \text{Uitwerken } \\ & =-a^2+((\frac{-5}{2})+\frac{19}{17})a+(\frac{-95}{34}) & \text{Neem samen} \\ &=-a^2-\frac{47}{34}a+(\frac{-95}{34}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(q-\frac{10}{15})(\frac{14}{5}-x)& =(\color{red}{q}+\color{orange}{\frac{-2}{3}}).(\color{green}{-x}+\color{blue}{\frac{14}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{14}{5})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{14}{5})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{14}{5}q+\frac{2}{3}x-\frac{2}{3}.\frac{14}{5}& \text{Uitwerken } \\ & =-qx+\frac{14}{5}q+\frac{2}{3}x-\frac{28}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-7}{15}+p)(p-\frac{6}{3})& =(\color{red}{p}+\color{orange}{\frac{-7}{15}}).(\color{green}{p}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-7}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pp-2p-\frac{7}{15}p+\frac{7}{15}.2& \text{Uitwerken } \\ & =p^2+((-2)+(\frac{-7}{15}))p+\frac{14}{15} & \text{Neem samen} \\ &=p^2-\frac{37}{15}p+\frac{14}{15} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(q+\frac{14}{14})(x-\frac{-6}{20})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{10}q+1x+1.\frac{3}{10}& \text{Uitwerken } \\ & =qx+\frac{3}{10}q+1x+\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)