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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{12}{11}-p)(\frac{-9}{15}-b)& =(\color{red}{-p}+\color{orange}{\frac{12}{11}}).(\color{green}{-b}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{12}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{12}{11})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{5}p-\frac{12}{11}b-\frac{12}{11}.\frac{3}{5}& \text{Uitwerken } \\ & =bp+\frac{3}{5}p-\frac{12}{11}b-\frac{36}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x+\frac{13}{13})(\frac{-11}{18}-q)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{-q}+\color{blue}{\frac{-11}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{18})} + \color{orange}{(1)} . \color{green}{(-q)} + \color{orange}{(1)} . \color{blue}{(\frac{-11}{18})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{11}{18}x-1q-1.\frac{11}{18}& \text{Uitwerken } \\ & =-qx-\frac{11}{18}x-1q-\frac{11}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-1}{17}-b)(\frac{-6}{3}-b)& =(\color{red}{-b}+\color{orange}{\frac{-1}{17}}).(\color{green}{-b}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-1}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bb+2b+\frac{1}{17}b+\frac{1}{17}.2& \text{Uitwerken } \\ & =b^2+(2+\frac{1}{17})b+\frac{2}{17} & \text{Neem samen} \\ &=b^2+\frac{35}{17}b+\frac{2}{17} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(q-\frac{-2}{4})(\frac{-14}{8}-b)& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{-b}+\color{blue}{\frac{-7}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{4})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-7}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{7}{4}q-\frac{1}{2}b-\frac{1}{2}.\frac{7}{4}& \text{Uitwerken } \\ & =-bq-\frac{7}{4}q-\frac{1}{2}b-\frac{7}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b+\frac{3}{11})(\frac{-9}{7}-p)& =(\color{red}{b}+\color{orange}{\frac{3}{11}}).(\color{green}{-p}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{3}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{11})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{9}{7}b-\frac{3}{11}p-\frac{3}{11}.\frac{9}{7}& \text{Uitwerken } \\ & =-bp-\frac{9}{7}b-\frac{3}{11}p-\frac{27}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{18}{3}+x)(\frac{18}{13}-a)& =(\color{red}{x}+\color{orange}{6}).(\color{green}{-a}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(6)} . \color{green}{(-a)} + \color{orange}{(6)} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{18}{13}x-6a+6.\frac{18}{13}& \text{Uitwerken } \\ & =-ax+\frac{18}{13}x-6a+\frac{108}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q+\frac{8}{11})(\frac{-15}{14}-p)& =(\color{red}{q}+\color{orange}{\frac{8}{11}}).(\color{green}{-p}+\color{blue}{\frac{-15}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-15}{14})} + \color{orange}{(\frac{8}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(\frac{-15}{14})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{15}{14}q-\frac{8}{11}p-\frac{8}{11}.\frac{15}{14}& \text{Uitwerken } \\ & =-pq-\frac{15}{14}q-\frac{8}{11}p-\frac{120}{154} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{15}{14}q-\frac{8}{11}p-\frac{60}{77} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{2}{15}-p)(\frac{9}{2}+b)& =(\color{red}{-p}+\color{orange}{\frac{2}{15}}).(\color{green}{b}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{2}{15})} . \color{green}{(b)} + \color{orange}{(\frac{2}{15})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{9}{2}p+\frac{2}{15}b+\frac{2}{15}.\frac{9}{2}& \text{Uitwerken } \\ & =-bp-\frac{9}{2}p+\frac{2}{15}b+\frac{18}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{9}{2}p+\frac{2}{15}b+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-18}{2}+x)(\frac{-17}{17}-q)& =(\color{red}{x}+\color{orange}{(-9)}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(-9)} . \color{green}{(-q)} + \color{orange}{(-9)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qx-1x+9q+9.1& \text{Uitwerken } \\ & =-qx-1x+9q+9 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x-\frac{6}{3})(\frac{-11}{2}+x)& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{11}{2}x-2x+2.\frac{11}{2}& \text{Uitwerken } \\ & =x^2+((\frac{-11}{2})+(-2))x+\frac{22}{2} & \text{Neem samen} \\ &=x^2-\frac{15}{2}x+\frac{22}{2} & \text{Maak de som} \\ &=x^2-\frac{15}{2}x+11 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
11. \(\begin{align}(a+\frac{-2}{20})(\frac{-13}{6}-q)& =(\color{red}{a}+\color{orange}{\frac{-1}{10}}).(\color{green}{-q}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{13}{6}a+\frac{1}{10}q+\frac{1}{10}.\frac{13}{6}& \text{Uitwerken } \\ & =-aq-\frac{13}{6}a+\frac{1}{10}q+\frac{13}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{17}{4}-x)(\frac{1}{11}-a)& =(\color{red}{-x}+\color{orange}{\frac{17}{4}}).(\color{green}{-a}+\color{blue}{\frac{1}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{11})} + \color{orange}{(\frac{17}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{17}{4})} . \color{blue}{(\frac{1}{11})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{11}x-\frac{17}{4}a+\frac{17}{4}.\frac{1}{11}& \text{Uitwerken } \\ & =ax-\frac{1}{11}x-\frac{17}{4}a+\frac{17}{44} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)