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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{8}{8}+b)(a+\frac{16}{6})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{8}{3}b+1a+1.\frac{8}{3}& \text{Uitwerken } \\ & =ab+\frac{8}{3}b+1a+\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q+\frac{-18}{20})(\frac{11}{5}-p)& =(\color{red}{q}+\color{orange}{\frac{-9}{10}}).(\color{green}{-p}+\color{blue}{\frac{11}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{11}{5})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(-p)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{11}{5})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{11}{5}q+\frac{9}{10}p-\frac{9}{10}.\frac{11}{5}& \text{Uitwerken } \\ & =-pq+\frac{11}{5}q+\frac{9}{10}p-\frac{99}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q+\frac{-19}{9})(a-\frac{-15}{7})& =(\color{red}{q}+\color{orange}{\frac{-19}{9}}).(\color{green}{a}+\color{blue}{\frac{15}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{15}{7})} + \color{orange}{(\frac{-19}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(\frac{15}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{15}{7}q-\frac{19}{9}a-\frac{19}{9}.\frac{15}{7}& \text{Uitwerken } \\ & =aq+\frac{15}{7}q-\frac{19}{9}a-\frac{285}{63} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{15}{7}q-\frac{19}{9}a-\frac{95}{21} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(a-\frac{13}{8})(a-\frac{4}{13})& =(\color{red}{a}+\color{orange}{\frac{-13}{8}}).(\color{green}{a}+\color{blue}{\frac{-4}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{13})} + \color{orange}{(\frac{-13}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{8})} . \color{blue}{(\frac{-4}{13})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{4}{13}a-\frac{13}{8}a+\frac{13}{8}.\frac{4}{13}& \text{Uitwerken } \\ & =a^2+((\frac{-4}{13})+(\frac{-13}{8}))a+\frac{52}{104} & \text{Neem samen} \\ &=a^2-\frac{201}{104}a+\frac{52}{104} & \text{Maak de som} \\ &=a^2-\frac{201}{104}a+\frac{1}{2} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
5. \(\begin{align}(\frac{2}{9}-q)(a+\frac{4}{16})& =(\color{red}{-q}+\color{orange}{\frac{2}{9}}).(\color{green}{a}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{2}{9})} . \color{green}{(a)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{4}q+\frac{2}{9}a+\frac{2}{9}.\frac{1}{4}& \text{Uitwerken } \\ & =-aq-\frac{1}{4}q+\frac{2}{9}a+\frac{2}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{1}{4}q+\frac{2}{9}a+\frac{1}{18} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{8}{14}-x)(a+\frac{11}{10})& =(\color{red}{-x}+\color{orange}{\frac{4}{7}}).(\color{green}{a}+\color{blue}{\frac{11}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{11}{10})} + \color{orange}{(\frac{4}{7})} . \color{green}{(a)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{11}{10})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{11}{10}x+\frac{4}{7}a+\frac{4}{7}.\frac{11}{10}& \text{Uitwerken } \\ & =-ax-\frac{11}{10}x+\frac{4}{7}a+\frac{44}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{11}{10}x+\frac{4}{7}a+\frac{22}{35} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-4}{11}+a)(\frac{11}{18}+x)& =(\color{red}{a}+\color{orange}{\frac{-4}{11}}).(\color{green}{x}+\color{blue}{\frac{11}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{11}{18})} + \color{orange}{(\frac{-4}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{11})} . \color{blue}{(\frac{11}{18})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{11}{18}a-\frac{4}{11}x-\frac{4}{11}.\frac{11}{18}& \text{Uitwerken } \\ & =ax+\frac{11}{18}a-\frac{4}{11}x-\frac{44}{198} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{11}{18}a-\frac{4}{11}x-\frac{2}{9} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-15}{14}-a)(x+\frac{15}{17})& =(\color{red}{-a}+\color{orange}{\frac{-15}{14}}).(\color{green}{x}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(\frac{-15}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{14})} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{15}{17}a-\frac{15}{14}x-\frac{15}{14}.\frac{15}{17}& \text{Uitwerken } \\ & =-ax-\frac{15}{17}a-\frac{15}{14}x-\frac{225}{238} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-16}{3}-q)(x-\frac{16}{16})& =(\color{red}{-q}+\color{orange}{\frac{-16}{3}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-16}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qx+1q-\frac{16}{3}x+\frac{16}{3}.1& \text{Uitwerken } \\ & =-qx+1q-\frac{16}{3}x+\frac{16}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a+\frac{14}{10})(x-\frac{-6}{13})& =(\color{red}{a}+\color{orange}{\frac{7}{5}}).(\color{green}{x}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{7}{5})} . \color{green}{(x)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{6}{13}a+\frac{7}{5}x+\frac{7}{5}.\frac{6}{13}& \text{Uitwerken } \\ & =ax+\frac{6}{13}a+\frac{7}{5}x+\frac{42}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{8}{18}-x)(p-\frac{-15}{11})& =(\color{red}{-x}+\color{orange}{\frac{4}{9}}).(\color{green}{p}+\color{blue}{\frac{15}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{15}{11})} + \color{orange}{(\frac{4}{9})} . \color{green}{(p)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{15}{11})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{15}{11}x+\frac{4}{9}p+\frac{4}{9}.\frac{15}{11}& \text{Uitwerken } \\ & =-px-\frac{15}{11}x+\frac{4}{9}p+\frac{60}{99} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{15}{11}x+\frac{4}{9}p+\frac{20}{33} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{11}{14}-p)(b+\frac{-2}{10})& =(\color{red}{-p}+\color{orange}{\frac{11}{14}}).(\color{green}{b}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{11}{14})} . \color{green}{(b)} + \color{orange}{(\frac{11}{14})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{5}p+\frac{11}{14}b-\frac{11}{14}.\frac{1}{5}& \text{Uitwerken } \\ & =-bp+\frac{1}{5}p+\frac{11}{14}b-\frac{11}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)