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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+2)(\frac{1}{17}-a)& =(\color{red}{b}+\color{orange}{2}).(\color{green}{-a}+\color{blue}{\frac{1}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{1}{17})} + \color{orange}{(2)} . \color{green}{(-a)} + \color{orange}{(2)} . \color{blue}{(\frac{1}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{17}b-2a+2.\frac{1}{17}& \text{Uitwerken } \\ & =-ab+\frac{1}{17}b-2a+\frac{2}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b+\frac{13}{18})(x+\frac{-19}{10})& =(\color{red}{b}+\color{orange}{\frac{13}{18}}).(\color{green}{x}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{13}{18})} . \color{green}{(x)} + \color{orange}{(\frac{13}{18})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{10}b+\frac{13}{18}x-\frac{13}{18}.\frac{19}{10}& \text{Uitwerken } \\ & =bx-\frac{19}{10}b+\frac{13}{18}x-\frac{247}{180} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b-\frac{20}{19})(b+\frac{11}{6})& =(\color{red}{b}+\color{orange}{\frac{-20}{19}}).(\color{green}{b}+\color{blue}{\frac{11}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{11}{6})} + \color{orange}{(\frac{-20}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-20}{19})} . \color{blue}{(\frac{11}{6})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{11}{6}b-\frac{20}{19}b-\frac{20}{19}.\frac{11}{6}& \text{Uitwerken } \\ & =b^2+(\frac{11}{6}+(\frac{-20}{19}))b-(\frac{-220}{114}) & \text{Neem samen} \\ &=b^2+\frac{89}{114}b-(\frac{-220}{114}) & \text{Maak de som} \\ &=b^2+\frac{89}{114}b+\frac{110}{57} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
4. \(\begin{align}(\frac{-18}{2}+b)(x+\frac{6}{20})& =(\color{red}{b}+\color{orange}{(-9)}).(\color{green}{x}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(-9)} . \color{green}{(x)} + \color{orange}{(-9)} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{10}b-9x-9.\frac{3}{10}& \text{Uitwerken } \\ & =bx+\frac{3}{10}b-9x-\frac{27}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-20}{11}-b)(x+\frac{-8}{2})& =(\color{red}{-b}+\color{orange}{\frac{-20}{11}}).(\color{green}{x}+\color{blue}{(-4)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(-4)} + \color{orange}{(\frac{-20}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -bx+4b-\frac{20}{11}x+\frac{20}{11}.4& \text{Uitwerken } \\ & =-bx+4b-\frac{20}{11}x+\frac{80}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-12}{14}-q)(\frac{12}{4}-a)& =(\color{red}{-q}+\color{orange}{\frac{-6}{7}}).(\color{green}{-a}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(3)} + \color{orange}{(\frac{-6}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = aq-3q+\frac{6}{7}a-\frac{6}{7}.3& \text{Uitwerken } \\ & =aq-3q+\frac{6}{7}a-\frac{18}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-11}{16}-q)(b-\frac{19}{20})& =(\color{red}{-q}+\color{orange}{\frac{-11}{16}}).(\color{green}{b}+\color{blue}{\frac{-19}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-19}{20})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{-19}{20})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{19}{20}q-\frac{11}{16}b+\frac{11}{16}.\frac{19}{20}& \text{Uitwerken } \\ & =-bq+\frac{19}{20}q-\frac{11}{16}b+\frac{209}{320} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-1}{13}-b)(\frac{2}{15}-p)& =(\color{red}{-b}+\color{orange}{\frac{-1}{13}}).(\color{green}{-p}+\color{blue}{\frac{2}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{2}{15})} + \color{orange}{(\frac{-1}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{13})} . \color{blue}{(\frac{2}{15})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{2}{15}b+\frac{1}{13}p-\frac{1}{13}.\frac{2}{15}& \text{Uitwerken } \\ & =bp-\frac{2}{15}b+\frac{1}{13}p-\frac{2}{195} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{8}{13}+p)(\frac{-17}{9}-p)& =(\color{red}{p}+\color{orange}{\frac{8}{13}}).(\color{green}{-p}+\color{blue}{\frac{-17}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{9})} + \color{orange}{(\frac{8}{13})} . \color{green}{(-p)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{-17}{9})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{17}{9}p-\frac{8}{13}p-\frac{8}{13}.\frac{17}{9}& \text{Uitwerken } \\ & =-p^2+((\frac{-17}{9})+(\frac{-8}{13}))p-\frac{136}{117} & \text{Neem samen} \\ &=-p^2-\frac{293}{117}p-\frac{136}{117} & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(x+\frac{-11}{12})(\frac{-9}{9}-p)& =(\color{red}{x}+\color{orange}{\frac{-11}{12}}).(\color{green}{-p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-11}{12})} . \color{green}{(-p)} + \color{orange}{(\frac{-11}{12})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -px-1x+\frac{11}{12}p+\frac{11}{12}.1& \text{Uitwerken } \\ & =-px-1x+\frac{11}{12}p+\frac{11}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a+\frac{-17}{6})(\frac{14}{20}-b)& =(\color{red}{a}+\color{orange}{\frac{-17}{6}}).(\color{green}{-b}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{-17}{6})} . \color{green}{(-b)} + \color{orange}{(\frac{-17}{6})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{7}{10}a+\frac{17}{6}b-\frac{17}{6}.\frac{7}{10}& \text{Uitwerken } \\ & =-ab+\frac{7}{10}a+\frac{17}{6}b-\frac{119}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{10}{4}-q)(a-\frac{9}{9})& =(\color{red}{-q}+\color{orange}{\frac{5}{2}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(-1)} + \color{orange}{(\frac{5}{2})} . \color{green}{(a)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -aq+1q+\frac{5}{2}a-\frac{5}{2}.1& \text{Uitwerken } \\ & =-aq+1q+\frac{5}{2}a-\frac{5}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)