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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-16}{12}-p)(a-\frac{-10}{14})& =(\color{red}{-p}+\color{orange}{\frac{-4}{3}}).(\color{green}{a}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{5}{7}p-\frac{4}{3}a-\frac{4}{3}.\frac{5}{7}& \text{Uitwerken } \\ & =-ap-\frac{5}{7}p-\frac{4}{3}a-\frac{20}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-12}{18}-b)(\frac{8}{7}-p)& =(\color{red}{-b}+\color{orange}{\frac{-2}{3}}).(\color{green}{-p}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{8}{7}b+\frac{2}{3}p-\frac{2}{3}.\frac{8}{7}& \text{Uitwerken } \\ & =bp-\frac{8}{7}b+\frac{2}{3}p-\frac{16}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{9}{10}-q)(\frac{18}{9}+q)& =(\color{red}{-q}+\color{orange}{\frac{9}{10}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(2)} + \color{orange}{(\frac{9}{10})} . \color{green}{(q)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -qq-2q+\frac{9}{10}q+\frac{9}{10}.2& \text{Uitwerken } \\ & =-q^2+((-2)+\frac{9}{10})q+(\frac{-18}{10}) & \text{Neem samen} \\ &=-q^2-\frac{11}{10}q+(\frac{-18}{10}) & \text{Maak de som} \\ &=-q^2-\frac{11}{10}q+(\frac{-9}{5}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
4. \(\begin{align}(a-\frac{2}{15})(\frac{4}{4}+x)& =(\color{red}{a}+\color{orange}{\frac{-2}{15}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{-2}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{15})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ax+1a-\frac{2}{15}x-\frac{2}{15}.1& \text{Uitwerken } \\ & =ax+1a-\frac{2}{15}x-\frac{2}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x-15)(\frac{-13}{7}+a)& =(\color{red}{x}+\color{orange}{(-15)}).(\color{green}{a}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(-15)} . \color{green}{(a)} + \color{orange}{(-15)} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{13}{7}x-15a+15.\frac{13}{7}& \text{Uitwerken } \\ & =ax-\frac{13}{7}x-15a+\frac{195}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q+\frac{-7}{5})(p-\frac{17}{12})& =(\color{red}{q}+\color{orange}{\frac{-7}{5}}).(\color{green}{p}+\color{blue}{\frac{-17}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{12})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{-17}{12})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{17}{12}q-\frac{7}{5}p+\frac{7}{5}.\frac{17}{12}& \text{Uitwerken } \\ & =pq-\frac{17}{12}q-\frac{7}{5}p+\frac{119}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b+\frac{-16}{16})(\frac{-7}{18}+b)& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-7}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{18})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-7}{18})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{7}{18}b-1b+1.\frac{7}{18}& \text{Uitwerken } \\ & =b^2+((\frac{-7}{18})+(-1))b+\frac{7}{18} & \text{Neem samen} \\ &=b^2-\frac{25}{18}b+\frac{7}{18} & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(q-8)(\frac{-8}{12}-b)& =(\color{red}{q}+\color{orange}{(-8)}).(\color{green}{-b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(-8)} . \color{green}{(-b)} + \color{orange}{(-8)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{2}{3}q+8b+8.\frac{2}{3}& \text{Uitwerken } \\ & =-bq-\frac{2}{3}q+8b+\frac{16}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-7}{10}-x)(p+\frac{-20}{18})& =(\color{red}{-x}+\color{orange}{\frac{-7}{10}}).(\color{green}{p}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{10}{9}x-\frac{7}{10}p+\frac{7}{10}.\frac{10}{9}& \text{Uitwerken } \\ & =-px+\frac{10}{9}x-\frac{7}{10}p+\frac{70}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{10}{9}x-\frac{7}{10}p+\frac{7}{9} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-14}{4}-x)(\frac{-2}{10}+p)& =(\color{red}{-x}+\color{orange}{\frac{-7}{2}}).(\color{green}{p}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{1}{5}x-\frac{7}{2}p+\frac{7}{2}.\frac{1}{5}& \text{Uitwerken } \\ & =-px+\frac{1}{5}x-\frac{7}{2}p+\frac{7}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{14}{17}-x)(x-\frac{8}{7})& =(\color{red}{-x}+\color{orange}{\frac{14}{17}}).(\color{green}{x}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{14}{17})} . \color{green}{(x)} + \color{orange}{(\frac{14}{17})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{8}{7}x+\frac{14}{17}x-\frac{14}{17}.\frac{8}{7}& \text{Uitwerken } \\ & =-x^2+(\frac{8}{7}+\frac{14}{17})x-\frac{112}{119} & \text{Neem samen} \\ &=-x^2+\frac{234}{119}x-\frac{112}{119} & \text{Maak de som} \\ &=-x^2+\frac{234}{119}x-\frac{16}{17} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
12. \(\begin{align}(b-\frac{-13}{4})(\frac{19}{3}-a)& =(\color{red}{b}+\color{orange}{\frac{13}{4}}).(\color{green}{-a}+\color{blue}{\frac{19}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{19}{3})} + \color{orange}{(\frac{13}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{13}{4})} . \color{blue}{(\frac{19}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{19}{3}b-\frac{13}{4}a+\frac{13}{4}.\frac{19}{3}& \text{Uitwerken } \\ & =-ab+\frac{19}{3}b-\frac{13}{4}a+\frac{247}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)