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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{19}{18}-b)(\frac{-14}{6}+a)& =(\color{red}{-b}+\color{orange}{\frac{19}{18}}).(\color{green}{a}+\color{blue}{\frac{-7}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{3})} + \color{orange}{(\frac{19}{18})} . \color{green}{(a)} + \color{orange}{(\frac{19}{18})} . \color{blue}{(\frac{-7}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{7}{3}b+\frac{19}{18}a-\frac{19}{18}.\frac{7}{3}& \text{Uitwerken } \\ & =-ab+\frac{7}{3}b+\frac{19}{18}a-\frac{133}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-20}{9}+q)(\frac{3}{18}-b)& =(\color{red}{q}+\color{orange}{\frac{-20}{9}}).(\color{green}{-b}+\color{blue}{\frac{1}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{6})} + \color{orange}{(\frac{-20}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-20}{9})} . \color{blue}{(\frac{1}{6})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{6}q+\frac{20}{9}b-\frac{20}{9}.\frac{1}{6}& \text{Uitwerken } \\ & =-bq+\frac{1}{6}q+\frac{20}{9}b-\frac{20}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{1}{6}q+\frac{20}{9}b-\frac{10}{27} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-1}{12}-a)(\frac{-6}{18}-b)& =(\color{red}{-a}+\color{orange}{\frac{-1}{12}}).(\color{green}{-b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-b)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-1}{12})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{12})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{3}a+\frac{1}{12}b+\frac{1}{12}.\frac{1}{3}& \text{Uitwerken } \\ & =ab+\frac{1}{3}a+\frac{1}{12}b+\frac{1}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{7}{13}-q)(\frac{14}{9}-x)& =(\color{red}{-q}+\color{orange}{\frac{7}{13}}).(\color{green}{-x}+\color{blue}{\frac{14}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{14}{9})} + \color{orange}{(\frac{7}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{13})} . \color{blue}{(\frac{14}{9})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{14}{9}q-\frac{7}{13}x+\frac{7}{13}.\frac{14}{9}& \text{Uitwerken } \\ & =qx-\frac{14}{9}q-\frac{7}{13}x+\frac{98}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p+\frac{-12}{2})(p+\frac{-15}{3})& =(\color{red}{p}+\color{orange}{(-6)}).(\color{green}{p}+\color{blue}{(-5)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(-5)} + \color{orange}{(-6)} . \color{green}{(p)} + \color{orange}{(-6)} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = pp-5p-6p+6.5& \text{Uitwerken } \\ & =p^2+((-5)+(-6))p+30 & \text{Neem samen} \\ &=p^2-11p+30 & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{-12}{16}-q)(\frac{-7}{18}+p)& =(\color{red}{-q}+\color{orange}{\frac{-3}{4}}).(\color{green}{p}+\color{blue}{\frac{-7}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-7}{18})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-7}{18})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{7}{18}q-\frac{3}{4}p+\frac{3}{4}.\frac{7}{18}& \text{Uitwerken } \\ & =-pq+\frac{7}{18}q-\frac{3}{4}p+\frac{21}{72} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{7}{18}q-\frac{3}{4}p+\frac{7}{24} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(q+7)(\frac{1}{12}-b)& =(\color{red}{q}+\color{orange}{7}).(\color{green}{-b}+\color{blue}{\frac{1}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{12})} + \color{orange}{(7)} . \color{green}{(-b)} + \color{orange}{(7)} . \color{blue}{(\frac{1}{12})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{12}q-7b+7.\frac{1}{12}& \text{Uitwerken } \\ & =-bq+\frac{1}{12}q-7b+\frac{7}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p+\frac{3}{7})(b-\frac{8}{10})& =(\color{red}{p}+\color{orange}{\frac{3}{7}}).(\color{green}{b}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{3}{7})} . \color{green}{(b)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{5}p+\frac{3}{7}b-\frac{3}{7}.\frac{4}{5}& \text{Uitwerken } \\ & =bp-\frac{4}{5}p+\frac{3}{7}b-\frac{12}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-17}{18}-x)(\frac{8}{4}+x)& =(\color{red}{-x}+\color{orange}{\frac{-17}{18}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(2)} + \color{orange}{(\frac{-17}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{18})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -xx-2x-\frac{17}{18}x-\frac{17}{18}.2& \text{Uitwerken } \\ & =-x^2+((-2)+(\frac{-17}{18}))x-\frac{34}{18} & \text{Neem samen} \\ &=-x^2-\frac{53}{18}x-\frac{34}{18} & \text{Maak de som} \\ &=-x^2-\frac{53}{18}x-\frac{17}{9} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
10. \(\begin{align}(q-\frac{3}{10})(x+\frac{13}{5})& =(\color{red}{q}+\color{orange}{\frac{-3}{10}}).(\color{green}{x}+\color{blue}{\frac{13}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{13}{5})} + \color{orange}{(\frac{-3}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(\frac{13}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{13}{5}q-\frac{3}{10}x-\frac{3}{10}.\frac{13}{5}& \text{Uitwerken } \\ & =qx+\frac{13}{5}q-\frac{3}{10}x-\frac{39}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p+\frac{3}{8})(a+(-11))& =(\color{red}{p}+\color{orange}{\frac{3}{8}}).(\color{green}{a}+\color{blue}{(-11)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-11)} + \color{orange}{(\frac{3}{8})} . \color{green}{(a)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(-11)}& \text{Boogjes en uitschrijven} \\ & = ap-11p+\frac{3}{8}a-\frac{3}{8}.11& \text{Uitwerken } \\ & =ap-11p+\frac{3}{8}a-\frac{33}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p+\frac{16}{14})(\frac{-17}{17}+q)& =(\color{red}{p}+\color{orange}{\frac{8}{7}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{8}{7})} . \color{green}{(q)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq-1p+\frac{8}{7}q-\frac{8}{7}.1& \text{Uitwerken } \\ & =pq-1p+\frac{8}{7}q-\frac{8}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)