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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{12}{11})((-19)-b)& =(\color{red}{p}+\color{orange}{\frac{-12}{11}}).(\color{green}{-b}+\color{blue}{(-19)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(-19)} + \color{orange}{(\frac{-12}{11})} . \color{green}{(-b)} + \color{orange}{(\frac{-12}{11})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = -bp-19p+\frac{12}{11}b+\frac{12}{11}.19& \text{Uitwerken } \\ & =-bp-19p+\frac{12}{11}b+\frac{228}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q-\frac{-12}{7})(\frac{17}{17}-q)& =(\color{red}{q}+\color{orange}{\frac{12}{7}}).(\color{green}{-q}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(1)} + \color{orange}{(\frac{12}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{12}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -qq+1q-\frac{12}{7}q+\frac{12}{7}.1& \text{Uitwerken } \\ & =-q^2+(1+(\frac{-12}{7}))q+(\frac{-12}{7}) & \text{Neem samen} \\ &=-q^2-\frac{5}{7}q+(\frac{-12}{7}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(\frac{16}{18}-q)(\frac{-19}{6}+a)& =(\color{red}{-q}+\color{orange}{\frac{8}{9}}).(\color{green}{a}+\color{blue}{\frac{-19}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-19}{6})} + \color{orange}{(\frac{8}{9})} . \color{green}{(a)} + \color{orange}{(\frac{8}{9})} . \color{blue}{(\frac{-19}{6})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{19}{6}q+\frac{8}{9}a-\frac{8}{9}.\frac{19}{6}& \text{Uitwerken } \\ & =-aq+\frac{19}{6}q+\frac{8}{9}a-\frac{152}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{19}{6}q+\frac{8}{9}a-\frac{76}{27} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{16}{13}+a)(x+\frac{-20}{8})& =(\color{red}{a}+\color{orange}{\frac{16}{13}}).(\color{green}{x}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{16}{13})} . \color{green}{(x)} + \color{orange}{(\frac{16}{13})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{2}a+\frac{16}{13}x-\frac{16}{13}.\frac{5}{2}& \text{Uitwerken } \\ & =ax-\frac{5}{2}a+\frac{16}{13}x-\frac{80}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{5}{2}a+\frac{16}{13}x-\frac{40}{13} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-4}{8}-q)(p-\frac{17}{4})& =(\color{red}{-q}+\color{orange}{\frac{-1}{2}}).(\color{green}{p}+\color{blue}{\frac{-17}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-17}{4})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-17}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{17}{4}q-\frac{1}{2}p+\frac{1}{2}.\frac{17}{4}& \text{Uitwerken } \\ & =-pq+\frac{17}{4}q-\frac{1}{2}p+\frac{17}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q+\frac{-18}{2})(q-\frac{-3}{4})& =(\color{red}{q}+\color{orange}{(-9)}).(\color{green}{q}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(-9)} . \color{green}{(q)} + \color{orange}{(-9)} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{3}{4}q-9q-9.\frac{3}{4}& \text{Uitwerken } \\ & =q^2+(\frac{3}{4}+(-9))q-(\frac{-27}{4}) & \text{Neem samen} \\ &=q^2-\frac{33}{4}q-(\frac{-27}{4}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(x+\frac{-7}{13})(b+\frac{-6}{14})& =(\color{red}{x}+\color{orange}{\frac{-7}{13}}).(\color{green}{b}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{-7}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{13})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{7}x-\frac{7}{13}b+\frac{7}{13}.\frac{3}{7}& \text{Uitwerken } \\ & =bx-\frac{3}{7}x-\frac{7}{13}b+\frac{21}{91} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{3}{7}x-\frac{7}{13}b+\frac{3}{13} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(a-\frac{15}{19})(\frac{-8}{2}+p)& =(\color{red}{a}+\color{orange}{\frac{-15}{19}}).(\color{green}{p}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-4)} + \color{orange}{(\frac{-15}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{19})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = ap-4a-\frac{15}{19}p+\frac{15}{19}.4& \text{Uitwerken } \\ & =ap-4a-\frac{15}{19}p+\frac{60}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-10}{14}+x)(\frac{-14}{14}-q)& =(\color{red}{x}+\color{orange}{\frac{-5}{7}}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-5}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qx-1x+\frac{5}{7}q+\frac{5}{7}.1& \text{Uitwerken } \\ & =-qx-1x+\frac{5}{7}q+\frac{5}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a-\frac{-3}{3})(\frac{3}{16}+x)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{x}+\color{blue}{\frac{3}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{3}{16})} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(\frac{3}{16})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{16}a+1x+1.\frac{3}{16}& \text{Uitwerken } \\ & =ax+\frac{3}{16}a+1x+\frac{3}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x-\frac{-17}{10})(q-\frac{17}{18})& =(\color{red}{x}+\color{orange}{\frac{17}{10}}).(\color{green}{q}+\color{blue}{\frac{-17}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{18})} + \color{orange}{(\frac{17}{10})} . \color{green}{(q)} + \color{orange}{(\frac{17}{10})} . \color{blue}{(\frac{-17}{18})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{17}{18}x+\frac{17}{10}q-\frac{17}{10}.\frac{17}{18}& \text{Uitwerken } \\ & =qx-\frac{17}{18}x+\frac{17}{10}q-\frac{289}{180} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q-\frac{14}{8})(\frac{-19}{12}+p)& =(\color{red}{q}+\color{orange}{\frac{-7}{4}}).(\color{green}{p}+\color{blue}{\frac{-19}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{12})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-19}{12})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{19}{12}q-\frac{7}{4}p+\frac{7}{4}.\frac{19}{12}& \text{Uitwerken } \\ & =pq-\frac{19}{12}q-\frac{7}{4}p+\frac{133}{48} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)