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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{2}{17}+q)(\frac{-15}{18}-b)& =(\color{red}{q}+\color{orange}{\frac{2}{17}}).(\color{green}{-b}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{2}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{2}{17})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{6}q-\frac{2}{17}b-\frac{2}{17}.\frac{5}{6}& \text{Uitwerken } \\ & =-bq-\frac{5}{6}q-\frac{2}{17}b-\frac{10}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{5}{6}q-\frac{2}{17}b-\frac{5}{51} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-18}{10}-q)(a+\frac{-5}{4})& =(\color{red}{-q}+\color{orange}{\frac{-9}{5}}).(\color{green}{a}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(\frac{-9}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{5}{4}q-\frac{9}{5}a+\frac{9}{5}.\frac{5}{4}& \text{Uitwerken } \\ & =-aq+\frac{5}{4}q-\frac{9}{5}a+\frac{45}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{5}{4}q-\frac{9}{5}a+\frac{9}{4} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(b+\frac{-11}{20})(\frac{9}{6}+b)& =(\color{red}{b}+\color{orange}{\frac{-11}{20}}).(\color{green}{b}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-11}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{20})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{3}{2}b-\frac{11}{20}b-\frac{11}{20}.\frac{3}{2}& \text{Uitwerken } \\ & =b^2+(\frac{3}{2}+(\frac{-11}{20}))b-(\frac{-33}{40}) & \text{Neem samen} \\ &=b^2+\frac{19}{20}b-(\frac{-33}{40}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{-8}{8}-a)(\frac{-19}{9}+a)& =(\color{red}{-a}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{19}{9}a-1a+1.\frac{19}{9}& \text{Uitwerken } \\ & =-a^2+(\frac{19}{9}+(-1))a+(\frac{-19}{9}) & \text{Neem samen} \\ &=-a^2+\frac{10}{9}a+(\frac{-19}{9}) & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(\frac{-17}{5}-q)(q+\frac{12}{5})& =(\color{red}{-q}+\color{orange}{\frac{-17}{5}}).(\color{green}{q}+\color{blue}{\frac{12}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{12}{5})} + \color{orange}{(\frac{-17}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{5})} . \color{blue}{(\frac{12}{5})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{12}{5}q-\frac{17}{5}q-\frac{17}{5}.\frac{12}{5}& \text{Uitwerken } \\ & =-q^2+((\frac{-12}{5})+(\frac{-17}{5}))q-\frac{204}{25} & \text{Neem samen} \\ &=-q^2-\frac{29}{5}q-\frac{204}{25} & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{-17}{14}+q)(a+4)& =(\color{red}{q}+\color{orange}{\frac{-17}{14}}).(\color{green}{a}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(4)} + \color{orange}{(\frac{-17}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{14})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = aq+4q-\frac{17}{14}a-\frac{17}{14}.4& \text{Uitwerken } \\ & =aq+4q-\frac{17}{14}a-\frac{68}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+4q-\frac{17}{14}a-\frac{34}{7} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(a+\frac{-14}{8})(\frac{-4}{20}-q)& =(\color{red}{a}+\color{orange}{\frac{-7}{4}}).(\color{green}{-q}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{5}a+\frac{7}{4}q+\frac{7}{4}.\frac{1}{5}& \text{Uitwerken } \\ & =-aq-\frac{1}{5}a+\frac{7}{4}q+\frac{7}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b+\frac{-9}{3})(\frac{-11}{18}-p)& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{-p}+\color{blue}{\frac{-11}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{18})} + \color{orange}{(-3)} . \color{green}{(-p)} + \color{orange}{(-3)} . \color{blue}{(\frac{-11}{18})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{11}{18}b+3p+3.\frac{11}{18}& \text{Uitwerken } \\ & =-bp-\frac{11}{18}b+3p+\frac{33}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{11}{18}b+3p+\frac{11}{6} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(p+\frac{-20}{12})(a-\frac{10}{5})& =(\color{red}{p}+\color{orange}{\frac{-5}{3}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = ap-2p-\frac{5}{3}a+\frac{5}{3}.2& \text{Uitwerken } \\ & =ap-2p-\frac{5}{3}a+\frac{10}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-5}{6}+x)(\frac{12}{5}+q)& =(\color{red}{x}+\color{orange}{\frac{-5}{6}}).(\color{green}{q}+\color{blue}{\frac{12}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{12}{5})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{12}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{12}{5}x-\frac{5}{6}q-\frac{5}{6}.\frac{12}{5}& \text{Uitwerken } \\ & =qx+\frac{12}{5}x-\frac{5}{6}q-\frac{60}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{12}{5}x-\frac{5}{6}q-2 & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(b-\frac{2}{11})(p-\frac{7}{5})& =(\color{red}{b}+\color{orange}{\frac{-2}{11}}).(\color{green}{p}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-2}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{7}{5}b-\frac{2}{11}p+\frac{2}{11}.\frac{7}{5}& \text{Uitwerken } \\ & =bp-\frac{7}{5}b-\frac{2}{11}p+\frac{14}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p+\frac{-3}{18})(\frac{-9}{9}-p)& =(\color{red}{p}+\color{orange}{\frac{-1}{6}}).(\color{green}{-p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -pp-1p+\frac{1}{6}p+\frac{1}{6}.1& \text{Uitwerken } \\ & =-p^2+((-1)+\frac{1}{6})p+(\frac{-1}{6}) & \text{Neem samen} \\ &=-p^2-\frac{5}{6}p+(\frac{-1}{6}) & \text{Maak de som} \\\end{align}\)