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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-11}{18}-x)(\frac{7}{10}-p)& =(\color{red}{-x}+\color{orange}{\frac{-11}{18}}).(\color{green}{-p}+\color{blue}{\frac{7}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-p)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{10})} + \color{orange}{(\frac{-11}{18})} . \color{green}{(-p)} + \color{orange}{(\frac{-11}{18})} . \color{blue}{(\frac{7}{10})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{7}{10}x+\frac{11}{18}p-\frac{11}{18}.\frac{7}{10}& \text{Uitwerken } \\ & =px-\frac{7}{10}x+\frac{11}{18}p-\frac{77}{180} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{19}{7}-b)(p+\frac{1}{5})& =(\color{red}{-b}+\color{orange}{\frac{19}{7}}).(\color{green}{p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{19}{7})} . \color{green}{(p)} + \color{orange}{(\frac{19}{7})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{5}b+\frac{19}{7}p+\frac{19}{7}.\frac{1}{5}& \text{Uitwerken } \\ & =-bp-\frac{1}{5}b+\frac{19}{7}p+\frac{19}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p-\frac{-3}{3})(a+\frac{16}{12})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{4}{3}p+1a+1.\frac{4}{3}& \text{Uitwerken } \\ & =ap+\frac{4}{3}p+1a+\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p-\frac{-9}{18})(x-\frac{-11}{3})& =(\color{red}{p}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{11}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{11}{3})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{11}{3})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{11}{3}p+\frac{1}{2}x+\frac{1}{2}.\frac{11}{3}& \text{Uitwerken } \\ & =px+\frac{11}{3}p+\frac{1}{2}x+\frac{11}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{18}{5}+p)(\frac{-8}{7}-q)& =(\color{red}{p}+\color{orange}{\frac{18}{5}}).(\color{green}{-q}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{18}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{18}{5})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{8}{7}p-\frac{18}{5}q-\frac{18}{5}.\frac{8}{7}& \text{Uitwerken } \\ & =-pq-\frac{8}{7}p-\frac{18}{5}q-\frac{144}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{13}{13}+q)(q-\frac{4}{7})& =(\color{red}{q}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{4}{7}q+1q-1.\frac{4}{7}& \text{Uitwerken } \\ & =q^2+((\frac{-4}{7})+1)q-(\frac{-4}{7}) & \text{Neem samen} \\ &=q^2+\frac{3}{7}q-(\frac{-4}{7}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{-3}{3}+x)(\frac{-20}{10}+b)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bx-2x-1b+1.2& \text{Uitwerken } \\ & =bx-2x-1b+2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p+8)(\frac{-16}{13}+p)& =(\color{red}{p}+\color{orange}{8}).(\color{green}{p}+\color{blue}{\frac{-16}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{13})} + \color{orange}{(8)} . \color{green}{(p)} + \color{orange}{(8)} . \color{blue}{(\frac{-16}{13})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{16}{13}p+8p-8.\frac{16}{13}& \text{Uitwerken } \\ & =p^2+((\frac{-16}{13})+8)p-(\frac{-128}{13}) & \text{Neem samen} \\ &=p^2+\frac{88}{13}p-(\frac{-128}{13}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(\frac{20}{7}-p)(x+\frac{20}{20})& =(\color{red}{-p}+\color{orange}{\frac{20}{7}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(1)} + \color{orange}{(\frac{20}{7})} . \color{green}{(x)} + \color{orange}{(\frac{20}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -px-1p+\frac{20}{7}x+\frac{20}{7}.1& \text{Uitwerken } \\ & =-px-1p+\frac{20}{7}x+\frac{20}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(b-\frac{14}{3})(\frac{17}{4}-b)& =(\color{red}{b}+\color{orange}{\frac{-14}{3}}).(\color{green}{-b}+\color{blue}{\frac{17}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{17}{4})} + \color{orange}{(\frac{-14}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-14}{3})} . \color{blue}{(\frac{17}{4})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{17}{4}b+\frac{14}{3}b-\frac{14}{3}.\frac{17}{4}& \text{Uitwerken } \\ & =-b^2+(\frac{17}{4}+\frac{14}{3})b-\frac{238}{12} & \text{Neem samen} \\ &=-b^2+\frac{107}{12}b-\frac{238}{12} & \text{Maak de som} \\ &=-b^2+\frac{107}{12}b-\frac{119}{6} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
11. \(\begin{align}(a+\frac{-19}{15})(\frac{-16}{16}-b)& =(\color{red}{a}+\color{orange}{\frac{-19}{15}}).(\color{green}{-b}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-19}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{15})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ab-1a+\frac{19}{15}b+\frac{19}{15}.1& \text{Uitwerken } \\ & =-ab-1a+\frac{19}{15}b+\frac{19}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-8}{19}+a)(\frac{1}{7}-q)& =(\color{red}{a}+\color{orange}{\frac{-8}{19}}).(\color{green}{-q}+\color{blue}{\frac{1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{7})} + \color{orange}{(\frac{-8}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{-8}{19})} . \color{blue}{(\frac{1}{7})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{1}{7}a+\frac{8}{19}q-\frac{8}{19}.\frac{1}{7}& \text{Uitwerken } \\ & =-aq+\frac{1}{7}a+\frac{8}{19}q-\frac{8}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)