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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{-1}{11})(b-\frac{4}{4})& =(\color{red}{a}+\color{orange}{\frac{-1}{11}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab-1a-\frac{1}{11}b+\frac{1}{11}.1& \text{Uitwerken } \\ & =ab-1a-\frac{1}{11}b+\frac{1}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b-\frac{-11}{18})(a-\frac{18}{15})& =(\color{red}{b}+\color{orange}{\frac{11}{18}}).(\color{green}{a}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{11}{18})} . \color{green}{(a)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{6}{5}b+\frac{11}{18}a-\frac{11}{18}.\frac{6}{5}& \text{Uitwerken } \\ & =ab-\frac{6}{5}b+\frac{11}{18}a-\frac{66}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{6}{5}b+\frac{11}{18}a-\frac{11}{15} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(x+\frac{-13}{14})(q-\frac{1}{12})& =(\color{red}{x}+\color{orange}{\frac{-13}{14}}).(\color{green}{q}+\color{blue}{\frac{-1}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{12})} + \color{orange}{(\frac{-13}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(\frac{-1}{12})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{12}x-\frac{13}{14}q+\frac{13}{14}.\frac{1}{12}& \text{Uitwerken } \\ & =qx-\frac{1}{12}x-\frac{13}{14}q+\frac{13}{168} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-13}{7}-p)(b+\frac{-11}{4})& =(\color{red}{-p}+\color{orange}{\frac{-13}{7}}).(\color{green}{b}+\color{blue}{\frac{-11}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-11}{4})} + \color{orange}{(\frac{-13}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{7})} . \color{blue}{(\frac{-11}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{11}{4}p-\frac{13}{7}b+\frac{13}{7}.\frac{11}{4}& \text{Uitwerken } \\ & =-bp+\frac{11}{4}p-\frac{13}{7}b+\frac{143}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(q+\frac{-5}{10})(q+\frac{-18}{6})& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(-3)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = qq-3q-\frac{1}{2}q+\frac{1}{2}.3& \text{Uitwerken } \\ & =q^2+((-3)+(\frac{-1}{2}))q+\frac{3}{2} & \text{Neem samen} \\ &=q^2-\frac{7}{2}q+\frac{3}{2} & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(x+\frac{7}{4})(\frac{13}{10}+q)& =(\color{red}{x}+\color{orange}{\frac{7}{4}}).(\color{green}{q}+\color{blue}{\frac{13}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{13}{10})} + \color{orange}{(\frac{7}{4})} . \color{green}{(q)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{13}{10})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{13}{10}x+\frac{7}{4}q+\frac{7}{4}.\frac{13}{10}& \text{Uitwerken } \\ & =qx+\frac{13}{10}x+\frac{7}{4}q+\frac{91}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{14}{7}+q)(q-\frac{2}{2})& =(\color{red}{q}+\color{orange}{2}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(2)} . \color{green}{(q)} + \color{orange}{(2)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qq-1q+2q-2.1& \text{Uitwerken } \\ & =q^2+((-1)+2)q-(-2) & \text{Neem samen} \\ &=q^2+1q-(-2) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(p-\frac{11}{3})(\frac{18}{15}-b)& =(\color{red}{p}+\color{orange}{\frac{-11}{3}}).(\color{green}{-b}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-11}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-11}{3})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{6}{5}p+\frac{11}{3}b-\frac{11}{3}.\frac{6}{5}& \text{Uitwerken } \\ & =-bp+\frac{6}{5}p+\frac{11}{3}b-\frac{66}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{6}{5}p+\frac{11}{3}b-\frac{22}{5} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(p-\frac{-8}{10})(\frac{15}{13}-p)& =(\color{red}{p}+\color{orange}{\frac{4}{5}}).(\color{green}{-p}+\color{blue}{\frac{15}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{15}{13})} + \color{orange}{(\frac{4}{5})} . \color{green}{(-p)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{15}{13})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{15}{13}p-\frac{4}{5}p+\frac{4}{5}.\frac{15}{13}& \text{Uitwerken } \\ & =-p^2+(\frac{15}{13}+(\frac{-4}{5}))p+(\frac{-60}{65}) & \text{Neem samen} \\ &=-p^2+\frac{23}{65}p+(\frac{-60}{65}) & \text{Maak de som} \\ &=-p^2+\frac{23}{65}p+(\frac{-12}{13}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
10. \(\begin{align}(\frac{-13}{5}+b)(\frac{-5}{2}-b)& =(\color{red}{b}+\color{orange}{\frac{-13}{5}}).(\color{green}{-b}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-13}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-13}{5})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{5}{2}b+\frac{13}{5}b+\frac{13}{5}.\frac{5}{2}& \text{Uitwerken } \\ & =-b^2+((\frac{-5}{2})+\frac{13}{5})b+(\frac{-65}{10}) & \text{Neem samen} \\ &=-b^2+\frac{1}{10}b+(\frac{-65}{10}) & \text{Maak de som} \\ &=-b^2+\frac{1}{10}b+(\frac{-13}{2}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
11. \(\begin{align}(q+\frac{2}{9})(\frac{-18}{15}+a)& =(\color{red}{q}+\color{orange}{\frac{2}{9}}).(\color{green}{a}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{2}{9})} . \color{green}{(a)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{6}{5}q+\frac{2}{9}a-\frac{2}{9}.\frac{6}{5}& \text{Uitwerken } \\ & =aq-\frac{6}{5}q+\frac{2}{9}a-\frac{12}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{6}{5}q+\frac{2}{9}a-\frac{4}{15} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(q-\frac{9}{14})(\frac{17}{19}+a)& =(\color{red}{q}+\color{orange}{\frac{-9}{14}}).(\color{green}{a}+\color{blue}{\frac{17}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{17}{19})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{17}{19})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{17}{19}q-\frac{9}{14}a-\frac{9}{14}.\frac{17}{19}& \text{Uitwerken } \\ & =aq+\frac{17}{19}q-\frac{9}{14}a-\frac{153}{266} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)