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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{-1}{11})(x-\frac{11}{20})& =(\color{red}{p}+\color{orange}{\frac{1}{11}}).(\color{green}{x}+\color{blue}{\frac{-11}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{20})} + \color{orange}{(\frac{1}{11})} . \color{green}{(x)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(\frac{-11}{20})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{11}{20}p+\frac{1}{11}x-\frac{1}{11}.\frac{11}{20}& \text{Uitwerken } \\ & =px-\frac{11}{20}p+\frac{1}{11}x-\frac{11}{220} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{11}{20}p+\frac{1}{11}x-\frac{1}{20} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-1}{6}-q)(x-\frac{-17}{16})& =(\color{red}{-q}+\color{orange}{\frac{-1}{6}}).(\color{green}{x}+\color{blue}{\frac{17}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{17}{16})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{17}{16})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{17}{16}q-\frac{1}{6}x-\frac{1}{6}.\frac{17}{16}& \text{Uitwerken } \\ & =-qx-\frac{17}{16}q-\frac{1}{6}x-\frac{17}{96} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b+\frac{-7}{8})(q-\frac{-13}{13})& =(\color{red}{b}+\color{orange}{\frac{-7}{8}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-7}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1b-\frac{7}{8}q-\frac{7}{8}.1& \text{Uitwerken } \\ & =bq+1b-\frac{7}{8}q-\frac{7}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-5}{2}+a)(p+\frac{-19}{11})& =(\color{red}{a}+\color{orange}{\frac{-5}{2}}).(\color{green}{p}+\color{blue}{\frac{-19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{11})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{-19}{11})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{11}a-\frac{5}{2}p+\frac{5}{2}.\frac{19}{11}& \text{Uitwerken } \\ & =ap-\frac{19}{11}a-\frac{5}{2}p+\frac{95}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-1}{14}-a)(\frac{-7}{5}+p)& =(\color{red}{-a}+\color{orange}{\frac{-1}{14}}).(\color{green}{p}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-1}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{14})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{7}{5}a-\frac{1}{14}p+\frac{1}{14}.\frac{7}{5}& \text{Uitwerken } \\ & =-ap+\frac{7}{5}a-\frac{1}{14}p+\frac{7}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{7}{5}a-\frac{1}{14}p+\frac{1}{10} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-20}{12}+b)(\frac{-11}{14}-b)& =(\color{red}{b}+\color{orange}{\frac{-5}{3}}).(\color{green}{-b}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{11}{14}b+\frac{5}{3}b+\frac{5}{3}.\frac{11}{14}& \text{Uitwerken } \\ & =-b^2+((\frac{-11}{14})+\frac{5}{3})b+(\frac{-55}{42}) & \text{Neem samen} \\ &=-b^2+\frac{37}{42}b+(\frac{-55}{42}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{-14}{20}-a)(a+\frac{14}{18})& =(\color{red}{-a}+\color{orange}{\frac{-7}{10}}).(\color{green}{a}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{7}{9}a-\frac{7}{10}a-\frac{7}{10}.\frac{7}{9}& \text{Uitwerken } \\ & =-a^2+((\frac{-7}{9})+(\frac{-7}{10}))a-\frac{49}{90} & \text{Neem samen} \\ &=-a^2-\frac{133}{90}a-\frac{49}{90} & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(p+12)(\frac{6}{11}-p)& =(\color{red}{p}+\color{orange}{12}).(\color{green}{-p}+\color{blue}{\frac{6}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{6}{11})} + \color{orange}{(12)} . \color{green}{(-p)} + \color{orange}{(12)} . \color{blue}{(\frac{6}{11})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{6}{11}p-12p+12.\frac{6}{11}& \text{Uitwerken } \\ & =-p^2+(\frac{6}{11}+(-12))p+(\frac{-72}{11}) & \text{Neem samen} \\ &=-p^2-\frac{126}{11}p+(\frac{-72}{11}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(\frac{3}{2}+q)(x+\frac{-8}{8})& =(\color{red}{q}+\color{orange}{\frac{3}{2}}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{3}{2})} . \color{green}{(x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = qx-1q+\frac{3}{2}x-\frac{3}{2}.1& \text{Uitwerken } \\ & =qx-1q+\frac{3}{2}x-\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a+\frac{-16}{6})(q-\frac{4}{13})& =(\color{red}{a}+\color{orange}{\frac{-8}{3}}).(\color{green}{q}+\color{blue}{\frac{-4}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{13})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{-4}{13})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{4}{13}a-\frac{8}{3}q+\frac{8}{3}.\frac{4}{13}& \text{Uitwerken } \\ & =aq-\frac{4}{13}a-\frac{8}{3}q+\frac{32}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-13}{18}+a)(b+\frac{-18}{18})& =(\color{red}{a}+\color{orange}{\frac{-13}{18}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-13}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{18})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab-1a-\frac{13}{18}b+\frac{13}{18}.1& \text{Uitwerken } \\ & =ab-1a-\frac{13}{18}b+\frac{13}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{4}{11}-q)(\frac{-17}{13}+p)& =(\color{red}{-q}+\color{orange}{\frac{4}{11}}).(\color{green}{p}+\color{blue}{\frac{-17}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-17}{13})} + \color{orange}{(\frac{4}{11})} . \color{green}{(p)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(\frac{-17}{13})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{17}{13}q+\frac{4}{11}p-\frac{4}{11}.\frac{17}{13}& \text{Uitwerken } \\ & =-pq+\frac{17}{13}q+\frac{4}{11}p-\frac{68}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)