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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{-20}{12})(\frac{8}{12}+x)& =(\color{red}{a}+\color{orange}{\frac{5}{3}}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{3}a+\frac{5}{3}x+\frac{5}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =ax+\frac{2}{3}a+\frac{5}{3}x+\frac{10}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-20}{20}-x)(a-(-20))& =(\color{red}{-x}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{20})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(20)} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(20)}& \text{Boogjes en uitschrijven} \\ & = -ax-20x-1a-1.20& \text{Uitwerken } \\ & =-ax-20x-1a-20 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x-\frac{-4}{11})(\frac{-19}{13}-q)& =(\color{red}{x}+\color{orange}{\frac{4}{11}}).(\color{green}{-q}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{4}{11})} . \color{green}{(-q)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{19}{13}x-\frac{4}{11}q-\frac{4}{11}.\frac{19}{13}& \text{Uitwerken } \\ & =-qx-\frac{19}{13}x-\frac{4}{11}q-\frac{76}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{4}{5}+b)(\frac{-3}{11}-a)& =(\color{red}{b}+\color{orange}{\frac{4}{5}}).(\color{green}{-a}+\color{blue}{\frac{-3}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{11})} + \color{orange}{(\frac{4}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-3}{11})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{3}{11}b-\frac{4}{5}a-\frac{4}{5}.\frac{3}{11}& \text{Uitwerken } \\ & =-ab-\frac{3}{11}b-\frac{4}{5}a-\frac{12}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{15}{5}-p)(\frac{-18}{20}-q)& =(\color{red}{-p}+\color{orange}{3}).(\color{green}{-q}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(3)} . \color{green}{(-q)} + \color{orange}{(3)} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{9}{10}p-3q-3.\frac{9}{10}& \text{Uitwerken } \\ & =pq+\frac{9}{10}p-3q-\frac{27}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-4}{16}+p)(q+\frac{-20}{20})& =(\color{red}{p}+\color{orange}{\frac{-1}{4}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq-1p-\frac{1}{4}q+\frac{1}{4}.1& \text{Uitwerken } \\ & =pq-1p-\frac{1}{4}q+\frac{1}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{19}{8}+b)(b-\frac{15}{11})& =(\color{red}{b}+\color{orange}{\frac{19}{8}}).(\color{green}{b}+\color{blue}{\frac{-15}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{11})} + \color{orange}{(\frac{19}{8})} . \color{green}{(b)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(\frac{-15}{11})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{15}{11}b+\frac{19}{8}b-\frac{19}{8}.\frac{15}{11}& \text{Uitwerken } \\ & =b^2+((\frac{-15}{11})+\frac{19}{8})b-(\frac{-285}{88}) & \text{Neem samen} \\ &=b^2+\frac{89}{88}b-(\frac{-285}{88}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(a-\frac{1}{19})(\frac{9}{3}+p)& =(\color{red}{a}+\color{orange}{\frac{-1}{19}}).(\color{green}{p}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(3)} + \color{orange}{(\frac{-1}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{19})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ap+3a-\frac{1}{19}p-\frac{1}{19}.3& \text{Uitwerken } \\ & =ap+3a-\frac{1}{19}p-\frac{3}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(q+\frac{-8}{20})(\frac{4}{13}+a)& =(\color{red}{q}+\color{orange}{\frac{-2}{5}}).(\color{green}{a}+\color{blue}{\frac{4}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{4}{13})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{4}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{4}{13}q-\frac{2}{5}a-\frac{2}{5}.\frac{4}{13}& \text{Uitwerken } \\ & =aq+\frac{4}{13}q-\frac{2}{5}a-\frac{8}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{3}{8}-p)(p+\frac{17}{6})& =(\color{red}{-p}+\color{orange}{\frac{3}{8}}).(\color{green}{p}+\color{blue}{\frac{17}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{17}{6})} + \color{orange}{(\frac{3}{8})} . \color{green}{(p)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{17}{6})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{17}{6}p+\frac{3}{8}p+\frac{3}{8}.\frac{17}{6}& \text{Uitwerken } \\ & =-p^2+((\frac{-17}{6})+\frac{3}{8})p+(\frac{-51}{48}) & \text{Neem samen} \\ &=-p^2-\frac{59}{24}p+(\frac{-51}{48}) & \text{Maak de som} \\ &=-p^2-\frac{59}{24}p+(\frac{-17}{16}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
11. \(\begin{align}(p+\frac{-1}{15})(\frac{9}{10}+b)& =(\color{red}{p}+\color{orange}{\frac{-1}{15}}).(\color{green}{b}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{10}p-\frac{1}{15}b-\frac{1}{15}.\frac{9}{10}& \text{Uitwerken } \\ & =bp+\frac{9}{10}p-\frac{1}{15}b-\frac{9}{150} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{9}{10}p-\frac{1}{15}b-\frac{3}{50} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(11+a)(\frac{20}{12}-x)& =(\color{red}{a}+\color{orange}{11}).(\color{green}{-x}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(11)} . \color{green}{(-x)} + \color{orange}{(11)} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{5}{3}a-11x+11.\frac{5}{3}& \text{Uitwerken } \\ & =-ax+\frac{5}{3}a-11x+\frac{55}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)