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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{8}{7})(p+\frac{7}{7})& =(\color{red}{a}+\color{orange}{\frac{-8}{7}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{-8}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ap+1a-\frac{8}{7}p-\frac{8}{7}.1& \text{Uitwerken } \\ & =ap+1a-\frac{8}{7}p-\frac{8}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-19}{12}-q)(\frac{13}{9}-b)& =(\color{red}{-q}+\color{orange}{\frac{-19}{12}}).(\color{green}{-b}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{13}{9}q+\frac{19}{12}b-\frac{19}{12}.\frac{13}{9}& \text{Uitwerken } \\ & =bq-\frac{13}{9}q+\frac{19}{12}b-\frac{247}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b-\frac{13}{10})(\frac{12}{20}+x)& =(\color{red}{b}+\color{orange}{\frac{-13}{10}}).(\color{green}{x}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-13}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{10})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{5}b-\frac{13}{10}x-\frac{13}{10}.\frac{3}{5}& \text{Uitwerken } \\ & =bx+\frac{3}{5}b-\frac{13}{10}x-\frac{39}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{11}{19}+x)(b-\frac{-7}{3})& =(\color{red}{x}+\color{orange}{\frac{11}{19}}).(\color{green}{b}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{11}{19})} . \color{green}{(b)} + \color{orange}{(\frac{11}{19})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{3}x+\frac{11}{19}b+\frac{11}{19}.\frac{7}{3}& \text{Uitwerken } \\ & =bx+\frac{7}{3}x+\frac{11}{19}b+\frac{77}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(q+\frac{5}{10})(p+\frac{-15}{6})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{p}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{1}{2})} . \color{green}{(p)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{2}q+\frac{1}{2}p-\frac{1}{2}.\frac{5}{2}& \text{Uitwerken } \\ & =pq-\frac{5}{2}q+\frac{1}{2}p-\frac{5}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-2}{13}+b)(\frac{20}{18}+x)& =(\color{red}{b}+\color{orange}{\frac{-2}{13}}).(\color{green}{x}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{-2}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{10}{9}b-\frac{2}{13}x-\frac{2}{13}.\frac{10}{9}& \text{Uitwerken } \\ & =bx+\frac{10}{9}b-\frac{2}{13}x-\frac{20}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{11}{17}-b)(\frac{-3}{20}-p)& =(\color{red}{-b}+\color{orange}{\frac{11}{17}}).(\color{green}{-p}+\color{blue}{\frac{-3}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{20})} + \color{orange}{(\frac{11}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{-3}{20})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{3}{20}b-\frac{11}{17}p-\frac{11}{17}.\frac{3}{20}& \text{Uitwerken } \\ & =bp+\frac{3}{20}b-\frac{11}{17}p-\frac{33}{340} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-14}{10}+b)(x-\frac{-14}{3})& =(\color{red}{b}+\color{orange}{\frac{-7}{5}}).(\color{green}{x}+\color{blue}{\frac{14}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{14}{3})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{14}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{14}{3}b-\frac{7}{5}x-\frac{7}{5}.\frac{14}{3}& \text{Uitwerken } \\ & =bx+\frac{14}{3}b-\frac{7}{5}x-\frac{98}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-13}{14}+b)(\frac{-11}{7}+b)& =(\color{red}{b}+\color{orange}{\frac{-13}{14}}).(\color{green}{b}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(\frac{-13}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{14})} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{11}{7}b-\frac{13}{14}b+\frac{13}{14}.\frac{11}{7}& \text{Uitwerken } \\ & =b^2+((\frac{-11}{7})+(\frac{-13}{14}))b+\frac{143}{98} & \text{Neem samen} \\ &=b^2-\frac{35}{14}b+\frac{143}{98} & \text{Maak de som} \\ &=b^2-\frac{5}{2}b+\frac{143}{98} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
10. \(\begin{align}(\frac{4}{13}-p)(\frac{11}{17}+p)& =(\color{red}{-p}+\color{orange}{\frac{4}{13}}).(\color{green}{p}+\color{blue}{\frac{11}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{11}{17})} + \color{orange}{(\frac{4}{13})} . \color{green}{(p)} + \color{orange}{(\frac{4}{13})} . \color{blue}{(\frac{11}{17})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{11}{17}p+\frac{4}{13}p+\frac{4}{13}.\frac{11}{17}& \text{Uitwerken } \\ & =-p^2+((\frac{-11}{17})+\frac{4}{13})p+(\frac{-44}{221}) & \text{Neem samen} \\ &=-p^2-\frac{75}{221}p+(\frac{-44}{221}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(p-17)(p-\frac{2}{6})& =(\color{red}{p}+\color{orange}{(-17)}).(\color{green}{p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(-17)} . \color{green}{(p)} + \color{orange}{(-17)} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{1}{3}p-17p+17.\frac{1}{3}& \text{Uitwerken } \\ & =p^2+((\frac{-1}{3})+(-17))p+\frac{17}{3} & \text{Neem samen} \\ &=p^2-\frac{52}{3}p+\frac{17}{3} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}((-7)-q)(q-\frac{-2}{11})& =(\color{red}{-q}+\color{orange}{(-7)}).(\color{green}{q}+\color{blue}{\frac{2}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{2}{11})} + \color{orange}{(-7)} . \color{green}{(q)} + \color{orange}{(-7)} . \color{blue}{(\frac{2}{11})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{2}{11}q-7q-7.\frac{2}{11}& \text{Uitwerken } \\ & =-q^2+((\frac{-2}{11})+(-7))q-\frac{14}{11} & \text{Neem samen} \\ &=-q^2-\frac{79}{11}q-\frac{14}{11} & \text{Maak de som} \\\end{align}\)