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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-11}{15}+x)(b+\frac{-19}{15})& =(\color{red}{x}+\color{orange}{\frac{-11}{15}}).(\color{green}{b}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{15}x-\frac{11}{15}b+\frac{11}{15}.\frac{19}{15}& \text{Uitwerken } \\ & =bx-\frac{19}{15}x-\frac{11}{15}b+\frac{209}{225} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b+\frac{-9}{3})(\frac{-4}{17}-b)& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{-b}+\color{blue}{\frac{-4}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{17})} + \color{orange}{(-3)} . \color{green}{(-b)} + \color{orange}{(-3)} . \color{blue}{(\frac{-4}{17})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{4}{17}b+3b+3.\frac{4}{17}& \text{Uitwerken } \\ & =-b^2+((\frac{-4}{17})+3)b+(\frac{-12}{17}) & \text{Neem samen} \\ &=-b^2+\frac{47}{17}b+(\frac{-12}{17}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(\frac{-9}{6}-p)(q+\frac{14}{19})& =(\color{red}{-p}+\color{orange}{\frac{-3}{2}}).(\color{green}{q}+\color{blue}{\frac{14}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{14}{19})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{14}{19})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{14}{19}p-\frac{3}{2}q-\frac{3}{2}.\frac{14}{19}& \text{Uitwerken } \\ & =-pq-\frac{14}{19}p-\frac{3}{2}q-\frac{42}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{14}{19}p-\frac{3}{2}q-\frac{21}{19} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(a-\frac{14}{16})(\frac{6}{9}-p)& =(\color{red}{a}+\color{orange}{\frac{-7}{8}}).(\color{green}{-p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-7}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{-7}{8})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{2}{3}a+\frac{7}{8}p-\frac{7}{8}.\frac{2}{3}& \text{Uitwerken } \\ & =-ap+\frac{2}{3}a+\frac{7}{8}p-\frac{14}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{2}{3}a+\frac{7}{8}p-\frac{7}{12} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(p-\frac{9}{10})(b+\frac{-1}{20})& =(\color{red}{p}+\color{orange}{\frac{-9}{10}}).(\color{green}{b}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{20}p-\frac{9}{10}b+\frac{9}{10}.\frac{1}{20}& \text{Uitwerken } \\ & =bp-\frac{1}{20}p-\frac{9}{10}b+\frac{9}{200} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b+\frac{10}{20})(q+\frac{-5}{2})& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{2}b+\frac{1}{2}q-\frac{1}{2}.\frac{5}{2}& \text{Uitwerken } \\ & =bq-\frac{5}{2}b+\frac{1}{2}q-\frac{5}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-5}{6}-q)(q-\frac{8}{14})& =(\color{red}{-q}+\color{orange}{\frac{-5}{6}}).(\color{green}{q}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = -qq+\frac{4}{7}q-\frac{5}{6}q+\frac{5}{6}.\frac{4}{7}& \text{Uitwerken } \\ & =-q^2+(\frac{4}{7}+(\frac{-5}{6}))q+(\frac{-20}{42}) & \text{Neem samen} \\ &=-q^2-\frac{11}{42}q+(\frac{-20}{42}) & \text{Maak de som} \\ &=-q^2-\frac{11}{42}q+(\frac{-10}{21}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
8. \(\begin{align}(\frac{-20}{9}-a)(b+\frac{-5}{17})& =(\color{red}{-a}+\color{orange}{\frac{-20}{9}}).(\color{green}{b}+\color{blue}{\frac{-5}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{17})} + \color{orange}{(\frac{-20}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-20}{9})} . \color{blue}{(\frac{-5}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{5}{17}a-\frac{20}{9}b+\frac{20}{9}.\frac{5}{17}& \text{Uitwerken } \\ & =-ab+\frac{5}{17}a-\frac{20}{9}b+\frac{100}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p+\frac{-5}{13})(\frac{12}{8}-a)& =(\color{red}{p}+\color{orange}{\frac{-5}{13}}).(\color{green}{-a}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-5}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{13})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{3}{2}p+\frac{5}{13}a-\frac{5}{13}.\frac{3}{2}& \text{Uitwerken } \\ & =-ap+\frac{3}{2}p+\frac{5}{13}a-\frac{15}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-16}{12}-x)(p+\frac{1}{4})& =(\color{red}{-x}+\color{orange}{\frac{-4}{3}}).(\color{green}{p}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{4}x-\frac{4}{3}p-\frac{4}{3}.\frac{1}{4}& \text{Uitwerken } \\ & =-px-\frac{1}{4}x-\frac{4}{3}p-\frac{4}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{1}{4}x-\frac{4}{3}p-\frac{1}{3} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(x-\frac{14}{7})(x+\frac{-3}{18})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{1}{6}x-2x+2.\frac{1}{6}& \text{Uitwerken } \\ & =x^2+((\frac{-1}{6})+(-2))x+\frac{2}{6} & \text{Neem samen} \\ &=x^2-\frac{13}{6}x+\frac{2}{6} & \text{Maak de som} \\ &=x^2-\frac{13}{6}x+\frac{1}{3} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
12. \(\begin{align}(b+\frac{-9}{17})(x-16)& =(\color{red}{b}+\color{orange}{\frac{-9}{17}}).(\color{green}{x}+\color{blue}{(-16)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-16)} + \color{orange}{(\frac{-9}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{17})} . \color{blue}{(-16)}& \text{Boogjes en uitschrijven} \\ & = bx-16b-\frac{9}{17}x+\frac{9}{17}.16& \text{Uitwerken } \\ & =bx-16b-\frac{9}{17}x+\frac{144}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)