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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-(-16))(q-\frac{-17}{9})& =(\color{red}{p}+\color{orange}{16}).(\color{green}{q}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(16)} . \color{green}{(q)} + \color{orange}{(16)} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{17}{9}p+16q+16.\frac{17}{9}& \text{Uitwerken } \\ & =pq+\frac{17}{9}p+16q+\frac{272}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(p-\frac{-16}{19})(b-\frac{-7}{12})& =(\color{red}{p}+\color{orange}{\frac{16}{19}}).(\color{green}{b}+\color{blue}{\frac{7}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{7}{12})} + \color{orange}{(\frac{16}{19})} . \color{green}{(b)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(\frac{7}{12})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{12}p+\frac{16}{19}b+\frac{16}{19}.\frac{7}{12}& \text{Uitwerken } \\ & =bp+\frac{7}{12}p+\frac{16}{19}b+\frac{112}{228} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{7}{12}p+\frac{16}{19}b+\frac{28}{57} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-19}{12}+p)(\frac{-5}{18}-x)& =(\color{red}{p}+\color{orange}{\frac{-19}{12}}).(\color{green}{-x}+\color{blue}{\frac{-5}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{18})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{-5}{18})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{5}{18}p+\frac{19}{12}x+\frac{19}{12}.\frac{5}{18}& \text{Uitwerken } \\ & =-px-\frac{5}{18}p+\frac{19}{12}x+\frac{95}{216} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{9}{8}+x)(x-\frac{2}{18})& =(\color{red}{x}+\color{orange}{\frac{9}{8}}).(\color{green}{x}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{9}{8})} . \color{green}{(x)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{1}{9}x+\frac{9}{8}x-\frac{9}{8}.\frac{1}{9}& \text{Uitwerken } \\ & =x^2+((\frac{-1}{9})+\frac{9}{8})x-(\frac{-9}{72}) & \text{Neem samen} \\ &=x^2+\frac{73}{72}x-(\frac{-9}{72}) & \text{Maak de som} \\ &=x^2+\frac{73}{72}x+\frac{1}{8} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
5. \(\begin{align}(\frac{-9}{17}+x)(a+\frac{-11}{18})& =(\color{red}{x}+\color{orange}{\frac{-9}{17}}).(\color{green}{a}+\color{blue}{\frac{-11}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{18})} + \color{orange}{(\frac{-9}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{17})} . \color{blue}{(\frac{-11}{18})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{11}{18}x-\frac{9}{17}a+\frac{9}{17}.\frac{11}{18}& \text{Uitwerken } \\ & =ax-\frac{11}{18}x-\frac{9}{17}a+\frac{99}{306} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{11}{18}x-\frac{9}{17}a+\frac{11}{34} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(q+\frac{-18}{13})(p-\frac{2}{11})& =(\color{red}{q}+\color{orange}{\frac{-18}{13}}).(\color{green}{p}+\color{blue}{\frac{-2}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{11})} + \color{orange}{(\frac{-18}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-18}{13})} . \color{blue}{(\frac{-2}{11})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{2}{11}q-\frac{18}{13}p+\frac{18}{13}.\frac{2}{11}& \text{Uitwerken } \\ & =pq-\frac{2}{11}q-\frac{18}{13}p+\frac{36}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}((-20)+a)(\frac{-1}{10}-p)& =(\color{red}{a}+\color{orange}{(-20)}).(\color{green}{-p}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(-20)} . \color{green}{(-p)} + \color{orange}{(-20)} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{10}a+20p+20.\frac{1}{10}& \text{Uitwerken } \\ & =-ap-\frac{1}{10}a+20p+\frac{20}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{1}{10}a+20p+2 & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{1}{18}-a)(\frac{10}{12}-q)& =(\color{red}{-a}+\color{orange}{\frac{1}{18}}).(\color{green}{-q}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{1}{18})} . \color{green}{(-q)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{5}{6}a-\frac{1}{18}q+\frac{1}{18}.\frac{5}{6}& \text{Uitwerken } \\ & =aq-\frac{5}{6}a-\frac{1}{18}q+\frac{5}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{18}{7}+b)(\frac{12}{6}+a)& =(\color{red}{b}+\color{orange}{\frac{18}{7}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(\frac{18}{7})} . \color{green}{(a)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ab+2b+\frac{18}{7}a+\frac{18}{7}.2& \text{Uitwerken } \\ & =ab+2b+\frac{18}{7}a+\frac{36}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a-(-15))(q+\frac{-6}{17})& =(\color{red}{a}+\color{orange}{15}).(\color{green}{q}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(15)} . \color{green}{(q)} + \color{orange}{(15)} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{6}{17}a+15q-15.\frac{6}{17}& \text{Uitwerken } \\ & =aq-\frac{6}{17}a+15q-\frac{90}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{15}{17}+b)(q-\frac{-8}{14})& =(\color{red}{b}+\color{orange}{\frac{15}{17}}).(\color{green}{q}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{15}{17})} . \color{green}{(q)} + \color{orange}{(\frac{15}{17})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{4}{7}b+\frac{15}{17}q+\frac{15}{17}.\frac{4}{7}& \text{Uitwerken } \\ & =bq+\frac{4}{7}b+\frac{15}{17}q+\frac{60}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{20}{8}-p)(\frac{19}{14}+q)& =(\color{red}{-p}+\color{orange}{\frac{5}{2}}).(\color{green}{q}+\color{blue}{\frac{19}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{14})} + \color{orange}{(\frac{5}{2})} . \color{green}{(q)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{19}{14})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{19}{14}p+\frac{5}{2}q+\frac{5}{2}.\frac{19}{14}& \text{Uitwerken } \\ & =-pq-\frac{19}{14}p+\frac{5}{2}q+\frac{95}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)