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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{9}{19})(\frac{-6}{16}-q)& =(\color{red}{p}+\color{orange}{\frac{9}{19}}).(\color{green}{-q}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{9}{19})} . \color{green}{(-q)} + \color{orange}{(\frac{9}{19})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{3}{8}p-\frac{9}{19}q-\frac{9}{19}.\frac{3}{8}& \text{Uitwerken } \\ & =-pq-\frac{3}{8}p-\frac{9}{19}q-\frac{27}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x-\frac{9}{7})(p-\frac{-9}{20})& =(\color{red}{x}+\color{orange}{\frac{-9}{7}}).(\color{green}{p}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(\frac{-9}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{9}{20}x-\frac{9}{7}p-\frac{9}{7}.\frac{9}{20}& \text{Uitwerken } \\ & =px+\frac{9}{20}x-\frac{9}{7}p-\frac{81}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-10}{5}-a)(\frac{15}{14}+q)& =(\color{red}{-a}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{15}{14}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{15}{14})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{15}{14})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{15}{14}a-2q-2.\frac{15}{14}& \text{Uitwerken } \\ & =-aq-\frac{15}{14}a-2q-\frac{30}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq-\frac{15}{14}a-2q-\frac{15}{7} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{6}{6}-q)(p+\frac{-3}{20})& =(\color{red}{-q}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-3}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{20})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-3}{20})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{3}{20}q+1p-1.\frac{3}{20}& \text{Uitwerken } \\ & =-pq+\frac{3}{20}q+1p-\frac{3}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-10}{12}-p)(\frac{-8}{16}+x)& =(\color{red}{-p}+\color{orange}{\frac{-5}{6}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{1}{2}p-\frac{5}{6}x+\frac{5}{6}.\frac{1}{2}& \text{Uitwerken } \\ & =-px+\frac{1}{2}p-\frac{5}{6}x+\frac{5}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}((-2)-b)(\frac{3}{17}+a)& =(\color{red}{-b}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{3}{17}b-2a-2.\frac{3}{17}& \text{Uitwerken } \\ & =-ab-\frac{3}{17}b-2a-\frac{6}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-1}{9}-q)(\frac{-1}{11}+p)& =(\color{red}{-q}+\color{orange}{\frac{-1}{9}}).(\color{green}{p}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{1}{11}q-\frac{1}{9}p+\frac{1}{9}.\frac{1}{11}& \text{Uitwerken } \\ & =-pq+\frac{1}{11}q-\frac{1}{9}p+\frac{1}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b+\frac{-1}{17})(b-\frac{15}{13})& =(\color{red}{b}+\color{orange}{\frac{-1}{17}}).(\color{green}{b}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(\frac{-1}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{15}{13}b-\frac{1}{17}b+\frac{1}{17}.\frac{15}{13}& \text{Uitwerken } \\ & =b^2+((\frac{-15}{13})+(\frac{-1}{17}))b+\frac{15}{221} & \text{Neem samen} \\ &=b^2-\frac{268}{221}b+\frac{15}{221} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(\frac{14}{8}+b)(b-\frac{17}{20})& =(\color{red}{b}+\color{orange}{\frac{7}{4}}).(\color{green}{b}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(\frac{7}{4})} . \color{green}{(b)} + \color{orange}{(\frac{7}{4})} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{17}{20}b+\frac{7}{4}b-\frac{7}{4}.\frac{17}{20}& \text{Uitwerken } \\ & =b^2+((\frac{-17}{20})+\frac{7}{4})b-(\frac{-119}{80}) & \text{Neem samen} \\ &=b^2+\frac{18}{20}b-(\frac{-119}{80}) & \text{Maak de som} \\ &=b^2+\frac{9}{10}b+\frac{119}{80} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
10. \(\begin{align}(\frac{8}{4}+q)(b-\frac{1}{14})& =(\color{red}{q}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{-1}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{14})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{-1}{14})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{1}{14}q+2b-2.\frac{1}{14}& \text{Uitwerken } \\ & =bq-\frac{1}{14}q+2b-\frac{2}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{1}{14}q+2b-\frac{1}{7} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(x-\frac{-3}{17})(\frac{-4}{9}+b)& =(\color{red}{x}+\color{orange}{\frac{3}{17}}).(\color{green}{b}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{3}{17})} . \color{green}{(b)} + \color{orange}{(\frac{3}{17})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{4}{9}x+\frac{3}{17}b-\frac{3}{17}.\frac{4}{9}& \text{Uitwerken } \\ & =bx-\frac{4}{9}x+\frac{3}{17}b-\frac{12}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{4}{9}x+\frac{3}{17}b-\frac{4}{51} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(p+\frac{-14}{14})(\frac{-9}{20}+q)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{-9}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-9}{20})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-9}{20})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{9}{20}p-1q+1.\frac{9}{20}& \text{Uitwerken } \\ & =pq-\frac{9}{20}p-1q+\frac{9}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)