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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{-11}{14})(\frac{14}{15}-p)& =(\color{red}{b}+\color{orange}{\frac{-11}{14}}).(\color{green}{-p}+\color{blue}{\frac{14}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{14}{15})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(-p)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{14}{15})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{14}{15}b+\frac{11}{14}p-\frac{11}{14}.\frac{14}{15}& \text{Uitwerken } \\ & =-bp+\frac{14}{15}b+\frac{11}{14}p-\frac{154}{210} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{14}{15}b+\frac{11}{14}p-\frac{11}{15} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{17}{7}-b)(\frac{-15}{8}-a)& =(\color{red}{-b}+\color{orange}{\frac{17}{7}}).(\color{green}{-a}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{17}{7})} . \color{green}{(-a)} + \color{orange}{(\frac{17}{7})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{15}{8}b-\frac{17}{7}a-\frac{17}{7}.\frac{15}{8}& \text{Uitwerken } \\ & =ab+\frac{15}{8}b-\frac{17}{7}a-\frac{255}{56} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x-\frac{4}{10})(\frac{17}{14}+a)& =(\color{red}{x}+\color{orange}{\frac{-2}{5}}).(\color{green}{a}+\color{blue}{\frac{17}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{17}{14})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{17}{14})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{14}x-\frac{2}{5}a-\frac{2}{5}.\frac{17}{14}& \text{Uitwerken } \\ & =ax+\frac{17}{14}x-\frac{2}{5}a-\frac{34}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+\frac{17}{14}x-\frac{2}{5}a-\frac{17}{35} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-10}{20}+p)(x+\frac{-17}{20})& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{-17}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{20})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-17}{20})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{17}{20}p-\frac{1}{2}x+\frac{1}{2}.\frac{17}{20}& \text{Uitwerken } \\ & =px-\frac{17}{20}p-\frac{1}{2}x+\frac{17}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b+\frac{-9}{13})(\frac{10}{11}-a)& =(\color{red}{b}+\color{orange}{\frac{-9}{13}}).(\color{green}{-a}+\color{blue}{\frac{10}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{10}{11})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{10}{11})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{10}{11}b+\frac{9}{13}a-\frac{9}{13}.\frac{10}{11}& \text{Uitwerken } \\ & =-ab+\frac{10}{11}b+\frac{9}{13}a-\frac{90}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-15}{13}+a)(b+\frac{-12}{19})& =(\color{red}{a}+\color{orange}{\frac{-15}{13}}).(\color{green}{b}+\color{blue}{\frac{-12}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-12}{19})} + \color{orange}{(\frac{-15}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{13})} . \color{blue}{(\frac{-12}{19})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{12}{19}a-\frac{15}{13}b+\frac{15}{13}.\frac{12}{19}& \text{Uitwerken } \\ & =ab-\frac{12}{19}a-\frac{15}{13}b+\frac{180}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-6}{4}-q)(p+\frac{10}{17})& =(\color{red}{-q}+\color{orange}{\frac{-3}{2}}).(\color{green}{p}+\color{blue}{\frac{10}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{10}{17})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{10}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{10}{17}q-\frac{3}{2}p-\frac{3}{2}.\frac{10}{17}& \text{Uitwerken } \\ & =-pq-\frac{10}{17}q-\frac{3}{2}p-\frac{30}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{10}{17}q-\frac{3}{2}p-\frac{15}{17} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(b-\frac{-2}{12})(\frac{-8}{3}-x)& =(\color{red}{b}+\color{orange}{\frac{1}{6}}).(\color{green}{-x}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{1}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{8}{3}b-\frac{1}{6}x-\frac{1}{6}.\frac{8}{3}& \text{Uitwerken } \\ & =-bx-\frac{8}{3}b-\frac{1}{6}x-\frac{8}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{8}{3}b-\frac{1}{6}x-\frac{4}{9} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(p+\frac{13}{12})(q-\frac{15}{14})& =(\color{red}{p}+\color{orange}{\frac{13}{12}}).(\color{green}{q}+\color{blue}{\frac{-15}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-15}{14})} + \color{orange}{(\frac{13}{12})} . \color{green}{(q)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(\frac{-15}{14})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{15}{14}p+\frac{13}{12}q-\frac{13}{12}.\frac{15}{14}& \text{Uitwerken } \\ & =pq-\frac{15}{14}p+\frac{13}{12}q-\frac{195}{168} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{15}{14}p+\frac{13}{12}q-\frac{65}{56} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p-\frac{8}{10})(\frac{17}{17}+q)& =(\color{red}{p}+\color{orange}{\frac{-4}{5}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-4}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pq+1p-\frac{4}{5}q-\frac{4}{5}.1& \text{Uitwerken } \\ & =pq+1p-\frac{4}{5}q-\frac{4}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-\frac{11}{6})(q-\frac{-19}{5})& =(\color{red}{a}+\color{orange}{\frac{-11}{6}}).(\color{green}{q}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(\frac{-11}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{6})} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{19}{5}a-\frac{11}{6}q-\frac{11}{6}.\frac{19}{5}& \text{Uitwerken } \\ & =aq+\frac{19}{5}a-\frac{11}{6}q-\frac{209}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{16}{4}+b)(\frac{-14}{4}-p)& =(\color{red}{b}+\color{orange}{4}).(\color{green}{-p}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(4)} . \color{green}{(-p)} + \color{orange}{(4)} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{7}{2}b-4p-4.\frac{7}{2}& \text{Uitwerken } \\ & =-bp-\frac{7}{2}b-4p-\frac{28}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{7}{2}b-4p-14 & \text{Vereenvoudig} \\\end{align}\)