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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b-\frac{13}{15})(a-\frac{-16}{18})& =(\color{red}{b}+\color{orange}{\frac{-13}{15}}).(\color{green}{a}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{-13}{15})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{15})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{8}{9}b-\frac{13}{15}a-\frac{13}{15}.\frac{8}{9}& \text{Uitwerken } \\ & =ab+\frac{8}{9}b-\frac{13}{15}a-\frac{104}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b+\frac{5}{2})(\frac{-13}{18}+p)& =(\color{red}{b}+\color{orange}{\frac{5}{2}}).(\color{green}{p}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(\frac{5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{13}{18}b+\frac{5}{2}p-\frac{5}{2}.\frac{13}{18}& \text{Uitwerken } \\ & =bp-\frac{13}{18}b+\frac{5}{2}p-\frac{65}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b+\frac{18}{9})(a+\frac{9}{12})& =(\color{red}{b}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{4}b+2a+2.\frac{3}{4}& \text{Uitwerken } \\ & =ab+\frac{3}{4}b+2a+\frac{6}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{3}{4}b+2a+\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{-2}{20}-q)(\frac{5}{12}-p)& =(\color{red}{-q}+\color{orange}{\frac{-1}{10}}).(\color{green}{-p}+\color{blue}{\frac{5}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{5}{12})} + \color{orange}{(\frac{-1}{10})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{10})} . \color{blue}{(\frac{5}{12})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{5}{12}q+\frac{1}{10}p-\frac{1}{10}.\frac{5}{12}& \text{Uitwerken } \\ & =pq-\frac{5}{12}q+\frac{1}{10}p-\frac{5}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{5}{12}q+\frac{1}{10}p-\frac{1}{24} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(p+\frac{19}{11})(\frac{17}{9}-x)& =(\color{red}{p}+\color{orange}{\frac{19}{11}}).(\color{green}{-x}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(\frac{19}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{11})} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{17}{9}p-\frac{19}{11}x+\frac{19}{11}.\frac{17}{9}& \text{Uitwerken } \\ & =-px+\frac{17}{9}p-\frac{19}{11}x+\frac{323}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(q+\frac{-6}{20})(\frac{-18}{9}+a)& =(\color{red}{q}+\color{orange}{\frac{-3}{10}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{-3}{10})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = aq-2q-\frac{3}{10}a+\frac{3}{10}.2& \text{Uitwerken } \\ & =aq-2q-\frac{3}{10}a+\frac{6}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-2q-\frac{3}{10}a+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{1}{12}+p)(b-(-17))& =(\color{red}{p}+\color{orange}{\frac{1}{12}}).(\color{green}{b}+\color{blue}{17})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(17)} + \color{orange}{(\frac{1}{12})} . \color{green}{(b)} + \color{orange}{(\frac{1}{12})} . \color{blue}{(17)}& \text{Boogjes en uitschrijven} \\ & = bp+17p+\frac{1}{12}b+\frac{1}{12}.17& \text{Uitwerken } \\ & =bp+17p+\frac{1}{12}b+\frac{17}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a-\frac{-4}{15})(q-19)& =(\color{red}{a}+\color{orange}{\frac{4}{15}}).(\color{green}{q}+\color{blue}{(-19)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-19)} + \color{orange}{(\frac{4}{15})} . \color{green}{(q)} + \color{orange}{(\frac{4}{15})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = aq-19a+\frac{4}{15}q-\frac{4}{15}.19& \text{Uitwerken } \\ & =aq-19a+\frac{4}{15}q-\frac{76}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x-\frac{-9}{15})(\frac{-10}{16}+q)& =(\color{red}{x}+\color{orange}{\frac{3}{5}}).(\color{green}{q}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{3}{5})} . \color{green}{(q)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{8}x+\frac{3}{5}q-\frac{3}{5}.\frac{5}{8}& \text{Uitwerken } \\ & =qx-\frac{5}{8}x+\frac{3}{5}q-\frac{15}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx-\frac{5}{8}x+\frac{3}{5}q-\frac{3}{8} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(a-\frac{1}{18})(\frac{20}{8}-p)& =(\color{red}{a}+\color{orange}{\frac{-1}{18}}).(\color{green}{-p}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{-1}{18})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{18})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{5}{2}a+\frac{1}{18}p-\frac{1}{18}.\frac{5}{2}& \text{Uitwerken } \\ & =-ap+\frac{5}{2}a+\frac{1}{18}p-\frac{5}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{12}{10}+b)(q-\frac{18}{20})& =(\color{red}{b}+\color{orange}{\frac{6}{5}}).(\color{green}{q}+\color{blue}{\frac{-9}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{10})} + \color{orange}{(\frac{6}{5})} . \color{green}{(q)} + \color{orange}{(\frac{6}{5})} . \color{blue}{(\frac{-9}{10})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{9}{10}b+\frac{6}{5}q-\frac{6}{5}.\frac{9}{10}& \text{Uitwerken } \\ & =bq-\frac{9}{10}b+\frac{6}{5}q-\frac{54}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{9}{10}b+\frac{6}{5}q-\frac{27}{25} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-2}{8}+p)(\frac{-5}{13}+p)& =(\color{red}{p}+\color{orange}{\frac{-1}{4}}).(\color{green}{p}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{13})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{5}{13}p-\frac{1}{4}p+\frac{1}{4}.\frac{5}{13}& \text{Uitwerken } \\ & =p^2+((\frac{-5}{13})+(\frac{-1}{4}))p+\frac{5}{52} & \text{Neem samen} \\ &=p^2-\frac{33}{52}p+\frac{5}{52} & \text{Maak de som} \\\end{align}\)