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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b-\frac{-10}{8})(\frac{-5}{3}+p)& =(\color{red}{b}+\color{orange}{\frac{5}{4}}).(\color{green}{p}+\color{blue}{\frac{-5}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{3})} + \color{orange}{(\frac{5}{4})} . \color{green}{(p)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-5}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{3}b+\frac{5}{4}p-\frac{5}{4}.\frac{5}{3}& \text{Uitwerken } \\ & =bp-\frac{5}{3}b+\frac{5}{4}p-\frac{25}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a-\frac{-10}{12})(\frac{2}{3}-q)& =(\color{red}{a}+\color{orange}{\frac{5}{6}}).(\color{green}{-q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{5}{6})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{2}{3}a-\frac{5}{6}q+\frac{5}{6}.\frac{2}{3}& \text{Uitwerken } \\ & =-aq+\frac{2}{3}a-\frac{5}{6}q+\frac{10}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{2}{3}a-\frac{5}{6}q+\frac{5}{9} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{1}{14}+q)(b-\frac{5}{7})& =(\color{red}{q}+\color{orange}{\frac{1}{14}}).(\color{green}{b}+\color{blue}{\frac{-5}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{7})} + \color{orange}{(\frac{1}{14})} . \color{green}{(b)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(\frac{-5}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{7}q+\frac{1}{14}b-\frac{1}{14}.\frac{5}{7}& \text{Uitwerken } \\ & =bq-\frac{5}{7}q+\frac{1}{14}b-\frac{5}{98} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(b-\frac{10}{18})(b-\frac{7}{2})& =(\color{red}{b}+\color{orange}{\frac{-5}{9}}).(\color{green}{b}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{7}{2}b-\frac{5}{9}b+\frac{5}{9}.\frac{7}{2}& \text{Uitwerken } \\ & =b^2+((\frac{-7}{2})+(\frac{-5}{9}))b+\frac{35}{18} & \text{Neem samen} \\ &=b^2-\frac{73}{18}b+\frac{35}{18} & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(b-\frac{18}{5})(\frac{13}{10}+x)& =(\color{red}{b}+\color{orange}{\frac{-18}{5}}).(\color{green}{x}+\color{blue}{\frac{13}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{13}{10})} + \color{orange}{(\frac{-18}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-18}{5})} . \color{blue}{(\frac{13}{10})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{13}{10}b-\frac{18}{5}x-\frac{18}{5}.\frac{13}{10}& \text{Uitwerken } \\ & =bx+\frac{13}{10}b-\frac{18}{5}x-\frac{234}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{13}{10}b-\frac{18}{5}x-\frac{117}{25} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(b-\frac{1}{15})(x-\frac{1}{9})& =(\color{red}{b}+\color{orange}{\frac{-1}{15}}).(\color{green}{x}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{9}b-\frac{1}{15}x+\frac{1}{15}.\frac{1}{9}& \text{Uitwerken } \\ & =bx-\frac{1}{9}b-\frac{1}{15}x+\frac{1}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p-\frac{-8}{4})(\frac{-12}{9}-q)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{-q}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(2)} . \color{green}{(-q)} + \color{orange}{(2)} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{4}{3}p-2q-2.\frac{4}{3}& \text{Uitwerken } \\ & =-pq-\frac{4}{3}p-2q-\frac{8}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{5}{7}+a)(b-\frac{3}{16})& =(\color{red}{a}+\color{orange}{\frac{5}{7}}).(\color{green}{b}+\color{blue}{\frac{-3}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{16})} + \color{orange}{(\frac{5}{7})} . \color{green}{(b)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(\frac{-3}{16})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{3}{16}a+\frac{5}{7}b-\frac{5}{7}.\frac{3}{16}& \text{Uitwerken } \\ & =ab-\frac{3}{16}a+\frac{5}{7}b-\frac{15}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p+\frac{-20}{12})(x+\frac{5}{17})& =(\color{red}{p}+\color{orange}{\frac{-5}{3}}).(\color{green}{x}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{5}{17}p-\frac{5}{3}x-\frac{5}{3}.\frac{5}{17}& \text{Uitwerken } \\ & =px+\frac{5}{17}p-\frac{5}{3}x-\frac{25}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(p-\frac{9}{14})(p-\frac{-8}{19})& =(\color{red}{p}+\color{orange}{\frac{-9}{14}}).(\color{green}{p}+\color{blue}{\frac{8}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{8}{19})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{8}{19})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{8}{19}p-\frac{9}{14}p-\frac{9}{14}.\frac{8}{19}& \text{Uitwerken } \\ & =p^2+(\frac{8}{19}+(\frac{-9}{14}))p-(\frac{-72}{266}) & \text{Neem samen} \\ &=p^2-\frac{59}{266}p-(\frac{-72}{266}) & \text{Maak de som} \\ &=p^2-\frac{59}{266}p+\frac{36}{133} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
11. \(\begin{align}(a-\frac{14}{11})(\frac{8}{13}+p)& =(\color{red}{a}+\color{orange}{\frac{-14}{11}}).(\color{green}{p}+\color{blue}{\frac{8}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{8}{13})} + \color{orange}{(\frac{-14}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-14}{11})} . \color{blue}{(\frac{8}{13})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{8}{13}a-\frac{14}{11}p-\frac{14}{11}.\frac{8}{13}& \text{Uitwerken } \\ & =ap+\frac{8}{13}a-\frac{14}{11}p-\frac{112}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{5}{2}+b)(p-\frac{-19}{11})& =(\color{red}{b}+\color{orange}{\frac{5}{2}}).(\color{green}{p}+\color{blue}{\frac{19}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{19}{11})} + \color{orange}{(\frac{5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{19}{11})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{11}b+\frac{5}{2}p+\frac{5}{2}.\frac{19}{11}& \text{Uitwerken } \\ & =bp+\frac{19}{11}b+\frac{5}{2}p+\frac{95}{22} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)