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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-16}{8}+q)(\frac{-1}{3}-p)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{-p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(-2)} . \color{green}{(-p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{3}q+2p+2.\frac{1}{3}& \text{Uitwerken } \\ & =-pq-\frac{1}{3}q+2p+\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(p-\frac{-20}{3})(\frac{-2}{3}-q)& =(\color{red}{p}+\color{orange}{\frac{20}{3}}).(\color{green}{-q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{20}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{20}{3})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{2}{3}p-\frac{20}{3}q-\frac{20}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =-pq-\frac{2}{3}p-\frac{20}{3}q-\frac{40}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-2}{16}+b)(\frac{-18}{18}-p)& =(\color{red}{b}+\color{orange}{\frac{-1}{8}}).(\color{green}{-p}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-1}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bp-1b+\frac{1}{8}p+\frac{1}{8}.1& \text{Uitwerken } \\ & =-bp-1b+\frac{1}{8}p+\frac{1}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{19}{7}+a)(q-\frac{15}{15})& =(\color{red}{a}+\color{orange}{\frac{19}{7}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{19}{7})} . \color{green}{(q)} + \color{orange}{(\frac{19}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aq-1a+\frac{19}{7}q-\frac{19}{7}.1& \text{Uitwerken } \\ & =aq-1a+\frac{19}{7}q-\frac{19}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-3}{12}-p)(\frac{-1}{4}-b)& =(\color{red}{-p}+\color{orange}{\frac{-1}{4}}).(\color{green}{-b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{4}p+\frac{1}{4}b+\frac{1}{4}.\frac{1}{4}& \text{Uitwerken } \\ & =bp+\frac{1}{4}p+\frac{1}{4}b+\frac{1}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p-\frac{14}{17})(\frac{16}{9}-x)& =(\color{red}{p}+\color{orange}{\frac{-14}{17}}).(\color{green}{-x}+\color{blue}{\frac{16}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{16}{9})} + \color{orange}{(\frac{-14}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-14}{17})} . \color{blue}{(\frac{16}{9})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{16}{9}p+\frac{14}{17}x-\frac{14}{17}.\frac{16}{9}& \text{Uitwerken } \\ & =-px+\frac{16}{9}p+\frac{14}{17}x-\frac{224}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{9}{9}-p)(b-\frac{10}{9})& =(\color{red}{-p}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{10}{9}p+1b-1.\frac{10}{9}& \text{Uitwerken } \\ & =-bp+\frac{10}{9}p+1b-\frac{10}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{6}{16}+a)(b-\frac{20}{14})& =(\color{red}{a}+\color{orange}{\frac{3}{8}}).(\color{green}{b}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{3}{8})} . \color{green}{(b)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{10}{7}a+\frac{3}{8}b-\frac{3}{8}.\frac{10}{7}& \text{Uitwerken } \\ & =ab-\frac{10}{7}a+\frac{3}{8}b-\frac{30}{56} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{10}{7}a+\frac{3}{8}b-\frac{15}{28} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(a-\frac{16}{14})(\frac{15}{11}-x)& =(\color{red}{a}+\color{orange}{\frac{-8}{7}}).(\color{green}{-x}+\color{blue}{\frac{15}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{15}{11})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{15}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{15}{11}a+\frac{8}{7}x-\frac{8}{7}.\frac{15}{11}& \text{Uitwerken } \\ & =-ax+\frac{15}{11}a+\frac{8}{7}x-\frac{120}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-15}{11}-a)(\frac{-10}{13}+p)& =(\color{red}{-a}+\color{orange}{\frac{-15}{11}}).(\color{green}{p}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{10}{13}a-\frac{15}{11}p+\frac{15}{11}.\frac{10}{13}& \text{Uitwerken } \\ & =-ap+\frac{10}{13}a-\frac{15}{11}p+\frac{150}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p-\frac{-18}{9})(\frac{5}{12}-b)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{-b}+\color{blue}{\frac{5}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{5}{12})} + \color{orange}{(2)} . \color{green}{(-b)} + \color{orange}{(2)} . \color{blue}{(\frac{5}{12})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{5}{12}p-2b+2.\frac{5}{12}& \text{Uitwerken } \\ & =-bp+\frac{5}{12}p-2b+\frac{10}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{5}{12}p-2b+\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-9}{6}-x)(\frac{14}{15}+p)& =(\color{red}{-x}+\color{orange}{\frac{-3}{2}}).(\color{green}{p}+\color{blue}{\frac{14}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{14}{15})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{14}{15})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{14}{15}x-\frac{3}{2}p-\frac{3}{2}.\frac{14}{15}& \text{Uitwerken } \\ & =-px-\frac{14}{15}x-\frac{3}{2}p-\frac{42}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{14}{15}x-\frac{3}{2}p-\frac{7}{5} & \text{Vereenvoudig} \\\end{align}\)