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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{9}{3}-x)(a-\frac{-11}{18})& =(\color{red}{-x}+\color{orange}{3}).(\color{green}{a}+\color{blue}{\frac{11}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{11}{18})} + \color{orange}{(3)} . \color{green}{(a)} + \color{orange}{(3)} . \color{blue}{(\frac{11}{18})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{11}{18}x+3a+3.\frac{11}{18}& \text{Uitwerken } \\ & =-ax-\frac{11}{18}x+3a+\frac{33}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{11}{18}x+3a+\frac{11}{6} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(p-\frac{-11}{13})(\frac{12}{14}+x)& =(\color{red}{p}+\color{orange}{\frac{11}{13}}).(\color{green}{x}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(\frac{11}{13})} . \color{green}{(x)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{6}{7}p+\frac{11}{13}x+\frac{11}{13}.\frac{6}{7}& \text{Uitwerken } \\ & =px+\frac{6}{7}p+\frac{11}{13}x+\frac{66}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{5}{5}-p)(\frac{19}{8}-p)& =(\color{red}{-p}+\color{orange}{1}).(\color{green}{-p}+\color{blue}{\frac{19}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{8})} + \color{orange}{(1)} . \color{green}{(-p)} + \color{orange}{(1)} . \color{blue}{(\frac{19}{8})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{19}{8}p-1p+1.\frac{19}{8}& \text{Uitwerken } \\ & =p^2+((\frac{-19}{8})+(-1))p+\frac{19}{8} & \text{Neem samen} \\ &=p^2-\frac{27}{8}p+\frac{19}{8} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(b+\frac{-10}{7})(\frac{5}{11}-p)& =(\color{red}{b}+\color{orange}{\frac{-10}{7}}).(\color{green}{-p}+\color{blue}{\frac{5}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{5}{11})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{5}{11})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{5}{11}b+\frac{10}{7}p-\frac{10}{7}.\frac{5}{11}& \text{Uitwerken } \\ & =-bp+\frac{5}{11}b+\frac{10}{7}p-\frac{50}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{13}{19}+x)(p-\frac{2}{17})& =(\color{red}{x}+\color{orange}{\frac{13}{19}}).(\color{green}{p}+\color{blue}{\frac{-2}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{17})} + \color{orange}{(\frac{13}{19})} . \color{green}{(p)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{-2}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{2}{17}x+\frac{13}{19}p-\frac{13}{19}.\frac{2}{17}& \text{Uitwerken } \\ & =px-\frac{2}{17}x+\frac{13}{19}p-\frac{26}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b-\frac{-15}{16})(\frac{1}{8}-b)& =(\color{red}{b}+\color{orange}{\frac{15}{16}}).(\color{green}{-b}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{15}{16})} . \color{green}{(-b)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{1}{8}b-\frac{15}{16}b+\frac{15}{16}.\frac{1}{8}& \text{Uitwerken } \\ & =-b^2+(\frac{1}{8}+(\frac{-15}{16}))b+(\frac{-15}{128}) & \text{Neem samen} \\ &=-b^2-\frac{13}{16}b+(\frac{-15}{128}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{20}{2}+x)(p+\frac{15}{17})& =(\color{red}{x}+\color{orange}{10}).(\color{green}{p}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(10)} . \color{green}{(p)} + \color{orange}{(10)} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{15}{17}x+10p+10.\frac{15}{17}& \text{Uitwerken } \\ & =px+\frac{15}{17}x+10p+\frac{150}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b+\frac{-3}{8})(\frac{-5}{2}-q)& =(\color{red}{b}+\color{orange}{\frac{-3}{8}}).(\color{green}{-q}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{2}b+\frac{3}{8}q+\frac{3}{8}.\frac{5}{2}& \text{Uitwerken } \\ & =-bq-\frac{5}{2}b+\frac{3}{8}q+\frac{15}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a-\frac{-1}{8})(\frac{19}{4}+x)& =(\color{red}{a}+\color{orange}{\frac{1}{8}}).(\color{green}{x}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{1}{8})} . \color{green}{(x)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{19}{4}a+\frac{1}{8}x+\frac{1}{8}.\frac{19}{4}& \text{Uitwerken } \\ & =ax+\frac{19}{4}a+\frac{1}{8}x+\frac{19}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(b+\frac{-3}{15})(\frac{-12}{6}+q)& =(\color{red}{b}+\color{orange}{\frac{-1}{5}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{-1}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bq-2b-\frac{1}{5}q+\frac{1}{5}.2& \text{Uitwerken } \\ & =bq-2b-\frac{1}{5}q+\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{16}{6}+x)(\frac{-11}{9}-x)& =(\color{red}{x}+\color{orange}{\frac{8}{3}}).(\color{green}{-x}+\color{blue}{\frac{-11}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{9})} + \color{orange}{(\frac{8}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{-11}{9})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{11}{9}x-\frac{8}{3}x-\frac{8}{3}.\frac{11}{9}& \text{Uitwerken } \\ & =-x^2+((\frac{-11}{9})+(\frac{-8}{3}))x-\frac{88}{27} & \text{Neem samen} \\ &=-x^2-\frac{35}{9}x-\frac{88}{27} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{11}{6}-a)(\frac{8}{8}+x)& =(\color{red}{-a}+\color{orange}{\frac{11}{6}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(1)} + \color{orange}{(\frac{11}{6})} . \color{green}{(x)} + \color{orange}{(\frac{11}{6})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -ax-1a+\frac{11}{6}x+\frac{11}{6}.1& \text{Uitwerken } \\ & =-ax-1a+\frac{11}{6}x+\frac{11}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)