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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-10}{5}-b)(\frac{6}{20}-b)& =(\color{red}{-b}+\color{orange}{(-2)}).(\color{green}{-b}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(-2)} . \color{green}{(-b)} + \color{orange}{(-2)} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{3}{10}b+2b-2.\frac{3}{10}& \text{Uitwerken } \\ & =b^2+((\frac{-3}{10})+2)b-(\frac{-6}{10}) & \text{Neem samen} \\ &=b^2+\frac{17}{10}b-(\frac{-6}{10}) & \text{Maak de som} \\ &=b^2+\frac{17}{10}b+\frac{3}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
2. \(\begin{align}(a-\frac{10}{16})(p-\frac{-19}{10})& =(\color{red}{a}+\color{orange}{\frac{-5}{8}}).(\color{green}{p}+\color{blue}{\frac{19}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{19}{10})} + \color{orange}{(\frac{-5}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(\frac{19}{10})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{19}{10}a-\frac{5}{8}p-\frac{5}{8}.\frac{19}{10}& \text{Uitwerken } \\ & =ap+\frac{19}{10}a-\frac{5}{8}p-\frac{95}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{19}{10}a-\frac{5}{8}p-\frac{19}{16} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{14}{16}+x)(a-\frac{-1}{2})& =(\color{red}{x}+\color{orange}{\frac{7}{8}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{7}{8})} . \color{green}{(a)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{2}x+\frac{7}{8}a+\frac{7}{8}.\frac{1}{2}& \text{Uitwerken } \\ & =ax+\frac{1}{2}x+\frac{7}{8}a+\frac{7}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(b-\frac{-1}{3})(\frac{-12}{8}+p)& =(\color{red}{b}+\color{orange}{\frac{1}{3}}).(\color{green}{p}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{2}b+\frac{1}{3}p-\frac{1}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =bp-\frac{3}{2}b+\frac{1}{3}p-\frac{3}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{3}{2}b+\frac{1}{3}p-\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(x-\frac{-1}{2})(a+\frac{-1}{20})& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{-1}{20}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{20})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-1}{20})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{1}{20}x+\frac{1}{2}a-\frac{1}{2}.\frac{1}{20}& \text{Uitwerken } \\ & =ax-\frac{1}{20}x+\frac{1}{2}a-\frac{1}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}((-5)+q)(\frac{13}{17}-x)& =(\color{red}{q}+\color{orange}{(-5)}).(\color{green}{-x}+\color{blue}{\frac{13}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{13}{17})} + \color{orange}{(-5)} . \color{green}{(-x)} + \color{orange}{(-5)} . \color{blue}{(\frac{13}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{13}{17}q+5x-5.\frac{13}{17}& \text{Uitwerken } \\ & =-qx+\frac{13}{17}q+5x-\frac{65}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{11}{5}-b)(\frac{15}{16}+x)& =(\color{red}{-b}+\color{orange}{\frac{11}{5}}).(\color{green}{x}+\color{blue}{\frac{15}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{15}{16})} + \color{orange}{(\frac{11}{5})} . \color{green}{(x)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(\frac{15}{16})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{15}{16}b+\frac{11}{5}x+\frac{11}{5}.\frac{15}{16}& \text{Uitwerken } \\ & =-bx-\frac{15}{16}b+\frac{11}{5}x+\frac{165}{80} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{15}{16}b+\frac{11}{5}x+\frac{33}{16} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-12}{8}-b)(\frac{15}{8}-b)& =(\color{red}{-b}+\color{orange}{\frac{-3}{2}}).(\color{green}{-b}+\color{blue}{\frac{15}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(\frac{15}{8})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{15}{8})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{15}{8}b+\frac{3}{2}b-\frac{3}{2}.\frac{15}{8}& \text{Uitwerken } \\ & =b^2+((\frac{-15}{8})+\frac{3}{2})b-(\frac{-45}{16}) & \text{Neem samen} \\ &=b^2-\frac{3}{8}b-(\frac{-45}{16}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(\frac{-19}{19}-p)(p-(-4))& =(\color{red}{-p}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(4)} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -pp-4p-1p-1.4& \text{Uitwerken } \\ & =-p^2+((-4)+(-1))p-4 & \text{Neem samen} \\ &=-p^2-5p-4 & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(b+\frac{-10}{15})(\frac{15}{16}+x)& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{x}+\color{blue}{\frac{15}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{15}{16})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{15}{16})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{15}{16}b-\frac{2}{3}x-\frac{2}{3}.\frac{15}{16}& \text{Uitwerken } \\ & =bx+\frac{15}{16}b-\frac{2}{3}x-\frac{30}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{15}{16}b-\frac{2}{3}x-\frac{5}{8} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(p-\frac{-19}{8})(q-5)& =(\color{red}{p}+\color{orange}{\frac{19}{8}}).(\color{green}{q}+\color{blue}{(-5)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-5)} + \color{orange}{(\frac{19}{8})} . \color{green}{(q)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = pq-5p+\frac{19}{8}q-\frac{19}{8}.5& \text{Uitwerken } \\ & =pq-5p+\frac{19}{8}q-\frac{95}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p+\frac{8}{13})(\frac{1}{5}+a)& =(\color{red}{p}+\color{orange}{\frac{8}{13}}).(\color{green}{a}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{8}{13})} . \color{green}{(a)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{5}p+\frac{8}{13}a+\frac{8}{13}.\frac{1}{5}& \text{Uitwerken } \\ & =ap+\frac{1}{5}p+\frac{8}{13}a+\frac{8}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)