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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-4}{5}-b)(q+\frac{16}{14})& =(\color{red}{-b}+\color{orange}{\frac{-4}{5}}).(\color{green}{q}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{8}{7}b-\frac{4}{5}q-\frac{4}{5}.\frac{8}{7}& \text{Uitwerken } \\ & =-bq-\frac{8}{7}b-\frac{4}{5}q-\frac{32}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q+\frac{-4}{10})(\frac{5}{8}-b)& =(\color{red}{q}+\color{orange}{\frac{-2}{5}}).(\color{green}{-b}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{8}q+\frac{2}{5}b-\frac{2}{5}.\frac{5}{8}& \text{Uitwerken } \\ & =-bq+\frac{5}{8}q+\frac{2}{5}b-\frac{10}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{5}{8}q+\frac{2}{5}b-\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(x-\frac{19}{8})(\frac{16}{12}+q)& =(\color{red}{x}+\color{orange}{\frac{-19}{8}}).(\color{green}{q}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{-19}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{8})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{4}{3}x-\frac{19}{8}q-\frac{19}{8}.\frac{4}{3}& \text{Uitwerken } \\ & =qx+\frac{4}{3}x-\frac{19}{8}q-\frac{76}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{4}{3}x-\frac{19}{8}q-\frac{19}{6} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(b-\frac{2}{16})(x-\frac{-12}{10})& =(\color{red}{b}+\color{orange}{\frac{-1}{8}}).(\color{green}{x}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{6}{5}b-\frac{1}{8}x-\frac{1}{8}.\frac{6}{5}& \text{Uitwerken } \\ & =bx+\frac{6}{5}b-\frac{1}{8}x-\frac{6}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{6}{5}b-\frac{1}{8}x-\frac{3}{20} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{3}{20}-p)(\frac{-16}{6}+b)& =(\color{red}{-p}+\color{orange}{\frac{3}{20}}).(\color{green}{b}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{3}{20})} . \color{green}{(b)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{8}{3}p+\frac{3}{20}b-\frac{3}{20}.\frac{8}{3}& \text{Uitwerken } \\ & =-bp+\frac{8}{3}p+\frac{3}{20}b-\frac{24}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{8}{3}p+\frac{3}{20}b-\frac{2}{5} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(x-\frac{4}{19})(b-\frac{11}{9})& =(\color{red}{x}+\color{orange}{\frac{-4}{19}}).(\color{green}{b}+\color{blue}{\frac{-11}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{9})} + \color{orange}{(\frac{-4}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{19})} . \color{blue}{(\frac{-11}{9})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{9}x-\frac{4}{19}b+\frac{4}{19}.\frac{11}{9}& \text{Uitwerken } \\ & =bx-\frac{11}{9}x-\frac{4}{19}b+\frac{44}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p-\frac{10}{13})(\frac{-10}{7}+a)& =(\color{red}{p}+\color{orange}{\frac{-10}{13}}).(\color{green}{a}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{-10}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{13})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{10}{7}p-\frac{10}{13}a+\frac{10}{13}.\frac{10}{7}& \text{Uitwerken } \\ & =ap-\frac{10}{7}p-\frac{10}{13}a+\frac{100}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b-\frac{17}{17})(\frac{20}{18}-p)& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{-p}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(-1)} . \color{green}{(-p)} + \color{orange}{(-1)} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{10}{9}b+1p-1.\frac{10}{9}& \text{Uitwerken } \\ & =-bp+\frac{10}{9}b+1p-\frac{10}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a-\frac{11}{16})(x+\frac{16}{8})& =(\color{red}{a}+\color{orange}{\frac{-11}{16}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{-11}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ax+2a-\frac{11}{16}x-\frac{11}{16}.2& \text{Uitwerken } \\ & =ax+2a-\frac{11}{16}x-\frac{22}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+2a-\frac{11}{16}x-\frac{11}{8} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-15}{20}+q)(b-\frac{16}{9})& =(\color{red}{q}+\color{orange}{\frac{-3}{4}}).(\color{green}{b}+\color{blue}{\frac{-16}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{9})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-16}{9})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{16}{9}q-\frac{3}{4}b+\frac{3}{4}.\frac{16}{9}& \text{Uitwerken } \\ & =bq-\frac{16}{9}q-\frac{3}{4}b+\frac{48}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{16}{9}q-\frac{3}{4}b+\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(b+\frac{7}{12})(\frac{7}{9}+p)& =(\color{red}{b}+\color{orange}{\frac{7}{12}}).(\color{green}{p}+\color{blue}{\frac{7}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{7}{9})} + \color{orange}{(\frac{7}{12})} . \color{green}{(p)} + \color{orange}{(\frac{7}{12})} . \color{blue}{(\frac{7}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{9}b+\frac{7}{12}p+\frac{7}{12}.\frac{7}{9}& \text{Uitwerken } \\ & =bp+\frac{7}{9}b+\frac{7}{12}p+\frac{49}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-1}{9}-b)(\frac{11}{20}-x)& =(\color{red}{-b}+\color{orange}{\frac{-1}{9}}).(\color{green}{-x}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{20}b+\frac{1}{9}x-\frac{1}{9}.\frac{11}{20}& \text{Uitwerken } \\ & =bx-\frac{11}{20}b+\frac{1}{9}x-\frac{11}{180} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)