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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-17}{15}-b)(q+\frac{-2}{13})& =(\color{red}{-b}+\color{orange}{\frac{-17}{15}}).(\color{green}{q}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(\frac{-17}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{15})} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{2}{13}b-\frac{17}{15}q+\frac{17}{15}.\frac{2}{13}& \text{Uitwerken } \\ & =-bq+\frac{2}{13}b-\frac{17}{15}q+\frac{34}{195} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{16}{12}-a)(x+\frac{1}{3})& =(\color{red}{-a}+\color{orange}{\frac{4}{3}}).(\color{green}{x}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{1}{3}a+\frac{4}{3}x+\frac{4}{3}.\frac{1}{3}& \text{Uitwerken } \\ & =-ax-\frac{1}{3}a+\frac{4}{3}x+\frac{4}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(a-\frac{6}{7})(\frac{18}{12}+p)& =(\color{red}{a}+\color{orange}{\frac{-6}{7}}).(\color{green}{p}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{3}{2}a-\frac{6}{7}p-\frac{6}{7}.\frac{3}{2}& \text{Uitwerken } \\ & =ap+\frac{3}{2}a-\frac{6}{7}p-\frac{18}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{3}{2}a-\frac{6}{7}p-\frac{9}{7} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{12}{19}+b)(b+\frac{7}{17})& =(\color{red}{b}+\color{orange}{\frac{12}{19}}).(\color{green}{b}+\color{blue}{\frac{7}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{7}{17})} + \color{orange}{(\frac{12}{19})} . \color{green}{(b)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(\frac{7}{17})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{7}{17}b+\frac{12}{19}b+\frac{12}{19}.\frac{7}{17}& \text{Uitwerken } \\ & =b^2+(\frac{7}{17}+\frac{12}{19})b+\frac{84}{323} & \text{Neem samen} \\ &=b^2+\frac{337}{323}b+\frac{84}{323} & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(x+\frac{5}{9})(\frac{-17}{8}+a)& =(\color{red}{x}+\color{orange}{\frac{5}{9}}).(\color{green}{a}+\color{blue}{\frac{-17}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{8})} + \color{orange}{(\frac{5}{9})} . \color{green}{(a)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{-17}{8})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{17}{8}x+\frac{5}{9}a-\frac{5}{9}.\frac{17}{8}& \text{Uitwerken } \\ & =ax-\frac{17}{8}x+\frac{5}{9}a-\frac{85}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-11}{13}-b)(\frac{11}{16}-x)& =(\color{red}{-b}+\color{orange}{\frac{-11}{13}}).(\color{green}{-x}+\color{blue}{\frac{11}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{16})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{11}{16})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{16}b+\frac{11}{13}x-\frac{11}{13}.\frac{11}{16}& \text{Uitwerken } \\ & =bx-\frac{11}{16}b+\frac{11}{13}x-\frac{121}{208} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-17}{17}+b)(b-\frac{17}{16})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-17}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{16})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-17}{16})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{17}{16}b-1b+1.\frac{17}{16}& \text{Uitwerken } \\ & =b^2+((\frac{-17}{16})+(-1))b+\frac{17}{16} & \text{Neem samen} \\ &=b^2-\frac{33}{16}b+\frac{17}{16} & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(a+\frac{-8}{9})(\frac{4}{10}-p)& =(\color{red}{a}+\color{orange}{\frac{-8}{9}}).(\color{green}{-p}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-8}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{2}{5}a+\frac{8}{9}p-\frac{8}{9}.\frac{2}{5}& \text{Uitwerken } \\ & =-ap+\frac{2}{5}a+\frac{8}{9}p-\frac{16}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-6}{3}+b)(a+\frac{-13}{10})& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{10}b-2a+2.\frac{13}{10}& \text{Uitwerken } \\ & =ab-\frac{13}{10}b-2a+\frac{26}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{13}{10}b-2a+\frac{13}{5} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(q-\frac{-3}{6})(x-\frac{17}{18})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{x}+\color{blue}{\frac{-17}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{18})} + \color{orange}{(\frac{1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-17}{18})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{17}{18}q+\frac{1}{2}x-\frac{1}{2}.\frac{17}{18}& \text{Uitwerken } \\ & =qx-\frac{17}{18}q+\frac{1}{2}x-\frac{17}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a+\frac{4}{16})(\frac{-17}{15}-b)& =(\color{red}{a}+\color{orange}{\frac{1}{4}}).(\color{green}{-b}+\color{blue}{\frac{-17}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-17}{15})} + \color{orange}{(\frac{1}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{-17}{15})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{17}{15}a-\frac{1}{4}b-\frac{1}{4}.\frac{17}{15}& \text{Uitwerken } \\ & =-ab-\frac{17}{15}a-\frac{1}{4}b-\frac{17}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-5}{5}+x)(a+\frac{12}{14})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{6}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{6}{7})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{6}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{6}{7}x-1a-1.\frac{6}{7}& \text{Uitwerken } \\ & =ax+\frac{6}{7}x-1a-\frac{6}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)