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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x+\frac{-4}{20})(b+\frac{-6}{19})& =(\color{red}{x}+\color{orange}{\frac{-1}{5}}).(\color{green}{b}+\color{blue}{\frac{-6}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{19})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-6}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{6}{19}x-\frac{1}{5}b+\frac{1}{5}.\frac{6}{19}& \text{Uitwerken } \\ & =bx-\frac{6}{19}x-\frac{1}{5}b+\frac{6}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a+\frac{1}{8})(b+\frac{12}{9})& =(\color{red}{a}+\color{orange}{\frac{1}{8}}).(\color{green}{b}+\color{blue}{\frac{4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{4}{3})} + \color{orange}{(\frac{1}{8})} . \color{green}{(b)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{4}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{4}{3}a+\frac{1}{8}b+\frac{1}{8}.\frac{4}{3}& \text{Uitwerken } \\ & =ab+\frac{4}{3}a+\frac{1}{8}b+\frac{4}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{4}{3}a+\frac{1}{8}b+\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(a+\frac{-15}{3})(\frac{-14}{14}-x)& =(\color{red}{a}+\color{orange}{(-5)}).(\color{green}{-x}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(-5)} . \color{green}{(-x)} + \color{orange}{(-5)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ax-1a+5x+5.1& \text{Uitwerken } \\ & =-ax-1a+5x+5 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a+\frac{12}{20})(\frac{9}{13}+x)& =(\color{red}{a}+\color{orange}{\frac{3}{5}}).(\color{green}{x}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{3}{5})} . \color{green}{(x)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{13}a+\frac{3}{5}x+\frac{3}{5}.\frac{9}{13}& \text{Uitwerken } \\ & =ax+\frac{9}{13}a+\frac{3}{5}x+\frac{27}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x-\frac{-8}{15})(b+\frac{11}{11})& =(\color{red}{x}+\color{orange}{\frac{8}{15}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{8}{15})} . \color{green}{(b)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx+1x+\frac{8}{15}b+\frac{8}{15}.1& \text{Uitwerken } \\ & =bx+1x+\frac{8}{15}b+\frac{8}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-11}{13}-a)(q-\frac{-1}{20})& =(\color{red}{-a}+\color{orange}{\frac{-11}{13}}).(\color{green}{q}+\color{blue}{\frac{1}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{1}{20})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{1}{20})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{20}a-\frac{11}{13}q-\frac{11}{13}.\frac{1}{20}& \text{Uitwerken } \\ & =-aq-\frac{1}{20}a-\frac{11}{13}q-\frac{11}{260} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x-\frac{6}{19})(\frac{-19}{10}+b)& =(\color{red}{x}+\color{orange}{\frac{-6}{19}}).(\color{green}{b}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{-6}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-6}{19})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{10}x-\frac{6}{19}b+\frac{6}{19}.\frac{19}{10}& \text{Uitwerken } \\ & =bx-\frac{19}{10}x-\frac{6}{19}b+\frac{114}{190} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{19}{10}x-\frac{6}{19}b+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-5}{2}-b)(p-\frac{-10}{15})& =(\color{red}{-b}+\color{orange}{\frac{-5}{2}}).(\color{green}{p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{2}{3}b-\frac{5}{2}p-\frac{5}{2}.\frac{2}{3}& \text{Uitwerken } \\ & =-bp-\frac{2}{3}b-\frac{5}{2}p-\frac{10}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{2}{3}b-\frac{5}{2}p-\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{12}{20}+q)(\frac{14}{10}+b)& =(\color{red}{q}+\color{orange}{\frac{3}{5}}).(\color{green}{b}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(\frac{3}{5})} . \color{green}{(b)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{7}{5}q+\frac{3}{5}b+\frac{3}{5}.\frac{7}{5}& \text{Uitwerken } \\ & =bq+\frac{7}{5}q+\frac{3}{5}b+\frac{21}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{17}{20}+q)(b+\frac{10}{16})& =(\color{red}{q}+\color{orange}{\frac{17}{20}}).(\color{green}{b}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{17}{20})} . \color{green}{(b)} + \color{orange}{(\frac{17}{20})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{8}q+\frac{17}{20}b+\frac{17}{20}.\frac{5}{8}& \text{Uitwerken } \\ & =bq+\frac{5}{8}q+\frac{17}{20}b+\frac{85}{160} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{5}{8}q+\frac{17}{20}b+\frac{17}{32} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-1}{8}+a)(\frac{8}{5}-x)& =(\color{red}{a}+\color{orange}{\frac{-1}{8}}).(\color{green}{-x}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{8}{5}a+\frac{1}{8}x-\frac{1}{8}.\frac{8}{5}& \text{Uitwerken } \\ & =-ax+\frac{8}{5}a+\frac{1}{8}x-\frac{8}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+\frac{8}{5}a+\frac{1}{8}x-\frac{1}{5} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(x-\frac{-10}{2})(x+\frac{-16}{17})& =(\color{red}{x}+\color{orange}{5}).(\color{green}{x}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(5)} . \color{green}{(x)} + \color{orange}{(5)} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{16}{17}x+5x-5.\frac{16}{17}& \text{Uitwerken } \\ & =x^2+((\frac{-16}{17})+5)x-(\frac{-80}{17}) & \text{Neem samen} \\ &=x^2+\frac{69}{17}x-(\frac{-80}{17}) & \text{Maak de som} \\\end{align}\)