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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-17}{15}+b)(\frac{-7}{10}+x)& =(\color{red}{b}+\color{orange}{\frac{-17}{15}}).(\color{green}{x}+\color{blue}{\frac{-7}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{10})} + \color{orange}{(\frac{-17}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{15})} . \color{blue}{(\frac{-7}{10})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{7}{10}b-\frac{17}{15}x+\frac{17}{15}.\frac{7}{10}& \text{Uitwerken } \\ & =bx-\frac{7}{10}b-\frac{17}{15}x+\frac{119}{150} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x+\frac{4}{16})(x+\frac{15}{16})& =(\color{red}{x}+\color{orange}{\frac{1}{4}}).(\color{green}{x}+\color{blue}{\frac{15}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{15}{16})} + \color{orange}{(\frac{1}{4})} . \color{green}{(x)} + \color{orange}{(\frac{1}{4})} . \color{blue}{(\frac{15}{16})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{15}{16}x+\frac{1}{4}x+\frac{1}{4}.\frac{15}{16}& \text{Uitwerken } \\ & =x^2+(\frac{15}{16}+\frac{1}{4})x+\frac{15}{64} & \text{Neem samen} \\ &=x^2+\frac{19}{16}x+\frac{15}{64} & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(\frac{-12}{16}+b)(a+\frac{-12}{18})& =(\color{red}{b}+\color{orange}{\frac{-3}{4}}).(\color{green}{a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{3}b-\frac{3}{4}a+\frac{3}{4}.\frac{2}{3}& \text{Uitwerken } \\ & =ab-\frac{2}{3}b-\frac{3}{4}a+\frac{6}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{2}{3}b-\frac{3}{4}a+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(a+\frac{-20}{13})(x+\frac{-14}{10})& =(\color{red}{a}+\color{orange}{\frac{-20}{13}}).(\color{green}{x}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{-20}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{13})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{5}a-\frac{20}{13}x+\frac{20}{13}.\frac{7}{5}& \text{Uitwerken } \\ & =ax-\frac{7}{5}a-\frac{20}{13}x+\frac{140}{65} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{7}{5}a-\frac{20}{13}x+\frac{28}{13} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-12}{3}-q)(\frac{-9}{17}+x)& =(\color{red}{-q}+\color{orange}{(-4)}).(\color{green}{x}+\color{blue}{\frac{-9}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(\frac{-9}{17})} + \color{orange}{(-4)} . \color{green}{(x)} + \color{orange}{(-4)} . \color{blue}{(\frac{-9}{17})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{9}{17}q-4x+4.\frac{9}{17}& \text{Uitwerken } \\ & =-qx+\frac{9}{17}q-4x+\frac{36}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b+\frac{-6}{12})(\frac{-11}{18}+q)& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{q}+\color{blue}{\frac{-11}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{18})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-11}{18})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{11}{18}b-\frac{1}{2}q+\frac{1}{2}.\frac{11}{18}& \text{Uitwerken } \\ & =bq-\frac{11}{18}b-\frac{1}{2}q+\frac{11}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{11}{6}-p)(a+\frac{-14}{14})& =(\color{red}{-p}+\color{orange}{\frac{11}{6}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(-1)} + \color{orange}{(\frac{11}{6})} . \color{green}{(a)} + \color{orange}{(\frac{11}{6})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ap+1p+\frac{11}{6}a-\frac{11}{6}.1& \text{Uitwerken } \\ & =-ap+1p+\frac{11}{6}a-\frac{11}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{11}{5}+q)(a-(-10))& =(\color{red}{q}+\color{orange}{\frac{11}{5}}).(\color{green}{a}+\color{blue}{10})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(10)} + \color{orange}{(\frac{11}{5})} . \color{green}{(a)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = aq+10q+\frac{11}{5}a+\frac{11}{5}.10& \text{Uitwerken } \\ & =aq+10q+\frac{11}{5}a+\frac{110}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+10q+\frac{11}{5}a+22 & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{4}{3}+q)(x-\frac{-16}{15})& =(\color{red}{q}+\color{orange}{\frac{4}{3}}).(\color{green}{x}+\color{blue}{\frac{16}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{16}{15})} + \color{orange}{(\frac{4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{16}{15})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{16}{15}q+\frac{4}{3}x+\frac{4}{3}.\frac{16}{15}& \text{Uitwerken } \\ & =qx+\frac{16}{15}q+\frac{4}{3}x+\frac{64}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a+\frac{-2}{6})(\frac{-14}{16}+b)& =(\color{red}{a}+\color{orange}{\frac{-1}{3}}).(\color{green}{b}+\color{blue}{\frac{-7}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{8})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-7}{8})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{8}a-\frac{1}{3}b+\frac{1}{3}.\frac{7}{8}& \text{Uitwerken } \\ & =ab-\frac{7}{8}a-\frac{1}{3}b+\frac{7}{24} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-\frac{-19}{20})(\frac{-8}{16}+b)& =(\color{red}{a}+\color{orange}{\frac{19}{20}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{19}{20})} . \color{green}{(b)} + \color{orange}{(\frac{19}{20})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{2}a+\frac{19}{20}b-\frac{19}{20}.\frac{1}{2}& \text{Uitwerken } \\ & =ab-\frac{1}{2}a+\frac{19}{20}b-\frac{19}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-7}{11}-x)(b-\frac{-10}{13})& =(\color{red}{-x}+\color{orange}{\frac{-7}{11}}).(\color{green}{b}+\color{blue}{\frac{10}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{10}{13})} + \color{orange}{(\frac{-7}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(\frac{10}{13})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{10}{13}x-\frac{7}{11}b-\frac{7}{11}.\frac{10}{13}& \text{Uitwerken } \\ & =-bx-\frac{10}{13}x-\frac{7}{11}b-\frac{70}{143} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)