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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{7}{14}+x)(q-\frac{1}{7})& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{7}x+\frac{1}{2}q-\frac{1}{2}.\frac{1}{7}& \text{Uitwerken } \\ & =qx-\frac{1}{7}x+\frac{1}{2}q-\frac{1}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b+\frac{-13}{16})(p+\frac{19}{16})& =(\color{red}{b}+\color{orange}{\frac{-13}{16}}).(\color{green}{p}+\color{blue}{\frac{19}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{19}{16})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{19}{16})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{16}b-\frac{13}{16}p-\frac{13}{16}.\frac{19}{16}& \text{Uitwerken } \\ & =bp+\frac{19}{16}b-\frac{13}{16}p-\frac{247}{256} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-5}{11}-b)(p+\frac{-13}{17})& =(\color{red}{-b}+\color{orange}{\frac{-5}{11}}).(\color{green}{p}+\color{blue}{\frac{-13}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-13}{17})} + \color{orange}{(\frac{-5}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(\frac{-13}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{13}{17}b-\frac{5}{11}p+\frac{5}{11}.\frac{13}{17}& \text{Uitwerken } \\ & =-bp+\frac{13}{17}b-\frac{5}{11}p+\frac{65}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x+\frac{15}{8})(a+\frac{-19}{8})& =(\color{red}{x}+\color{orange}{\frac{15}{8}}).(\color{green}{a}+\color{blue}{\frac{-19}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{8})} + \color{orange}{(\frac{15}{8})} . \color{green}{(a)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(\frac{-19}{8})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{19}{8}x+\frac{15}{8}a-\frac{15}{8}.\frac{19}{8}& \text{Uitwerken } \\ & =ax-\frac{19}{8}x+\frac{15}{8}a-\frac{285}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(a-\frac{20}{6})(\frac{1}{16}-b)& =(\color{red}{a}+\color{orange}{\frac{-10}{3}}).(\color{green}{-b}+\color{blue}{\frac{1}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{16})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{1}{16})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{1}{16}a+\frac{10}{3}b-\frac{10}{3}.\frac{1}{16}& \text{Uitwerken } \\ & =-ab+\frac{1}{16}a+\frac{10}{3}b-\frac{10}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{1}{16}a+\frac{10}{3}b-\frac{5}{24} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{8}{15}-p)(\frac{-2}{20}+a)& =(\color{red}{-p}+\color{orange}{\frac{8}{15}}).(\color{green}{a}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{8}{15})} . \color{green}{(a)} + \color{orange}{(\frac{8}{15})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{10}p+\frac{8}{15}a-\frac{8}{15}.\frac{1}{10}& \text{Uitwerken } \\ & =-ap+\frac{1}{10}p+\frac{8}{15}a-\frac{8}{150} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap+\frac{1}{10}p+\frac{8}{15}a-\frac{4}{75} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-1}{15}-q)(p+\frac{-5}{16})& =(\color{red}{-q}+\color{orange}{\frac{-1}{15}}).(\color{green}{p}+\color{blue}{\frac{-5}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{16})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{-5}{16})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{5}{16}q-\frac{1}{15}p+\frac{1}{15}.\frac{5}{16}& \text{Uitwerken } \\ & =-pq+\frac{5}{16}q-\frac{1}{15}p+\frac{5}{240} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{5}{16}q-\frac{1}{15}p+\frac{1}{48} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(b-\frac{2}{11})(b-\frac{8}{15})& =(\color{red}{b}+\color{orange}{\frac{-2}{11}}).(\color{green}{b}+\color{blue}{\frac{-8}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{15})} + \color{orange}{(\frac{-2}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(\frac{-8}{15})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{8}{15}b-\frac{2}{11}b+\frac{2}{11}.\frac{8}{15}& \text{Uitwerken } \\ & =b^2+((\frac{-8}{15})+(\frac{-2}{11}))b+\frac{16}{165} & \text{Neem samen} \\ &=b^2-\frac{118}{165}b+\frac{16}{165} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(\frac{17}{19}-x)(\frac{14}{6}-a)& =(\color{red}{-x}+\color{orange}{\frac{17}{19}}).(\color{green}{-a}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{17}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{17}{19})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{7}{3}x-\frac{17}{19}a+\frac{17}{19}.\frac{7}{3}& \text{Uitwerken } \\ & =ax-\frac{7}{3}x-\frac{17}{19}a+\frac{119}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{9}{3}+q)(\frac{-2}{7}+b)& =(\color{red}{q}+\color{orange}{3}).(\color{green}{b}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{2}{7}q+3b-3.\frac{2}{7}& \text{Uitwerken } \\ & =bq-\frac{2}{7}q+3b-\frac{6}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(q-\frac{15}{11})(q-\frac{-8}{11})& =(\color{red}{q}+\color{orange}{\frac{-15}{11}}).(\color{green}{q}+\color{blue}{\frac{8}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{8}{11})} + \color{orange}{(\frac{-15}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(\frac{8}{11})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{8}{11}q-\frac{15}{11}q-\frac{15}{11}.\frac{8}{11}& \text{Uitwerken } \\ & =q^2+(\frac{8}{11}+(\frac{-15}{11}))q-(\frac{-120}{121}) & \text{Neem samen} \\ &=q^2-\frac{7}{11}q-(\frac{-120}{121}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{17}{7}+a)(b-\frac{19}{19})& =(\color{red}{a}+\color{orange}{\frac{17}{7}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{17}{7})} . \color{green}{(b)} + \color{orange}{(\frac{17}{7})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab-1a+\frac{17}{7}b-\frac{17}{7}.1& \text{Uitwerken } \\ & =ab-1a+\frac{17}{7}b-\frac{17}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)