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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{1}{8})(\frac{-10}{15}-p)& =(\color{red}{b}+\color{orange}{\frac{1}{8}}).(\color{green}{-p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{1}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{2}{3}b-\frac{1}{8}p-\frac{1}{8}.\frac{2}{3}& \text{Uitwerken } \\ & =-bp-\frac{2}{3}b-\frac{1}{8}p-\frac{2}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{2}{3}b-\frac{1}{8}p-\frac{1}{12} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(b-\frac{7}{18})(\frac{1}{15}+x)& =(\color{red}{b}+\color{orange}{\frac{-7}{18}}).(\color{green}{x}+\color{blue}{\frac{1}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{15})} + \color{orange}{(\frac{-7}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{18})} . \color{blue}{(\frac{1}{15})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{15}b-\frac{7}{18}x-\frac{7}{18}.\frac{1}{15}& \text{Uitwerken } \\ & =bx+\frac{1}{15}b-\frac{7}{18}x-\frac{7}{270} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p+\frac{-5}{7})(a+\frac{-16}{19})& =(\color{red}{p}+\color{orange}{\frac{-5}{7}}).(\color{green}{a}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{16}{19}p-\frac{5}{7}a+\frac{5}{7}.\frac{16}{19}& \text{Uitwerken } \\ & =ap-\frac{16}{19}p-\frac{5}{7}a+\frac{80}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a-\frac{19}{17})(b-\frac{-6}{14})& =(\color{red}{a}+\color{orange}{\frac{-19}{17}}).(\color{green}{b}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{-19}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{17})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{7}a-\frac{19}{17}b-\frac{19}{17}.\frac{3}{7}& \text{Uitwerken } \\ & =ab+\frac{3}{7}a-\frac{19}{17}b-\frac{57}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x-\frac{11}{8})(q+\frac{4}{20})& =(\color{red}{x}+\color{orange}{\frac{-11}{8}}).(\color{green}{q}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-11}{8})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{8})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{5}x-\frac{11}{8}q-\frac{11}{8}.\frac{1}{5}& \text{Uitwerken } \\ & =qx+\frac{1}{5}x-\frac{11}{8}q-\frac{11}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{6}{9}+b)(\frac{-17}{17}+q)& =(\color{red}{b}+\color{orange}{\frac{2}{3}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-1)} + \color{orange}{(\frac{2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bq-1b+\frac{2}{3}q-\frac{2}{3}.1& \text{Uitwerken } \\ & =bq-1b+\frac{2}{3}q-\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p+\frac{14}{10})(\frac{7}{12}-x)& =(\color{red}{p}+\color{orange}{\frac{7}{5}}).(\color{green}{-x}+\color{blue}{\frac{7}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{7}{12})} + \color{orange}{(\frac{7}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{5})} . \color{blue}{(\frac{7}{12})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{7}{12}p-\frac{7}{5}x+\frac{7}{5}.\frac{7}{12}& \text{Uitwerken } \\ & =-px+\frac{7}{12}p-\frac{7}{5}x+\frac{49}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{3}{10}-b)(b-\frac{-10}{3})& =(\color{red}{-b}+\color{orange}{\frac{3}{10}}).(\color{green}{b}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{3}{10})} . \color{green}{(b)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{10}{3}b+\frac{3}{10}b+\frac{3}{10}.\frac{10}{3}& \text{Uitwerken } \\ & =-b^2+((\frac{-10}{3})+\frac{3}{10})b+(\frac{-30}{30}) & \text{Neem samen} \\ &=-b^2-\frac{91}{30}b+(\frac{-30}{30}) & \text{Maak de som} \\ &=-b^2-\frac{91}{30}b+(-1) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
9. \(\begin{align}(\frac{16}{3}-a)(\frac{16}{10}+p)& =(\color{red}{-a}+\color{orange}{\frac{16}{3}}).(\color{green}{p}+\color{blue}{\frac{8}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{8}{5})} + \color{orange}{(\frac{16}{3})} . \color{green}{(p)} + \color{orange}{(\frac{16}{3})} . \color{blue}{(\frac{8}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{8}{5}a+\frac{16}{3}p+\frac{16}{3}.\frac{8}{5}& \text{Uitwerken } \\ & =-ap-\frac{8}{5}a+\frac{16}{3}p+\frac{128}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x+\frac{11}{17})(\frac{20}{16}-a)& =(\color{red}{x}+\color{orange}{\frac{11}{17}}).(\color{green}{-a}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{11}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{11}{17})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{5}{4}x-\frac{11}{17}a+\frac{11}{17}.\frac{5}{4}& \text{Uitwerken } \\ & =-ax+\frac{5}{4}x-\frac{11}{17}a+\frac{55}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-\frac{-1}{9})(a-\frac{-10}{5})& =(\color{red}{a}+\color{orange}{\frac{1}{9}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{1}{9})} . \color{green}{(a)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = aa+2a+\frac{1}{9}a+\frac{1}{9}.2& \text{Uitwerken } \\ & =a^2+(2+\frac{1}{9})a+\frac{2}{9} & \text{Neem samen} \\ &=a^2+\frac{19}{9}a+\frac{2}{9} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{-20}{11}+b)(b-\frac{-16}{4})& =(\color{red}{b}+\color{orange}{\frac{-20}{11}}).(\color{green}{b}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(4)} + \color{orange}{(\frac{-20}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-20}{11})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = bb+4b-\frac{20}{11}b-\frac{20}{11}.4& \text{Uitwerken } \\ & =b^2+(4+(\frac{-20}{11}))b-(\frac{-80}{11}) & \text{Neem samen} \\ &=b^2+\frac{24}{11}b-(\frac{-80}{11}) & \text{Maak de som} \\\end{align}\)