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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{-9}{12})(x+(-20))& =(\color{red}{a}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{(-20)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-20)} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = ax-20a+\frac{3}{4}x-\frac{3}{4}.20& \text{Uitwerken } \\ & =ax-20a+\frac{3}{4}x-\frac{60}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-20a+\frac{3}{4}x-15 & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(b+\frac{7}{18})(b+\frac{1}{11})& =(\color{red}{b}+\color{orange}{\frac{7}{18}}).(\color{green}{b}+\color{blue}{\frac{1}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{11})} + \color{orange}{(\frac{7}{18})} . \color{green}{(b)} + \color{orange}{(\frac{7}{18})} . \color{blue}{(\frac{1}{11})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{11}b+\frac{7}{18}b+\frac{7}{18}.\frac{1}{11}& \text{Uitwerken } \\ & =b^2+(\frac{1}{11}+\frac{7}{18})b+\frac{7}{198} & \text{Neem samen} \\ &=b^2+\frac{95}{198}b+\frac{7}{198} & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(b+\frac{17}{5})(b-\frac{-16}{7})& =(\color{red}{b}+\color{orange}{\frac{17}{5}}).(\color{green}{b}+\color{blue}{\frac{16}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{16}{7})} + \color{orange}{(\frac{17}{5})} . \color{green}{(b)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{16}{7})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{16}{7}b+\frac{17}{5}b+\frac{17}{5}.\frac{16}{7}& \text{Uitwerken } \\ & =b^2+(\frac{16}{7}+\frac{17}{5})b+\frac{272}{35} & \text{Neem samen} \\ &=b^2+\frac{199}{35}b+\frac{272}{35} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(b+\frac{3}{8})(\frac{9}{18}+p)& =(\color{red}{b}+\color{orange}{\frac{3}{8}}).(\color{green}{p}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{3}{8})} . \color{green}{(p)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{2}b+\frac{3}{8}p+\frac{3}{8}.\frac{1}{2}& \text{Uitwerken } \\ & =bp+\frac{1}{2}b+\frac{3}{8}p+\frac{3}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(q-\frac{-20}{19})(\frac{2}{6}+b)& =(\color{red}{q}+\color{orange}{\frac{20}{19}}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{20}{19})} . \color{green}{(b)} + \color{orange}{(\frac{20}{19})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{1}{3}q+\frac{20}{19}b+\frac{20}{19}.\frac{1}{3}& \text{Uitwerken } \\ & =bq+\frac{1}{3}q+\frac{20}{19}b+\frac{20}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p-\frac{20}{13})(x-4)& =(\color{red}{p}+\color{orange}{\frac{-20}{13}}).(\color{green}{x}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-4)} + \color{orange}{(\frac{-20}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-20}{13})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = px-4p-\frac{20}{13}x+\frac{20}{13}.4& \text{Uitwerken } \\ & =px-4p-\frac{20}{13}x+\frac{80}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-11}{15}-b)(\frac{19}{12}+p)& =(\color{red}{-b}+\color{orange}{\frac{-11}{15}}).(\color{green}{p}+\color{blue}{\frac{19}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{12})} + \color{orange}{(\frac{-11}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{15})} . \color{blue}{(\frac{19}{12})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{19}{12}b-\frac{11}{15}p-\frac{11}{15}.\frac{19}{12}& \text{Uitwerken } \\ & =-bp-\frac{19}{12}b-\frac{11}{15}p-\frac{209}{180} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b-\frac{19}{17})(x-\frac{18}{2})& =(\color{red}{b}+\color{orange}{\frac{-19}{17}}).(\color{green}{x}+\color{blue}{(-9)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(-9)} + \color{orange}{(\frac{-19}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{17})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = bx-9b-\frac{19}{17}x+\frac{19}{17}.9& \text{Uitwerken } \\ & =bx-9b-\frac{19}{17}x+\frac{171}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-8}{12}+a)(p+\frac{-11}{8})& =(\color{red}{a}+\color{orange}{\frac{-2}{3}}).(\color{green}{p}+\color{blue}{\frac{-11}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{8})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-11}{8})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{11}{8}a-\frac{2}{3}p+\frac{2}{3}.\frac{11}{8}& \text{Uitwerken } \\ & =ap-\frac{11}{8}a-\frac{2}{3}p+\frac{22}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{11}{8}a-\frac{2}{3}p+\frac{11}{12} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(b+13)(p+\frac{1}{13})& =(\color{red}{b}+\color{orange}{13}).(\color{green}{p}+\color{blue}{\frac{1}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{13})} + \color{orange}{(13)} . \color{green}{(p)} + \color{orange}{(13)} . \color{blue}{(\frac{1}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{13}b+13p+13.\frac{1}{13}& \text{Uitwerken } \\ & =bp+\frac{1}{13}b+13p+\frac{13}{13} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{1}{13}b+13p+1 & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-16}{20}+b)(a+\frac{18}{16})& =(\color{red}{b}+\color{orange}{\frac{-4}{5}}).(\color{green}{a}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{9}{8}b-\frac{4}{5}a-\frac{4}{5}.\frac{9}{8}& \text{Uitwerken } \\ & =ab+\frac{9}{8}b-\frac{4}{5}a-\frac{36}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{9}{8}b-\frac{4}{5}a-\frac{9}{10} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{3}{17}+a)(x-\frac{10}{18})& =(\color{red}{a}+\color{orange}{\frac{3}{17}}).(\color{green}{x}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(\frac{3}{17})} . \color{green}{(x)} + \color{orange}{(\frac{3}{17})} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{9}a+\frac{3}{17}x-\frac{3}{17}.\frac{5}{9}& \text{Uitwerken } \\ & =ax-\frac{5}{9}a+\frac{3}{17}x-\frac{15}{153} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{5}{9}a+\frac{3}{17}x-\frac{5}{51} & \text{Vereenvoudig} \\\end{align}\)