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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b-\frac{19}{6})(p+\frac{2}{20})& =(\color{red}{b}+\color{orange}{\frac{-19}{6}}).(\color{green}{p}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{-19}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{6})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{10}b-\frac{19}{6}p-\frac{19}{6}.\frac{1}{10}& \text{Uitwerken } \\ & =bp+\frac{1}{10}b-\frac{19}{6}p-\frac{19}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{9}{9}+a)(\frac{9}{9}-q)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{-q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(1)} . \color{green}{(-q)} + \color{orange}{(1)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -aq+1a-1q+1.1& \text{Uitwerken } \\ & =-aq+1a-1q+1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b-\frac{4}{6})(b+\frac{12}{2})& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{b}+\color{blue}{6})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(6)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = bb+6b-\frac{2}{3}b-\frac{2}{3}.6& \text{Uitwerken } \\ & =b^2+(6+(\frac{-2}{3}))b-(\frac{-12}{3}) & \text{Neem samen} \\ &=b^2+\frac{16}{3}b-(\frac{-12}{3}) & \text{Maak de som} \\ &=b^2+\frac{16}{3}b+4 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
4. \(\begin{align}(a+\frac{16}{6})(b+\frac{6}{20})& =(\color{red}{a}+\color{orange}{\frac{8}{3}}).(\color{green}{b}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{8}{3})} . \color{green}{(b)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{10}a+\frac{8}{3}b+\frac{8}{3}.\frac{3}{10}& \text{Uitwerken } \\ & =ab+\frac{3}{10}a+\frac{8}{3}b+\frac{24}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{3}{10}a+\frac{8}{3}b+\frac{4}{5} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(b-17)(\frac{18}{7}+q)& =(\color{red}{b}+\color{orange}{(-17)}).(\color{green}{q}+\color{blue}{\frac{18}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{18}{7})} + \color{orange}{(-17)} . \color{green}{(q)} + \color{orange}{(-17)} . \color{blue}{(\frac{18}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{18}{7}b-17q-17.\frac{18}{7}& \text{Uitwerken } \\ & =bq+\frac{18}{7}b-17q-\frac{306}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{18}{18}+b)(\frac{-1}{9}-b)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{-b}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(1)} . \color{green}{(-b)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{1}{9}b-1b-1.\frac{1}{9}& \text{Uitwerken } \\ & =-b^2+((\frac{-1}{9})+(-1))b-\frac{1}{9} & \text{Neem samen} \\ &=-b^2-\frac{10}{9}b-\frac{1}{9} & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(q-\frac{1}{11})(q+\frac{11}{2})& =(\color{red}{q}+\color{orange}{\frac{-1}{11}}).(\color{green}{q}+\color{blue}{\frac{11}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{11}{2})} + \color{orange}{(\frac{-1}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{11})} . \color{blue}{(\frac{11}{2})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{11}{2}q-\frac{1}{11}q-\frac{1}{11}.\frac{11}{2}& \text{Uitwerken } \\ & =q^2+(\frac{11}{2}+(\frac{-1}{11}))q-(\frac{-11}{22}) & \text{Neem samen} \\ &=q^2+\frac{119}{22}q-(\frac{-11}{22}) & \text{Maak de som} \\ &=q^2+\frac{119}{22}q+\frac{1}{2} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
8. \(\begin{align}(\frac{-1}{7}+p)(\frac{17}{7}-b)& =(\color{red}{p}+\color{orange}{\frac{-1}{7}}).(\color{green}{-b}+\color{blue}{\frac{17}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{17}{7})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{17}{7})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{17}{7}p+\frac{1}{7}b-\frac{1}{7}.\frac{17}{7}& \text{Uitwerken } \\ & =-bp+\frac{17}{7}p+\frac{1}{7}b-\frac{17}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+\frac{-11}{19})(\frac{16}{3}+x)& =(\color{red}{x}+\color{orange}{\frac{-11}{19}}).(\color{green}{x}+\color{blue}{\frac{16}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{16}{3})} + \color{orange}{(\frac{-11}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{19})} . \color{blue}{(\frac{16}{3})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{16}{3}x-\frac{11}{19}x-\frac{11}{19}.\frac{16}{3}& \text{Uitwerken } \\ & =x^2+(\frac{16}{3}+(\frac{-11}{19}))x-(\frac{-176}{57}) & \text{Neem samen} \\ &=x^2+\frac{271}{57}x-(\frac{-176}{57}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(a+\frac{9}{8})(a+\frac{9}{18})& =(\color{red}{a}+\color{orange}{\frac{9}{8}}).(\color{green}{a}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{9}{8})} . \color{green}{(a)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{2}a+\frac{9}{8}a+\frac{9}{8}.\frac{1}{2}& \text{Uitwerken } \\ & =a^2+(\frac{1}{2}+\frac{9}{8})a+\frac{9}{16} & \text{Neem samen} \\ &=a^2+\frac{13}{8}a+\frac{9}{16} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(p+\frac{-7}{14})(x+\frac{3}{13})& =(\color{red}{p}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{\frac{3}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{3}{13})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{3}{13})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{13}p-\frac{1}{2}x-\frac{1}{2}.\frac{3}{13}& \text{Uitwerken } \\ & =px+\frac{3}{13}p-\frac{1}{2}x-\frac{3}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(a-\frac{-7}{17})(a+\frac{-19}{13})& =(\color{red}{a}+\color{orange}{\frac{7}{17}}).(\color{green}{a}+\color{blue}{\frac{-19}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{13})} + \color{orange}{(\frac{7}{17})} . \color{green}{(a)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(\frac{-19}{13})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{19}{13}a+\frac{7}{17}a-\frac{7}{17}.\frac{19}{13}& \text{Uitwerken } \\ & =a^2+((\frac{-19}{13})+\frac{7}{17})a-(\frac{-133}{221}) & \text{Neem samen} \\ &=a^2-\frac{232}{221}a-(\frac{-133}{221}) & \text{Maak de som} \\\end{align}\)