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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{8}{11}+q)(\frac{-20}{19}-p)& =(\color{red}{q}+\color{orange}{\frac{8}{11}}).(\color{green}{-p}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{8}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{20}{19}q-\frac{8}{11}p-\frac{8}{11}.\frac{20}{19}& \text{Uitwerken } \\ & =-pq-\frac{20}{19}q-\frac{8}{11}p-\frac{160}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{19}{13}+x)(\frac{-4}{15}+x)& =(\color{red}{x}+\color{orange}{\frac{19}{13}}).(\color{green}{x}+\color{blue}{\frac{-4}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{15})} + \color{orange}{(\frac{19}{13})} . \color{green}{(x)} + \color{orange}{(\frac{19}{13})} . \color{blue}{(\frac{-4}{15})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{4}{15}x+\frac{19}{13}x-\frac{19}{13}.\frac{4}{15}& \text{Uitwerken } \\ & =x^2+((\frac{-4}{15})+\frac{19}{13})x-(\frac{-76}{195}) & \text{Neem samen} \\ &=x^2+\frac{233}{195}x-(\frac{-76}{195}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(p-\frac{-19}{4})(\frac{5}{18}-p)& =(\color{red}{p}+\color{orange}{\frac{19}{4}}).(\color{green}{-p}+\color{blue}{\frac{5}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{5}{18})} + \color{orange}{(\frac{19}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{19}{4})} . \color{blue}{(\frac{5}{18})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{5}{18}p-\frac{19}{4}p+\frac{19}{4}.\frac{5}{18}& \text{Uitwerken } \\ & =-p^2+(\frac{5}{18}+(\frac{-19}{4}))p+(\frac{-95}{72}) & \text{Neem samen} \\ &=-p^2-\frac{161}{36}p+(\frac{-95}{72}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{11}{4}+x)(b+\frac{15}{2})& =(\color{red}{x}+\color{orange}{\frac{11}{4}}).(\color{green}{b}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(\frac{11}{4})} . \color{green}{(b)} + \color{orange}{(\frac{11}{4})} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{15}{2}x+\frac{11}{4}b+\frac{11}{4}.\frac{15}{2}& \text{Uitwerken } \\ & =bx+\frac{15}{2}x+\frac{11}{4}b+\frac{165}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x+\frac{-7}{16})(\frac{18}{12}-q)& =(\color{red}{x}+\color{orange}{\frac{-7}{16}}).(\color{green}{-q}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(\frac{-7}{16})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{16})} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{3}{2}x+\frac{7}{16}q-\frac{7}{16}.\frac{3}{2}& \text{Uitwerken } \\ & =-qx+\frac{3}{2}x+\frac{7}{16}q-\frac{21}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{4}{5}+b)(\frac{-1}{4}+b)& =(\color{red}{b}+\color{orange}{\frac{4}{5}}).(\color{green}{b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{1}{4}b+\frac{4}{5}b-\frac{4}{5}.\frac{1}{4}& \text{Uitwerken } \\ & =b^2+((\frac{-1}{4})+\frac{4}{5})b-(\frac{-4}{20}) & \text{Neem samen} \\ &=b^2+\frac{11}{20}b-(\frac{-4}{20}) & \text{Maak de som} \\ &=b^2+\frac{11}{20}b+\frac{1}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
7. \(\begin{align}(\frac{-4}{20}+x)(a-\frac{13}{9})& =(\color{red}{x}+\color{orange}{\frac{-1}{5}}).(\color{green}{a}+\color{blue}{\frac{-13}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{9})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-13}{9})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{13}{9}x-\frac{1}{5}a+\frac{1}{5}.\frac{13}{9}& \text{Uitwerken } \\ & =ax-\frac{13}{9}x-\frac{1}{5}a+\frac{13}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b+\frac{6}{16})(a+\frac{-18}{10})& =(\color{red}{b}+\color{orange}{\frac{3}{8}}).(\color{green}{a}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{3}{8})} . \color{green}{(a)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{9}{5}b+\frac{3}{8}a-\frac{3}{8}.\frac{9}{5}& \text{Uitwerken } \\ & =ab-\frac{9}{5}b+\frac{3}{8}a-\frac{27}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-14}{2}-a)(a-\frac{6}{2})& =(\color{red}{-a}+\color{orange}{(-7)}).(\color{green}{a}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(-3)} + \color{orange}{(-7)} . \color{green}{(a)} + \color{orange}{(-7)} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -aa+3a-7a+7.3& \text{Uitwerken } \\ & =-a^2+(3+(-7))a+(-21) & \text{Neem samen} \\ &=-a^2-4a+(-21) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(p-\frac{6}{13})(\frac{12}{12}-q)& =(\color{red}{p}+\color{orange}{\frac{-6}{13}}).(\color{green}{-q}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{-6}{13})} . \color{green}{(-q)} + \color{orange}{(\frac{-6}{13})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -pq+1p+\frac{6}{13}q-\frac{6}{13}.1& \text{Uitwerken } \\ & =-pq+1p+\frac{6}{13}q-\frac{6}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-15}{2}-b)(x+\frac{2}{18})& =(\color{red}{-b}+\color{orange}{\frac{-15}{2}}).(\color{green}{x}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(\frac{-15}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{9}b-\frac{15}{2}x-\frac{15}{2}.\frac{1}{9}& \text{Uitwerken } \\ & =-bx-\frac{1}{9}b-\frac{15}{2}x-\frac{15}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{1}{9}b-\frac{15}{2}x-\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{6}{2}-x)(b+\frac{6}{5})& =(\color{red}{-x}+\color{orange}{3}).(\color{green}{b}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{6}{5}x+3b+3.\frac{6}{5}& \text{Uitwerken } \\ & =-bx-\frac{6}{5}x+3b+\frac{18}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)