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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{6}{19}+p)(a-\frac{8}{16})& =(\color{red}{p}+\color{orange}{\frac{6}{19}}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{6}{19})} . \color{green}{(a)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{2}p+\frac{6}{19}a-\frac{6}{19}.\frac{1}{2}& \text{Uitwerken } \\ & =ap-\frac{1}{2}p+\frac{6}{19}a-\frac{6}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{1}{2}p+\frac{6}{19}a-\frac{3}{19} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(a-\frac{-3}{20})(p+\frac{10}{5})& =(\color{red}{a}+\color{orange}{\frac{3}{20}}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{3}{20})} . \color{green}{(p)} + \color{orange}{(\frac{3}{20})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ap+2a+\frac{3}{20}p+\frac{3}{20}.2& \text{Uitwerken } \\ & =ap+2a+\frac{3}{20}p+\frac{6}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+2a+\frac{3}{20}p+\frac{3}{10} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{16}{2}-p)(b-\frac{10}{5})& =(\color{red}{-p}+\color{orange}{8}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(-2)} + \color{orange}{(8)} . \color{green}{(b)} + \color{orange}{(8)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -bp+2p+8b-8.2& \text{Uitwerken } \\ & =-bp+2p+8b-16 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q-\frac{-19}{7})(\frac{-13}{3}+x)& =(\color{red}{q}+\color{orange}{\frac{19}{7}}).(\color{green}{x}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(\frac{19}{7})} . \color{green}{(x)} + \color{orange}{(\frac{19}{7})} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{13}{3}q+\frac{19}{7}x-\frac{19}{7}.\frac{13}{3}& \text{Uitwerken } \\ & =qx-\frac{13}{3}q+\frac{19}{7}x-\frac{247}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b-\frac{17}{19})(p+\frac{10}{18})& =(\color{red}{b}+\color{orange}{\frac{-17}{19}}).(\color{green}{p}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{-17}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{9}b-\frac{17}{19}p-\frac{17}{19}.\frac{5}{9}& \text{Uitwerken } \\ & =bp+\frac{5}{9}b-\frac{17}{19}p-\frac{85}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-7}{18}-a)(\frac{12}{15}-q)& =(\color{red}{-a}+\color{orange}{\frac{-7}{18}}).(\color{green}{-q}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{-7}{18})} . \color{green}{(-q)} + \color{orange}{(\frac{-7}{18})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{4}{5}a+\frac{7}{18}q-\frac{7}{18}.\frac{4}{5}& \text{Uitwerken } \\ & =aq-\frac{4}{5}a+\frac{7}{18}q-\frac{28}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{4}{5}a+\frac{7}{18}q-\frac{14}{45} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(15-x)(b+\frac{13}{19})& =(\color{red}{-x}+\color{orange}{15}).(\color{green}{b}+\color{blue}{\frac{13}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{13}{19})} + \color{orange}{(15)} . \color{green}{(b)} + \color{orange}{(15)} . \color{blue}{(\frac{13}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{13}{19}x+15b+15.\frac{13}{19}& \text{Uitwerken } \\ & =-bx-\frac{13}{19}x+15b+\frac{195}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a-\frac{16}{9})(\frac{-3}{10}+a)& =(\color{red}{a}+\color{orange}{\frac{-16}{9}}).(\color{green}{a}+\color{blue}{\frac{-3}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{10})} + \color{orange}{(\frac{-16}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-16}{9})} . \color{blue}{(\frac{-3}{10})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{3}{10}a-\frac{16}{9}a+\frac{16}{9}.\frac{3}{10}& \text{Uitwerken } \\ & =a^2+((\frac{-3}{10})+(\frac{-16}{9}))a+\frac{48}{90} & \text{Neem samen} \\ &=a^2-\frac{187}{90}a+\frac{48}{90} & \text{Maak de som} \\ &=a^2-\frac{187}{90}a+\frac{8}{15} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
9. \(\begin{align}(b-\frac{4}{12})(p+\frac{12}{7})& =(\color{red}{b}+\color{orange}{\frac{-1}{3}}).(\color{green}{p}+\color{blue}{\frac{12}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{12}{7})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{12}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{12}{7}b-\frac{1}{3}p-\frac{1}{3}.\frac{12}{7}& \text{Uitwerken } \\ & =bp+\frac{12}{7}b-\frac{1}{3}p-\frac{12}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{12}{7}b-\frac{1}{3}p-\frac{4}{7} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-4}{7}+x)(q-\frac{-1}{13})& =(\color{red}{x}+\color{orange}{\frac{-4}{7}}).(\color{green}{q}+\color{blue}{\frac{1}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{13})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{1}{13})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{13}x-\frac{4}{7}q-\frac{4}{7}.\frac{1}{13}& \text{Uitwerken } \\ & =qx+\frac{1}{13}x-\frac{4}{7}q-\frac{4}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(q-\frac{-3}{16})(x-\frac{-6}{16})& =(\color{red}{q}+\color{orange}{\frac{3}{16}}).(\color{green}{x}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{3}{16})} . \color{green}{(x)} + \color{orange}{(\frac{3}{16})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{3}{8}q+\frac{3}{16}x+\frac{3}{16}.\frac{3}{8}& \text{Uitwerken } \\ & =qx+\frac{3}{8}q+\frac{3}{16}x+\frac{9}{128} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-19}{11}-x)(b-\frac{5}{17})& =(\color{red}{-x}+\color{orange}{\frac{-19}{11}}).(\color{green}{b}+\color{blue}{\frac{-5}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-5}{17})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{-5}{17})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{5}{17}x-\frac{19}{11}b+\frac{19}{11}.\frac{5}{17}& \text{Uitwerken } \\ & =-bx+\frac{5}{17}x-\frac{19}{11}b+\frac{95}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)