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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{-16}{13})(\frac{4}{19}+b)& =(\color{red}{a}+\color{orange}{\frac{-16}{13}}).(\color{green}{b}+\color{blue}{\frac{4}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{4}{19})} + \color{orange}{(\frac{-16}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{13})} . \color{blue}{(\frac{4}{19})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{4}{19}a-\frac{16}{13}b-\frac{16}{13}.\frac{4}{19}& \text{Uitwerken } \\ & =ab+\frac{4}{19}a-\frac{16}{13}b-\frac{64}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-10}{8}-q)(b+\frac{8}{11})& =(\color{red}{-q}+\color{orange}{\frac{-5}{4}}).(\color{green}{b}+\color{blue}{\frac{8}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{8}{11})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{8}{11})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{8}{11}q-\frac{5}{4}b-\frac{5}{4}.\frac{8}{11}& \text{Uitwerken } \\ & =-bq-\frac{8}{11}q-\frac{5}{4}b-\frac{40}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{8}{11}q-\frac{5}{4}b-\frac{10}{11} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(a+\frac{19}{5})((-10)-x)& =(\color{red}{a}+\color{orange}{\frac{19}{5}}).(\color{green}{-x}+\color{blue}{(-10)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(-10)} + \color{orange}{(\frac{19}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{5})} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -ax-10a-\frac{19}{5}x-\frac{19}{5}.10& \text{Uitwerken } \\ & =-ax-10a-\frac{19}{5}x-\frac{190}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-10a-\frac{19}{5}x-38 & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(x-\frac{-4}{15})(12+p)& =(\color{red}{x}+\color{orange}{\frac{4}{15}}).(\color{green}{p}+\color{blue}{12})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(12)} + \color{orange}{(\frac{4}{15})} . \color{green}{(p)} + \color{orange}{(\frac{4}{15})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = px+12x+\frac{4}{15}p+\frac{4}{15}.12& \text{Uitwerken } \\ & =px+12x+\frac{4}{15}p+\frac{48}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+12x+\frac{4}{15}p+\frac{16}{5} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{12}{9}-p)(x-\frac{-2}{17})& =(\color{red}{-p}+\color{orange}{\frac{4}{3}}).(\color{green}{x}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{4}{3})} . \color{green}{(x)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{2}{17}p+\frac{4}{3}x+\frac{4}{3}.\frac{2}{17}& \text{Uitwerken } \\ & =-px-\frac{2}{17}p+\frac{4}{3}x+\frac{8}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-1}{6}+q)(p-\frac{-2}{13})& =(\color{red}{q}+\color{orange}{\frac{-1}{6}}).(\color{green}{p}+\color{blue}{\frac{2}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{2}{13})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{2}{13})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{2}{13}q-\frac{1}{6}p-\frac{1}{6}.\frac{2}{13}& \text{Uitwerken } \\ & =pq+\frac{2}{13}q-\frac{1}{6}p-\frac{2}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{2}{13}q-\frac{1}{6}p-\frac{1}{39} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(a-\frac{16}{17})(\frac{-20}{11}-x)& =(\color{red}{a}+\color{orange}{\frac{-16}{17}}).(\color{green}{-x}+\color{blue}{\frac{-20}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{11})} + \color{orange}{(\frac{-16}{17})} . \color{green}{(-x)} + \color{orange}{(\frac{-16}{17})} . \color{blue}{(\frac{-20}{11})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{20}{11}a+\frac{16}{17}x+\frac{16}{17}.\frac{20}{11}& \text{Uitwerken } \\ & =-ax-\frac{20}{11}a+\frac{16}{17}x+\frac{320}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(x+\frac{-17}{9})(\frac{16}{7}-q)& =(\color{red}{x}+\color{orange}{\frac{-17}{9}}).(\color{green}{-q}+\color{blue}{\frac{16}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{16}{7})} + \color{orange}{(\frac{-17}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{-17}{9})} . \color{blue}{(\frac{16}{7})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{16}{7}x+\frac{17}{9}q-\frac{17}{9}.\frac{16}{7}& \text{Uitwerken } \\ & =-qx+\frac{16}{7}x+\frac{17}{9}q-\frac{272}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{15}{9}-b)(p-\frac{-18}{16})& =(\color{red}{-b}+\color{orange}{\frac{5}{3}}).(\color{green}{p}+\color{blue}{\frac{9}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{9}{8})} + \color{orange}{(\frac{5}{3})} . \color{green}{(p)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{9}{8})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{9}{8}b+\frac{5}{3}p+\frac{5}{3}.\frac{9}{8}& \text{Uitwerken } \\ & =-bp-\frac{9}{8}b+\frac{5}{3}p+\frac{45}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{9}{8}b+\frac{5}{3}p+\frac{15}{8} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(a-\frac{-3}{13})(\frac{-9}{2}+p)& =(\color{red}{a}+\color{orange}{\frac{3}{13}}).(\color{green}{p}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{3}{13})} . \color{green}{(p)} + \color{orange}{(\frac{3}{13})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{9}{2}a+\frac{3}{13}p-\frac{3}{13}.\frac{9}{2}& \text{Uitwerken } \\ & =ap-\frac{9}{2}a+\frac{3}{13}p-\frac{27}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-\frac{-19}{3})(a-\frac{7}{17})& =(\color{red}{a}+\color{orange}{\frac{19}{3}}).(\color{green}{a}+\color{blue}{\frac{-7}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{17})} + \color{orange}{(\frac{19}{3})} . \color{green}{(a)} + \color{orange}{(\frac{19}{3})} . \color{blue}{(\frac{-7}{17})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{7}{17}a+\frac{19}{3}a-\frac{19}{3}.\frac{7}{17}& \text{Uitwerken } \\ & =a^2+((\frac{-7}{17})+\frac{19}{3})a-(\frac{-133}{51}) & \text{Neem samen} \\ &=a^2+\frac{302}{51}a-(\frac{-133}{51}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(p+\frac{9}{9})(b-\frac{-18}{17})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{b}+\color{blue}{\frac{18}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{18}{17})} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(\frac{18}{17})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{18}{17}p+1b+1.\frac{18}{17}& \text{Uitwerken } \\ & =bp+\frac{18}{17}p+1b+\frac{18}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)