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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x-1)(b-\frac{-19}{16})& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{19}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{19}{16})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{19}{16})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{19}{16}x-1b-1.\frac{19}{16}& \text{Uitwerken } \\ & =bx+\frac{19}{16}x-1b-\frac{19}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q-\frac{16}{6})(a-\frac{-6}{17})& =(\color{red}{q}+\color{orange}{\frac{-8}{3}}).(\color{green}{a}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{6}{17}q-\frac{8}{3}a-\frac{8}{3}.\frac{6}{17}& \text{Uitwerken } \\ & =aq+\frac{6}{17}q-\frac{8}{3}a-\frac{48}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{6}{17}q-\frac{8}{3}a-\frac{16}{17} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{10}{5}-q)(\frac{-5}{5}+a)& =(\color{red}{-q}+\color{orange}{2}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(-1)} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -aq+1q+2a-2.1& \text{Uitwerken } \\ & =-aq+1q+2a-2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-8}{19}+p)(a-\frac{19}{16})& =(\color{red}{p}+\color{orange}{\frac{-8}{19}}).(\color{green}{a}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(\frac{-8}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-8}{19})} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{16}p-\frac{8}{19}a+\frac{8}{19}.\frac{19}{16}& \text{Uitwerken } \\ & =ap-\frac{19}{16}p-\frac{8}{19}a+\frac{152}{304} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{19}{16}p-\frac{8}{19}a+\frac{1}{2} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(x-\frac{-12}{6})(\frac{-6}{7}+x)& =(\color{red}{x}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{6}{7}x+2x-2.\frac{6}{7}& \text{Uitwerken } \\ & =x^2+((\frac{-6}{7})+2)x-(\frac{-12}{7}) & \text{Neem samen} \\ &=x^2+\frac{8}{7}x-(\frac{-12}{7}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{1}{7}+q)(a+\frac{9}{19})& =(\color{red}{q}+\color{orange}{\frac{1}{7}}).(\color{green}{a}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(\frac{1}{7})} . \color{green}{(a)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{9}{19}q+\frac{1}{7}a+\frac{1}{7}.\frac{9}{19}& \text{Uitwerken } \\ & =aq+\frac{9}{19}q+\frac{1}{7}a+\frac{9}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p+19)(\frac{9}{11}-b)& =(\color{red}{p}+\color{orange}{19}).(\color{green}{-b}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(19)} . \color{green}{(-b)} + \color{orange}{(19)} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{9}{11}p-19b+19.\frac{9}{11}& \text{Uitwerken } \\ & =-bp+\frac{9}{11}p-19b+\frac{171}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{13}{6}+a)(p-\frac{2}{11})& =(\color{red}{a}+\color{orange}{\frac{13}{6}}).(\color{green}{p}+\color{blue}{\frac{-2}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{11})} + \color{orange}{(\frac{13}{6})} . \color{green}{(p)} + \color{orange}{(\frac{13}{6})} . \color{blue}{(\frac{-2}{11})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{11}a+\frac{13}{6}p-\frac{13}{6}.\frac{2}{11}& \text{Uitwerken } \\ & =ap-\frac{2}{11}a+\frac{13}{6}p-\frac{26}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{2}{11}a+\frac{13}{6}p-\frac{13}{33} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-3}{18}-q)(\frac{-2}{4}-p)& =(\color{red}{-q}+\color{orange}{\frac{-1}{6}}).(\color{green}{-p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{2}q+\frac{1}{6}p+\frac{1}{6}.\frac{1}{2}& \text{Uitwerken } \\ & =pq+\frac{1}{2}q+\frac{1}{6}p+\frac{1}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x-\frac{-9}{15})(\frac{-2}{20}-q)& =(\color{red}{x}+\color{orange}{\frac{3}{5}}).(\color{green}{-q}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{3}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{1}{10}x-\frac{3}{5}q-\frac{3}{5}.\frac{1}{10}& \text{Uitwerken } \\ & =-qx-\frac{1}{10}x-\frac{3}{5}q-\frac{3}{50} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p+\frac{5}{9})(q+\frac{2}{19})& =(\color{red}{p}+\color{orange}{\frac{5}{9}}).(\color{green}{q}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(\frac{5}{9})} . \color{green}{(q)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{2}{19}p+\frac{5}{9}q+\frac{5}{9}.\frac{2}{19}& \text{Uitwerken } \\ & =pq+\frac{2}{19}p+\frac{5}{9}q+\frac{10}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q+\frac{-12}{15})(a+\frac{18}{13})& =(\color{red}{q}+\color{orange}{\frac{-4}{5}}).(\color{green}{a}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{18}{13}q-\frac{4}{5}a-\frac{4}{5}.\frac{18}{13}& \text{Uitwerken } \\ & =aq+\frac{18}{13}q-\frac{4}{5}a-\frac{72}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)