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

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Werk uit en vereenvoudig

1. \((q-(-5))(\frac{19}{14}+p)\)
2. \((x-\frac{-3}{4})(p+\frac{13}{4})\)
3. \((a-\frac{15}{19})(x+\frac{9}{12})\)
4. \((p+\frac{-15}{14})(b+\frac{-3}{11})\)
5. \((b-\frac{10}{14})(\frac{-16}{17}+x)\)
6. \((\frac{18}{2}+p)(\frac{-8}{2}-q)\)
7. \((a+\frac{-2}{2})(b-\frac{-2}{18})\)
8. \((p+\frac{8}{8})(\frac{17}{13}-x)\)
9. \((\frac{-6}{13}+a)(q-\frac{-16}{14})\)
10. \((x+\frac{-19}{2})(\frac{1}{4}-b)\)
11. \((\frac{8}{6}-b)(\frac{-16}{18}-x)\)
12. \((\frac{-7}{20}+b)(x-\frac{-15}{16})\)

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-(-5))(\frac{19}{14}+p)& =(\color{red}{q}+\color{orange}{5}).(\color{green}{p}+\color{blue}{\frac{19}{14}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{19}{14})} + \color{orange}{(5)} . \color{green}{(p)} + \color{orange}{(5)} . \color{blue}{(\frac{19}{14})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{19}{14}q+5p+5.\frac{19}{14}& \text{Uitwerken } \\ & =pq+\frac{19}{14}q+5p+\frac{95}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x-\frac{-3}{4})(p+\frac{13}{4})& =(\color{red}{x}+\color{orange}{\frac{3}{4}}).(\color{green}{p}+\color{blue}{\frac{13}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{13}{4})} + \color{orange}{(\frac{3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{13}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{13}{4}x+\frac{3}{4}p+\frac{3}{4}.\frac{13}{4}& \text{Uitwerken } \\ & =px+\frac{13}{4}x+\frac{3}{4}p+\frac{39}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(a-\frac{15}{19})(x+\frac{9}{12})& =(\color{red}{a}+\color{orange}{\frac{-15}{19}}).(\color{green}{x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-15}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{19})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{3}{4}a-\frac{15}{19}x-\frac{15}{19}.\frac{3}{4}& \text{Uitwerken } \\ & =ax+\frac{3}{4}a-\frac{15}{19}x-\frac{45}{76} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p+\frac{-15}{14})(b+\frac{-3}{11})& =(\color{red}{p}+\color{orange}{\frac{-15}{14}}).(\color{green}{b}+\color{blue}{\frac{-3}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{11})} + \color{orange}{(\frac{-15}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{14})} . \color{blue}{(\frac{-3}{11})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{11}p-\frac{15}{14}b+\frac{15}{14}.\frac{3}{11}& \text{Uitwerken } \\ & =bp-\frac{3}{11}p-\frac{15}{14}b+\frac{45}{154} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b-\frac{10}{14})(\frac{-16}{17}+x)& =(\color{red}{b}+\color{orange}{\frac{-5}{7}}).(\color{green}{x}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{16}{17}b-\frac{5}{7}x+\frac{5}{7}.\frac{16}{17}& \text{Uitwerken } \\ & =bx-\frac{16}{17}b-\frac{5}{7}x+\frac{80}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{18}{2}+p)(\frac{-8}{2}-q)& =(\color{red}{p}+\color{orange}{9}).(\color{green}{-q}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(-4)} + \color{orange}{(9)} . \color{green}{(-q)} + \color{orange}{(9)} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -pq-4p-9q-9.4& \text{Uitwerken } \\ & =-pq-4p-9q-36 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a+\frac{-2}{2})(b-\frac{-2}{18})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{9}a-1b-1.\frac{1}{9}& \text{Uitwerken } \\ & =ab+\frac{1}{9}a-1b-\frac{1}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p+\frac{8}{8})(\frac{17}{13}-x)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{-x}+\color{blue}{\frac{17}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{17}{13})} + \color{orange}{(1)} . \color{green}{(-x)} + \color{orange}{(1)} . \color{blue}{(\frac{17}{13})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{17}{13}p-1x+1.\frac{17}{13}& \text{Uitwerken } \\ & =-px+\frac{17}{13}p-1x+\frac{17}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-6}{13}+a)(q-\frac{-16}{14})& =(\color{red}{a}+\color{orange}{\frac{-6}{13}}).(\color{green}{q}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{-6}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-6}{13})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{8}{7}a-\frac{6}{13}q-\frac{6}{13}.\frac{8}{7}& \text{Uitwerken } \\ & =aq+\frac{8}{7}a-\frac{6}{13}q-\frac{48}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x+\frac{-19}{2})(\frac{1}{4}-b)& =(\color{red}{x}+\color{orange}{\frac{-19}{2}}).(\color{green}{-b}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-19}{2})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{4}x+\frac{19}{2}b-\frac{19}{2}.\frac{1}{4}& \text{Uitwerken } \\ & =-bx+\frac{1}{4}x+\frac{19}{2}b-\frac{19}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{8}{6}-b)(\frac{-16}{18}-x)& =(\color{red}{-b}+\color{orange}{\frac{4}{3}}).(\color{green}{-x}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{4}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{8}{9}b-\frac{4}{3}x-\frac{4}{3}.\frac{8}{9}& \text{Uitwerken } \\ & =bx+\frac{8}{9}b-\frac{4}{3}x-\frac{32}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-7}{20}+b)(x-\frac{-15}{16})& =(\color{red}{b}+\color{orange}{\frac{-7}{20}}).(\color{green}{x}+\color{blue}{\frac{15}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{15}{16})} + \color{orange}{(\frac{-7}{20})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(\frac{15}{16})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{15}{16}b-\frac{7}{20}x-\frac{7}{20}.\frac{15}{16}& \text{Uitwerken } \\ & =bx+\frac{15}{16}b-\frac{7}{20}x-\frac{105}{320} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{15}{16}b-\frac{7}{20}x-\frac{21}{64} & \text{Vereenvoudig} \\\end{align}\)