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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-10}{4}-b)(\frac{11}{16}+x)& =(\color{red}{-b}+\color{orange}{\frac{-5}{2}}).(\color{green}{x}+\color{blue}{\frac{11}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{16})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{11}{16})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{11}{16}b-\frac{5}{2}x-\frac{5}{2}.\frac{11}{16}& \text{Uitwerken } \\ & =-bx-\frac{11}{16}b-\frac{5}{2}x-\frac{55}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b-\frac{17}{16})(x+\frac{18}{11})& =(\color{red}{b}+\color{orange}{\frac{-17}{16}}).(\color{green}{x}+\color{blue}{\frac{18}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{18}{11})} + \color{orange}{(\frac{-17}{16})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{16})} . \color{blue}{(\frac{18}{11})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{18}{11}b-\frac{17}{16}x-\frac{17}{16}.\frac{18}{11}& \text{Uitwerken } \\ & =bx+\frac{18}{11}b-\frac{17}{16}x-\frac{306}{176} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{18}{11}b-\frac{17}{16}x-\frac{153}{88} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(x-\frac{-17}{5})(a+\frac{-15}{5})& =(\color{red}{x}+\color{orange}{\frac{17}{5}}).(\color{green}{a}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-3)} + \color{orange}{(\frac{17}{5})} . \color{green}{(a)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = ax-3x+\frac{17}{5}a-\frac{17}{5}.3& \text{Uitwerken } \\ & =ax-3x+\frac{17}{5}a-\frac{51}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-5}{5}+x)(\frac{-15}{19}-a)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{-a}+\color{blue}{\frac{-15}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{-15}{19})} + \color{orange}{(-1)} . \color{green}{(-a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-15}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{15}{19}x+1a+1.\frac{15}{19}& \text{Uitwerken } \\ & =-ax-\frac{15}{19}x+1a+\frac{15}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(a-\frac{-3}{2})(\frac{15}{18}+p)& =(\color{red}{a}+\color{orange}{\frac{3}{2}}).(\color{green}{p}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{5}{6}a+\frac{3}{2}p+\frac{3}{2}.\frac{5}{6}& \text{Uitwerken } \\ & =ap+\frac{5}{6}a+\frac{3}{2}p+\frac{15}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{5}{6}a+\frac{3}{2}p+\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(b+\frac{-19}{17})(q-\frac{-20}{5})& =(\color{red}{b}+\color{orange}{\frac{-19}{17}}).(\color{green}{q}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(4)} + \color{orange}{(\frac{-19}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-19}{17})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = bq+4b-\frac{19}{17}q-\frac{19}{17}.4& \text{Uitwerken } \\ & =bq+4b-\frac{19}{17}q-\frac{76}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{5}{4}-p)(b-\frac{-13}{18})& =(\color{red}{-p}+\color{orange}{\frac{5}{4}}).(\color{green}{b}+\color{blue}{\frac{13}{18}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{13}{18})} + \color{orange}{(\frac{5}{4})} . \color{green}{(b)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{13}{18})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{13}{18}p+\frac{5}{4}b+\frac{5}{4}.\frac{13}{18}& \text{Uitwerken } \\ & =-bp-\frac{13}{18}p+\frac{5}{4}b+\frac{65}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{19}{8}+p)(x+\frac{-10}{5})& =(\color{red}{p}+\color{orange}{\frac{19}{8}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{19}{8})} . \color{green}{(x)} + \color{orange}{(\frac{19}{8})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = px-2p+\frac{19}{8}x-\frac{19}{8}.2& \text{Uitwerken } \\ & =px-2p+\frac{19}{8}x-\frac{38}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-2p+\frac{19}{8}x-\frac{19}{4} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-8}{12}-x)(\frac{5}{3}+q)& =(\color{red}{-x}+\color{orange}{\frac{-2}{3}}).(\color{green}{q}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{5}{3}x-\frac{2}{3}q-\frac{2}{3}.\frac{5}{3}& \text{Uitwerken } \\ & =-qx-\frac{5}{3}x-\frac{2}{3}q-\frac{10}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{8}{14}+p)(\frac{-4}{17}+a)& =(\color{red}{p}+\color{orange}{\frac{4}{7}}).(\color{green}{a}+\color{blue}{\frac{-4}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{17})} + \color{orange}{(\frac{4}{7})} . \color{green}{(a)} + \color{orange}{(\frac{4}{7})} . \color{blue}{(\frac{-4}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{4}{17}p+\frac{4}{7}a-\frac{4}{7}.\frac{4}{17}& \text{Uitwerken } \\ & =ap-\frac{4}{17}p+\frac{4}{7}a-\frac{16}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(10-p)(\frac{-16}{8}-q)& =(\color{red}{-p}+\color{orange}{10}).(\color{green}{-q}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(-2)} + \color{orange}{(10)} . \color{green}{(-q)} + \color{orange}{(10)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pq+2p-10q-10.2& \text{Uitwerken } \\ & =pq+2p-10q-20 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q-\frac{7}{17})(q-\frac{19}{17})& =(\color{red}{q}+\color{orange}{\frac{-7}{17}}).(\color{green}{q}+\color{blue}{\frac{-19}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{17})} + \color{orange}{(\frac{-7}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(\frac{-19}{17})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{19}{17}q-\frac{7}{17}q+\frac{7}{17}.\frac{19}{17}& \text{Uitwerken } \\ & =q^2+((\frac{-19}{17})+(\frac{-7}{17}))q+\frac{133}{289} & \text{Neem samen} \\ &=q^2-\frac{26}{17}q+\frac{133}{289} & \text{Maak de som} \\\end{align}\)