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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-19}{18}-b)(x+\frac{-12}{3})& =(\color{red}{-b}+\color{orange}{\frac{-19}{18}}).(\color{green}{x}+\color{blue}{(-4)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(-4)} + \color{orange}{(\frac{-19}{18})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{18})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -bx+4b-\frac{19}{18}x+\frac{19}{18}.4& \text{Uitwerken } \\ & =-bx+4b-\frac{19}{18}x+\frac{76}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx+4b-\frac{19}{18}x+\frac{38}{9} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(b-\frac{12}{12})(a+\frac{-16}{18})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{8}{9}b-1a+1.\frac{8}{9}& \text{Uitwerken } \\ & =ab-\frac{8}{9}b-1a+\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b-\frac{15}{15})(x-\frac{-6}{9})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{2}{3}b-1x-1.\frac{2}{3}& \text{Uitwerken } \\ & =bx+\frac{2}{3}b-1x-\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-7}{17}-p)(x+\frac{19}{6})& =(\color{red}{-p}+\color{orange}{\frac{-7}{17}}).(\color{green}{x}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(\frac{-7}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{19}{6}p-\frac{7}{17}x-\frac{7}{17}.\frac{19}{6}& \text{Uitwerken } \\ & =-px-\frac{19}{6}p-\frac{7}{17}x-\frac{133}{102} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b-\frac{19}{9})(\frac{-16}{13}-b)& =(\color{red}{b}+\color{orange}{\frac{-19}{9}}).(\color{green}{-b}+\color{blue}{\frac{-16}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{13})} + \color{orange}{(\frac{-19}{9})} . \color{green}{(-b)} + \color{orange}{(\frac{-19}{9})} . \color{blue}{(\frac{-16}{13})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{16}{13}b+\frac{19}{9}b+\frac{19}{9}.\frac{16}{13}& \text{Uitwerken } \\ & =-b^2+((\frac{-16}{13})+\frac{19}{9})b+(\frac{-304}{117}) & \text{Neem samen} \\ &=-b^2+\frac{103}{117}b+(\frac{-304}{117}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{-4}{4}+a)(q-\frac{12}{12})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = aq-1a-1q+1.1& \text{Uitwerken } \\ & =aq-1a-1q+1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(15-p)(\frac{-19}{2}-a)& =(\color{red}{-p}+\color{orange}{15}).(\color{green}{-a}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(15)} . \color{green}{(-a)} + \color{orange}{(15)} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{19}{2}p-15a-15.\frac{19}{2}& \text{Uitwerken } \\ & =ap+\frac{19}{2}p-15a-\frac{285}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b+\frac{20}{10})(b-(-19))& =(\color{red}{b}+\color{orange}{2}).(\color{green}{b}+\color{blue}{19})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(19)} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(19)}& \text{Boogjes en uitschrijven} \\ & = bb+19b+2b+2.19& \text{Uitwerken } \\ & =b^2+(19+2)b+38 & \text{Neem samen} \\ &=b^2+21b+38 & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(p-\frac{18}{15})(\frac{-16}{14}-x)& =(\color{red}{p}+\color{orange}{\frac{-6}{5}}).(\color{green}{-x}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{8}{7}p+\frac{6}{5}x+\frac{6}{5}.\frac{8}{7}& \text{Uitwerken } \\ & =-px-\frac{8}{7}p+\frac{6}{5}x+\frac{48}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(p+\frac{-10}{15})(b+\frac{13}{12})& =(\color{red}{p}+\color{orange}{\frac{-2}{3}}).(\color{green}{b}+\color{blue}{\frac{13}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{13}{12})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{13}{12})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{13}{12}p-\frac{2}{3}b-\frac{2}{3}.\frac{13}{12}& \text{Uitwerken } \\ & =bp+\frac{13}{12}p-\frac{2}{3}b-\frac{26}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{13}{12}p-\frac{2}{3}b-\frac{13}{18} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(a+\frac{-18}{16})(a-\frac{-19}{6})& =(\color{red}{a}+\color{orange}{\frac{-9}{8}}).(\color{green}{a}+\color{blue}{\frac{19}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{19}{6})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{19}{6})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{19}{6}a-\frac{9}{8}a-\frac{9}{8}.\frac{19}{6}& \text{Uitwerken } \\ & =a^2+(\frac{19}{6}+(\frac{-9}{8}))a-(\frac{-171}{48}) & \text{Neem samen} \\ &=a^2+\frac{49}{24}a-(\frac{-171}{48}) & \text{Maak de som} \\ &=a^2+\frac{49}{24}a+\frac{57}{16} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
12. \(\begin{align}(\frac{-12}{18}-q)(x-20)& =(\color{red}{-q}+\color{orange}{\frac{-2}{3}}).(\color{green}{x}+\color{blue}{(-20)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(x)} + \color{red}{(-q)} . \color{blue}{(-20)} + \color{orange}{(\frac{-2}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = -qx+20q-\frac{2}{3}x+\frac{2}{3}.20& \text{Uitwerken } \\ & =-qx+20q-\frac{2}{3}x+\frac{40}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)