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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-5}{6}-x)(q-\frac{-10}{12})& =(\color{red}{-x}+\color{orange}{\frac{-5}{6}}).(\color{green}{q}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{5}{6}x-\frac{5}{6}q-\frac{5}{6}.\frac{5}{6}& \text{Uitwerken } \\ & =-qx-\frac{5}{6}x-\frac{5}{6}q-\frac{25}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x-(-11))(\frac{-19}{12}+b)& =(\color{red}{x}+\color{orange}{11}).(\color{green}{b}+\color{blue}{\frac{-19}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{12})} + \color{orange}{(11)} . \color{green}{(b)} + \color{orange}{(11)} . \color{blue}{(\frac{-19}{12})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{19}{12}x+11b-11.\frac{19}{12}& \text{Uitwerken } \\ & =bx-\frac{19}{12}x+11b-\frac{209}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x-\frac{11}{19})(a-\frac{-8}{8})& =(\color{red}{x}+\color{orange}{\frac{-11}{19}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-11}{19})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{19})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ax+1x-\frac{11}{19}a-\frac{11}{19}.1& \text{Uitwerken } \\ & =ax+1x-\frac{11}{19}a-\frac{11}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x+\frac{16}{7})(\frac{12}{4}-p)& =(\color{red}{x}+\color{orange}{\frac{16}{7}}).(\color{green}{-p}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(3)} + \color{orange}{(\frac{16}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{16}{7})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -px+3x-\frac{16}{7}p+\frac{16}{7}.3& \text{Uitwerken } \\ & =-px+3x-\frac{16}{7}p+\frac{48}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b+\frac{-14}{13})(\frac{6}{18}+b)& =(\color{red}{b}+\color{orange}{\frac{-14}{13}}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-14}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-14}{13})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{3}b-\frac{14}{13}b-\frac{14}{13}.\frac{1}{3}& \text{Uitwerken } \\ & =b^2+(\frac{1}{3}+(\frac{-14}{13}))b-(\frac{-14}{39}) & \text{Neem samen} \\ &=b^2-\frac{29}{39}b-(\frac{-14}{39}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(x-\frac{7}{4})(\frac{-12}{6}-b)& =(\color{red}{x}+\color{orange}{\frac{-7}{4}}).(\color{green}{-b}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(-2)} + \color{orange}{(\frac{-7}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -bx-2x+\frac{7}{4}b+\frac{7}{4}.2& \text{Uitwerken } \\ & =-bx-2x+\frac{7}{4}b+\frac{14}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-2x+\frac{7}{4}b+\frac{7}{2} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-20}{6}-p)(x-(-4))& =(\color{red}{-p}+\color{orange}{\frac{-10}{3}}).(\color{green}{x}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(4)} + \color{orange}{(\frac{-10}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -px-4p-\frac{10}{3}x-\frac{10}{3}.4& \text{Uitwerken } \\ & =-px-4p-\frac{10}{3}x-\frac{40}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{1}{19}+p)(b+\frac{-8}{17})& =(\color{red}{p}+\color{orange}{\frac{1}{19}}).(\color{green}{b}+\color{blue}{\frac{-8}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{17})} + \color{orange}{(\frac{1}{19})} . \color{green}{(b)} + \color{orange}{(\frac{1}{19})} . \color{blue}{(\frac{-8}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{8}{17}p+\frac{1}{19}b-\frac{1}{19}.\frac{8}{17}& \text{Uitwerken } \\ & =bp-\frac{8}{17}p+\frac{1}{19}b-\frac{8}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(q+\frac{9}{4})(\frac{3}{9}+a)& =(\color{red}{q}+\color{orange}{\frac{9}{4}}).(\color{green}{a}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{9}{4})} . \color{green}{(a)} + \color{orange}{(\frac{9}{4})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{3}q+\frac{9}{4}a+\frac{9}{4}.\frac{1}{3}& \text{Uitwerken } \\ & =aq+\frac{1}{3}q+\frac{9}{4}a+\frac{9}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{1}{3}q+\frac{9}{4}a+\frac{3}{4} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(a-\frac{-15}{7})(q-\frac{18}{3})& =(\color{red}{a}+\color{orange}{\frac{15}{7}}).(\color{green}{q}+\color{blue}{(-6)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(-6)} + \color{orange}{(\frac{15}{7})} . \color{green}{(q)} + \color{orange}{(\frac{15}{7})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = aq-6a+\frac{15}{7}q-\frac{15}{7}.6& \text{Uitwerken } \\ & =aq-6a+\frac{15}{7}q-\frac{90}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{1}{10}-q)(\frac{-3}{7}-b)& =(\color{red}{-q}+\color{orange}{\frac{1}{10}}).(\color{green}{-b}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{1}{10})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{3}{7}q-\frac{1}{10}b-\frac{1}{10}.\frac{3}{7}& \text{Uitwerken } \\ & =bq+\frac{3}{7}q-\frac{1}{10}b-\frac{3}{70} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-15}{3}-a)(\frac{8}{15}-q)& =(\color{red}{-a}+\color{orange}{(-5)}).(\color{green}{-q}+\color{blue}{\frac{8}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{8}{15})} + \color{orange}{(-5)} . \color{green}{(-q)} + \color{orange}{(-5)} . \color{blue}{(\frac{8}{15})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{8}{15}a+5q-5.\frac{8}{15}& \text{Uitwerken } \\ & =aq-\frac{8}{15}a+5q-\frac{40}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{8}{15}a+5q-\frac{8}{3} & \text{Vereenvoudig} \\\end{align}\)