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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{11}{6})(b-\frac{3}{13})& =(\color{red}{p}+\color{orange}{\frac{-11}{6}}).(\color{green}{b}+\color{blue}{\frac{-3}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{13})} + \color{orange}{(\frac{-11}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{6})} . \color{blue}{(\frac{-3}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{13}p-\frac{11}{6}b+\frac{11}{6}.\frac{3}{13}& \text{Uitwerken } \\ & =bp-\frac{3}{13}p-\frac{11}{6}b+\frac{33}{78} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{3}{13}p-\frac{11}{6}b+\frac{11}{26} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{3}{3}-q)(\frac{-14}{2}+b)& =(\color{red}{-q}+\color{orange}{1}).(\color{green}{b}+\color{blue}{(-7)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(-7)} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = -bq+7q+1b-1.7& \text{Uitwerken } \\ & =-bq+7q+1b-7 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{10}{13}-p)(b-\frac{-4}{17})& =(\color{red}{-p}+\color{orange}{\frac{10}{13}}).(\color{green}{b}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(\frac{10}{13})} . \color{green}{(b)} + \color{orange}{(\frac{10}{13})} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{4}{17}p+\frac{10}{13}b+\frac{10}{13}.\frac{4}{17}& \text{Uitwerken } \\ & =-bp-\frac{4}{17}p+\frac{10}{13}b+\frac{40}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p-\frac{6}{10})(\frac{-18}{5}-x)& =(\color{red}{p}+\color{orange}{\frac{-3}{5}}).(\color{green}{-x}+\color{blue}{\frac{-18}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-18}{5})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{-18}{5})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{18}{5}p+\frac{3}{5}x+\frac{3}{5}.\frac{18}{5}& \text{Uitwerken } \\ & =-px-\frac{18}{5}p+\frac{3}{5}x+\frac{54}{25} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p+\frac{-10}{10})(\frac{7}{3}-x)& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{-x}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(-1)} . \color{green}{(-x)} + \color{orange}{(-1)} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{7}{3}p+1x-1.\frac{7}{3}& \text{Uitwerken } \\ & =-px+\frac{7}{3}p+1x-\frac{7}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-18}{2}+x)((-6)+x)& =(\color{red}{x}+\color{orange}{(-9)}).(\color{green}{x}+\color{blue}{(-6)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(-6)} + \color{orange}{(-9)} . \color{green}{(x)} + \color{orange}{(-9)} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = xx-6x-9x+9.6& \text{Uitwerken } \\ & =x^2+((-6)+(-9))x+54 & \text{Neem samen} \\ &=x^2-15x+54 & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{-19}{18}+q)(\frac{-16}{16}+p)& =(\color{red}{q}+\color{orange}{\frac{-19}{18}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-19}{18})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{18})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = pq-1q-\frac{19}{18}p+\frac{19}{18}.1& \text{Uitwerken } \\ & =pq-1q-\frac{19}{18}p+\frac{19}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{3}{10}-b)(\frac{12}{12}-p)& =(\color{red}{-b}+\color{orange}{\frac{3}{10}}).(\color{green}{-p}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(1)} + \color{orange}{(\frac{3}{10})} . \color{green}{(-p)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp-1b-\frac{3}{10}p+\frac{3}{10}.1& \text{Uitwerken } \\ & =bp-1b-\frac{3}{10}p+\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{6}{13}+x)(\frac{4}{12}-x)& =(\color{red}{x}+\color{orange}{\frac{6}{13}}).(\color{green}{-x}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{6}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{6}{13})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{1}{3}x-\frac{6}{13}x+\frac{6}{13}.\frac{1}{3}& \text{Uitwerken } \\ & =-x^2+(\frac{1}{3}+(\frac{-6}{13}))x+(\frac{-6}{39}) & \text{Neem samen} \\ &=-x^2-\frac{5}{39}x+(\frac{-6}{39}) & \text{Maak de som} \\ &=-x^2-\frac{5}{39}x+(\frac{-2}{13}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
10. \(\begin{align}(\frac{1}{15}-p)(b-\frac{-5}{5})& =(\color{red}{-p}+\color{orange}{\frac{1}{15}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{15})} . \color{green}{(b)} + \color{orange}{(\frac{1}{15})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bp-1p+\frac{1}{15}b+\frac{1}{15}.1& \text{Uitwerken } \\ & =-bp-1p+\frac{1}{15}b+\frac{1}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-20}{6}-b)(b-\frac{9}{13})& =(\color{red}{-b}+\color{orange}{\frac{-10}{3}}).(\color{green}{b}+\color{blue}{\frac{-9}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-9}{13})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-9}{13})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{9}{13}b-\frac{10}{3}b+\frac{10}{3}.\frac{9}{13}& \text{Uitwerken } \\ & =-b^2+(\frac{9}{13}+(\frac{-10}{3}))b+(\frac{-90}{39}) & \text{Neem samen} \\ &=-b^2-\frac{103}{39}b+(\frac{-90}{39}) & \text{Maak de som} \\ &=-b^2-\frac{103}{39}b+(\frac{-30}{13}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
12. \(\begin{align}(b-\frac{11}{4})(a+\frac{20}{7})& =(\color{red}{b}+\color{orange}{\frac{-11}{4}}).(\color{green}{a}+\color{blue}{\frac{20}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{20}{7})} + \color{orange}{(\frac{-11}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{4})} . \color{blue}{(\frac{20}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{20}{7}b-\frac{11}{4}a-\frac{11}{4}.\frac{20}{7}& \text{Uitwerken } \\ & =ab+\frac{20}{7}b-\frac{11}{4}a-\frac{220}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{20}{7}b-\frac{11}{4}a-\frac{55}{7} & \text{Vereenvoudig} \\\end{align}\)