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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-11}{13}-x)(\frac{-1}{2}+q)& =(\color{red}{-x}+\color{orange}{\frac{-11}{13}}).(\color{green}{q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{2}x-\frac{11}{13}q+\frac{11}{13}.\frac{1}{2}& \text{Uitwerken } \\ & =-qx+\frac{1}{2}x-\frac{11}{13}q+\frac{11}{26} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-13}{4}-p)(\frac{10}{10}-q)& =(\color{red}{-p}+\color{orange}{\frac{-13}{4}}).(\color{green}{-q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(1)} + \color{orange}{(\frac{-13}{4})} . \color{green}{(-q)} + \color{orange}{(\frac{-13}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pq-1p+\frac{13}{4}q-\frac{13}{4}.1& \text{Uitwerken } \\ & =pq-1p+\frac{13}{4}q-\frac{13}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p-17)(\frac{-16}{12}-q)& =(\color{red}{p}+\color{orange}{(-17)}).(\color{green}{-q}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(-17)} . \color{green}{(-q)} + \color{orange}{(-17)} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{4}{3}p+17q+17.\frac{4}{3}& \text{Uitwerken } \\ & =-pq-\frac{4}{3}p+17q+\frac{68}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{14}{16}+b)(a-\frac{3}{20})& =(\color{red}{b}+\color{orange}{\frac{7}{8}}).(\color{green}{a}+\color{blue}{\frac{-3}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{20})} + \color{orange}{(\frac{7}{8})} . \color{green}{(a)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(\frac{-3}{20})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{3}{20}b+\frac{7}{8}a-\frac{7}{8}.\frac{3}{20}& \text{Uitwerken } \\ & =ab-\frac{3}{20}b+\frac{7}{8}a-\frac{21}{160} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-9}{3}+b)(x+\frac{19}{5})& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{x}+\color{blue}{\frac{19}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{19}{5})} + \color{orange}{(-3)} . \color{green}{(x)} + \color{orange}{(-3)} . \color{blue}{(\frac{19}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{19}{5}b-3x-3.\frac{19}{5}& \text{Uitwerken } \\ & =bx+\frac{19}{5}b-3x-\frac{57}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x-\frac{-15}{20})(\frac{20}{14}+x)& =(\color{red}{x}+\color{orange}{\frac{3}{4}}).(\color{green}{x}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{10}{7}x+\frac{3}{4}x+\frac{3}{4}.\frac{10}{7}& \text{Uitwerken } \\ & =x^2+(\frac{10}{7}+\frac{3}{4})x+\frac{30}{28} & \text{Neem samen} \\ &=x^2+\frac{61}{28}x+\frac{30}{28} & \text{Maak de som} \\ &=x^2+\frac{61}{28}x+\frac{15}{14} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
7. \(\begin{align}(\frac{13}{20}+x)((-4)+x)& =(\color{red}{x}+\color{orange}{\frac{13}{20}}).(\color{green}{x}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(-4)} + \color{orange}{(\frac{13}{20})} . \color{green}{(x)} + \color{orange}{(\frac{13}{20})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = xx-4x+\frac{13}{20}x-\frac{13}{20}.4& \text{Uitwerken } \\ & =x^2+((-4)+\frac{13}{20})x-(\frac{-52}{20}) & \text{Neem samen} \\ &=x^2-\frac{67}{20}x-(\frac{-52}{20}) & \text{Maak de som} \\ &=x^2-\frac{67}{20}x+\frac{13}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
8. \(\begin{align}(\frac{2}{9}+x)(b-\frac{18}{18})& =(\color{red}{x}+\color{orange}{\frac{2}{9}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{2}{9})} . \color{green}{(b)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bx-1x+\frac{2}{9}b-\frac{2}{9}.1& \text{Uitwerken } \\ & =bx-1x+\frac{2}{9}b-\frac{2}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-1}{19}-b)(p+\frac{8}{17})& =(\color{red}{-b}+\color{orange}{\frac{-1}{19}}).(\color{green}{p}+\color{blue}{\frac{8}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{8}{17})} + \color{orange}{(\frac{-1}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{19})} . \color{blue}{(\frac{8}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{8}{17}b-\frac{1}{19}p-\frac{1}{19}.\frac{8}{17}& \text{Uitwerken } \\ & =-bp-\frac{8}{17}b-\frac{1}{19}p-\frac{8}{323} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{9}{9}+p)(\frac{9}{19}-p)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{-p}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(1)} . \color{green}{(-p)} + \color{orange}{(1)} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{9}{19}p-1p+1.\frac{9}{19}& \text{Uitwerken } \\ & =-p^2+(\frac{9}{19}+(-1))p+(\frac{-9}{19}) & \text{Neem samen} \\ &=-p^2-\frac{10}{19}p+(\frac{-9}{19}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(q-\frac{-20}{16})(\frac{20}{16}-b)& =(\color{red}{q}+\color{orange}{\frac{5}{4}}).(\color{green}{-b}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{5}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{4}q-\frac{5}{4}b+\frac{5}{4}.\frac{5}{4}& \text{Uitwerken } \\ & =-bq+\frac{5}{4}q-\frac{5}{4}b+\frac{25}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b+\frac{-12}{2})(x+\frac{6}{8})& =(\color{red}{b}+\color{orange}{(-6)}).(\color{green}{x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(-6)} . \color{green}{(x)} + \color{orange}{(-6)} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{4}b-6x-6.\frac{3}{4}& \text{Uitwerken } \\ & =bx+\frac{3}{4}b-6x-\frac{18}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{3}{4}b-6x-\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)