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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{6}{12})(a-\frac{1}{19})& =(\color{red}{a}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{1}{19}a-\frac{1}{2}a+\frac{1}{2}.\frac{1}{19}& \text{Uitwerken } \\ & =a^2+((\frac{-1}{19})+(\frac{-1}{2}))a+\frac{1}{38} & \text{Neem samen} \\ &=a^2-\frac{21}{38}a+\frac{1}{38} & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(p-\frac{-13}{7})(\frac{15}{12}+q)& =(\color{red}{p}+\color{orange}{\frac{13}{7}}).(\color{green}{q}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{13}{7})} . \color{green}{(q)} + \color{orange}{(\frac{13}{7})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{5}{4}p+\frac{13}{7}q+\frac{13}{7}.\frac{5}{4}& \text{Uitwerken } \\ & =pq+\frac{5}{4}p+\frac{13}{7}q+\frac{65}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(x-\frac{17}{6})(\frac{14}{7}+b)& =(\color{red}{x}+\color{orange}{\frac{-17}{6}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{-17}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-17}{6})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bx+2x-\frac{17}{6}b-\frac{17}{6}.2& \text{Uitwerken } \\ & =bx+2x-\frac{17}{6}b-\frac{34}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+2x-\frac{17}{6}b-\frac{17}{3} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(b+\frac{-10}{15})(\frac{16}{5}+q)& =(\color{red}{b}+\color{orange}{\frac{-2}{3}}).(\color{green}{q}+\color{blue}{\frac{16}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{16}{5})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{16}{5})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{16}{5}b-\frac{2}{3}q-\frac{2}{3}.\frac{16}{5}& \text{Uitwerken } \\ & =bq+\frac{16}{5}b-\frac{2}{3}q-\frac{32}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{12}{18}+p)(\frac{11}{11}-b)& =(\color{red}{p}+\color{orange}{\frac{2}{3}}).(\color{green}{-b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{2}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bp+1p-\frac{2}{3}b+\frac{2}{3}.1& \text{Uitwerken } \\ & =-bp+1p-\frac{2}{3}b+\frac{2}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{12}{7}-p)(\frac{-13}{19}+x)& =(\color{red}{-p}+\color{orange}{\frac{12}{7}}).(\color{green}{x}+\color{blue}{\frac{-13}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-13}{19})} + \color{orange}{(\frac{12}{7})} . \color{green}{(x)} + \color{orange}{(\frac{12}{7})} . \color{blue}{(\frac{-13}{19})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{13}{19}p+\frac{12}{7}x-\frac{12}{7}.\frac{13}{19}& \text{Uitwerken } \\ & =-px+\frac{13}{19}p+\frac{12}{7}x-\frac{156}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(q-\frac{-8}{12})(p+\frac{10}{9})& =(\color{red}{q}+\color{orange}{\frac{2}{3}}).(\color{green}{p}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{2}{3})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{10}{9}q+\frac{2}{3}p+\frac{2}{3}.\frac{10}{9}& \text{Uitwerken } \\ & =pq+\frac{10}{9}q+\frac{2}{3}p+\frac{20}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p-\frac{13}{19})(x+\frac{-16}{6})& =(\color{red}{p}+\color{orange}{\frac{-13}{19}}).(\color{green}{x}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-13}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{19})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{8}{3}p-\frac{13}{19}x+\frac{13}{19}.\frac{8}{3}& \text{Uitwerken } \\ & =px-\frac{8}{3}p-\frac{13}{19}x+\frac{104}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{5}{19}+b)(\frac{-8}{18}-b)& =(\color{red}{b}+\color{orange}{\frac{5}{19}}).(\color{green}{-b}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{5}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{19})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{4}{9}b-\frac{5}{19}b-\frac{5}{19}.\frac{4}{9}& \text{Uitwerken } \\ & =-b^2+((\frac{-4}{9})+(\frac{-5}{19}))b-\frac{20}{171} & \text{Neem samen} \\ &=-b^2-\frac{121}{171}b-\frac{20}{171} & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(\frac{20}{4}-a)(p+\frac{17}{6})& =(\color{red}{-a}+\color{orange}{5}).(\color{green}{p}+\color{blue}{\frac{17}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{17}{6})} + \color{orange}{(5)} . \color{green}{(p)} + \color{orange}{(5)} . \color{blue}{(\frac{17}{6})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{17}{6}a+5p+5.\frac{17}{6}& \text{Uitwerken } \\ & =-ap-\frac{17}{6}a+5p+\frac{85}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(q-\frac{4}{9})(\frac{-14}{18}-a)& =(\color{red}{q}+\color{orange}{\frac{-4}{9}}).(\color{green}{-a}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{-4}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-4}{9})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{7}{9}q+\frac{4}{9}a+\frac{4}{9}.\frac{7}{9}& \text{Uitwerken } \\ & =-aq-\frac{7}{9}q+\frac{4}{9}a+\frac{28}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-1}{16}+b)(q+\frac{-15}{7})& =(\color{red}{b}+\color{orange}{\frac{-1}{16}}).(\color{green}{q}+\color{blue}{\frac{-15}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{7})} + \color{orange}{(\frac{-1}{16})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{16})} . \color{blue}{(\frac{-15}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{15}{7}b-\frac{1}{16}q+\frac{1}{16}.\frac{15}{7}& \text{Uitwerken } \\ & =bq-\frac{15}{7}b-\frac{1}{16}q+\frac{15}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)