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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{1}{10}-p)(x-\frac{-5}{9})& =(\color{red}{-p}+\color{orange}{\frac{1}{10}}).(\color{green}{x}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{1}{10})} . \color{green}{(x)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{5}{9}p+\frac{1}{10}x+\frac{1}{10}.\frac{5}{9}& \text{Uitwerken } \\ & =-px-\frac{5}{9}p+\frac{1}{10}x+\frac{5}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{5}{9}p+\frac{1}{10}x+\frac{1}{18} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(a-\frac{-10}{4})(\frac{-2}{4}-q)& =(\color{red}{a}+\color{orange}{\frac{5}{2}}).(\color{green}{-q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{5}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{5}{2})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{1}{2}a-\frac{5}{2}q-\frac{5}{2}.\frac{1}{2}& \text{Uitwerken } \\ & =-aq-\frac{1}{2}a-\frac{5}{2}q-\frac{5}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b+\frac{7}{7})(\frac{1}{2}-x)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{-x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(1)} . \color{green}{(-x)} + \color{orange}{(1)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{1}{2}b-1x+1.\frac{1}{2}& \text{Uitwerken } \\ & =-bx+\frac{1}{2}b-1x+\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-15}{11}+q)(q-\frac{-12}{6})& =(\color{red}{q}+\color{orange}{\frac{-15}{11}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(2)} + \color{orange}{(\frac{-15}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{11})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = qq+2q-\frac{15}{11}q-\frac{15}{11}.2& \text{Uitwerken } \\ & =q^2+(2+(\frac{-15}{11}))q-(\frac{-30}{11}) & \text{Neem samen} \\ &=q^2+\frac{7}{11}q-(\frac{-30}{11}) & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(b-\frac{-18}{7})(\frac{-18}{10}+b)& =(\color{red}{b}+\color{orange}{\frac{18}{7}}).(\color{green}{b}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{18}{7})} . \color{green}{(b)} + \color{orange}{(\frac{18}{7})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{9}{5}b+\frac{18}{7}b-\frac{18}{7}.\frac{9}{5}& \text{Uitwerken } \\ & =b^2+((\frac{-9}{5})+\frac{18}{7})b-(\frac{-162}{35}) & \text{Neem samen} \\ &=b^2+\frac{27}{35}b-(\frac{-162}{35}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(b+\frac{-10}{4})(p+\frac{18}{19})& =(\color{red}{b}+\color{orange}{\frac{-5}{2}}).(\color{green}{p}+\color{blue}{\frac{18}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{18}{19})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{18}{19})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{18}{19}b-\frac{5}{2}p-\frac{5}{2}.\frac{18}{19}& \text{Uitwerken } \\ & =bp+\frac{18}{19}b-\frac{5}{2}p-\frac{90}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{18}{19}b-\frac{5}{2}p-\frac{45}{19} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-6}{6}+q)(\frac{-13}{18}+a)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{13}{18}q-1a+1.\frac{13}{18}& \text{Uitwerken } \\ & =aq-\frac{13}{18}q-1a+\frac{13}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-16}{3}+a)(\frac{15}{5}+b)& =(\color{red}{a}+\color{orange}{\frac{-16}{3}}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(3)} + \color{orange}{(\frac{-16}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{3})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = ab+3a-\frac{16}{3}b-\frac{16}{3}.3& \text{Uitwerken } \\ & =ab+3a-\frac{16}{3}b-\frac{48}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+3a-\frac{16}{3}b-16 & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(b+\frac{6}{16})(\frac{11}{6}+x)& =(\color{red}{b}+\color{orange}{\frac{3}{8}}).(\color{green}{x}+\color{blue}{\frac{11}{6}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{11}{6})} + \color{orange}{(\frac{3}{8})} . \color{green}{(x)} + \color{orange}{(\frac{3}{8})} . \color{blue}{(\frac{11}{6})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{6}b+\frac{3}{8}x+\frac{3}{8}.\frac{11}{6}& \text{Uitwerken } \\ & =bx+\frac{11}{6}b+\frac{3}{8}x+\frac{33}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{11}{6}b+\frac{3}{8}x+\frac{11}{16} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(q-\frac{20}{14})(\frac{-19}{12}-p)& =(\color{red}{q}+\color{orange}{\frac{-10}{7}}).(\color{green}{-p}+\color{blue}{\frac{-19}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-19}{12})} + \color{orange}{(\frac{-10}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(\frac{-19}{12})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{19}{12}q+\frac{10}{7}p+\frac{10}{7}.\frac{19}{12}& \text{Uitwerken } \\ & =-pq-\frac{19}{12}q+\frac{10}{7}p+\frac{190}{84} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{19}{12}q+\frac{10}{7}p+\frac{95}{42} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(q+\frac{20}{10})(\frac{-6}{13}+x)& =(\color{red}{q}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{6}{13}q+2x-2.\frac{6}{13}& \text{Uitwerken } \\ & =qx-\frac{6}{13}q+2x-\frac{12}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-7}{2}-x)(\frac{18}{14}-a)& =(\color{red}{-x}+\color{orange}{\frac{-7}{2}}).(\color{green}{-a}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-a)} + \color{red}{(-x)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{-7}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{2})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{9}{7}x+\frac{7}{2}a-\frac{7}{2}.\frac{9}{7}& \text{Uitwerken } \\ & =ax-\frac{9}{7}x+\frac{7}{2}a-\frac{63}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{9}{7}x+\frac{7}{2}a-\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)