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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(q-\frac{9}{8})(x+\frac{-5}{14})& =(\color{red}{q}+\color{orange}{\frac{-9}{8}}).(\color{green}{x}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{5}{14}q-\frac{9}{8}x+\frac{9}{8}.\frac{5}{14}& \text{Uitwerken } \\ & =qx-\frac{5}{14}q-\frac{9}{8}x+\frac{45}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-10}{13}-b)(q+\frac{-2}{7})& =(\color{red}{-b}+\color{orange}{\frac{-10}{13}}).(\color{green}{q}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{-10}{13})} . \color{green}{(q)} + \color{orange}{(\frac{-10}{13})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{2}{7}b-\frac{10}{13}q+\frac{10}{13}.\frac{2}{7}& \text{Uitwerken } \\ & =-bq+\frac{2}{7}b-\frac{10}{13}q+\frac{20}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b+\frac{-6}{8})(x+\frac{15}{18})& =(\color{red}{b}+\color{orange}{\frac{-3}{4}}).(\color{green}{x}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{5}{6}b-\frac{3}{4}x-\frac{3}{4}.\frac{5}{6}& \text{Uitwerken } \\ & =bx+\frac{5}{6}b-\frac{3}{4}x-\frac{15}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{5}{6}b-\frac{3}{4}x-\frac{5}{8} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{5}{6}-q)(b-\frac{18}{2})& =(\color{red}{-q}+\color{orange}{\frac{5}{6}}).(\color{green}{b}+\color{blue}{(-9)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(-9)} + \color{orange}{(\frac{5}{6})} . \color{green}{(b)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(-9)}& \text{Boogjes en uitschrijven} \\ & = -bq+9q+\frac{5}{6}b-\frac{5}{6}.9& \text{Uitwerken } \\ & =-bq+9q+\frac{5}{6}b-\frac{45}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+9q+\frac{5}{6}b-\frac{15}{2} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(p-\frac{-4}{18})(x-\frac{-19}{19})& =(\color{red}{p}+\color{orange}{\frac{2}{9}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{2}{9})} . \color{green}{(x)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = px+1p+\frac{2}{9}x+\frac{2}{9}.1& \text{Uitwerken } \\ & =px+1p+\frac{2}{9}x+\frac{2}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{12}{9}+q)(a-\frac{3}{4})& =(\color{red}{q}+\color{orange}{\frac{4}{3}}).(\color{green}{a}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{3}{4}q+\frac{4}{3}a-\frac{4}{3}.\frac{3}{4}& \text{Uitwerken } \\ & =aq-\frac{3}{4}q+\frac{4}{3}a-\frac{12}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{3}{4}q+\frac{4}{3}a-1 & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{8}{17}-x)(b-\frac{8}{5})& =(\color{red}{-x}+\color{orange}{\frac{8}{17}}).(\color{green}{b}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{8}{17})} . \color{green}{(b)} + \color{orange}{(\frac{8}{17})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{8}{5}x+\frac{8}{17}b-\frac{8}{17}.\frac{8}{5}& \text{Uitwerken } \\ & =-bx+\frac{8}{5}x+\frac{8}{17}b-\frac{64}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p+\frac{-14}{10})(b+\frac{-16}{13})& =(\color{red}{p}+\color{orange}{\frac{-7}{5}}).(\color{green}{b}+\color{blue}{\frac{-16}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{13})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{-16}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{16}{13}p-\frac{7}{5}b+\frac{7}{5}.\frac{16}{13}& \text{Uitwerken } \\ & =bp-\frac{16}{13}p-\frac{7}{5}b+\frac{112}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p+\frac{-10}{6})(\frac{2}{4}-b)& =(\color{red}{p}+\color{orange}{\frac{-5}{3}}).(\color{green}{-b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{1}{2}p+\frac{5}{3}b-\frac{5}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =-bp+\frac{1}{2}p+\frac{5}{3}b-\frac{5}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x-\frac{11}{19})(\frac{-6}{4}+p)& =(\color{red}{x}+\color{orange}{\frac{-11}{19}}).(\color{green}{p}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-11}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{19})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{3}{2}x-\frac{11}{19}p+\frac{11}{19}.\frac{3}{2}& \text{Uitwerken } \\ & =px-\frac{3}{2}x-\frac{11}{19}p+\frac{33}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x+\frac{-6}{2})(\frac{-9}{15}+b)& =(\color{red}{x}+\color{orange}{(-3)}).(\color{green}{b}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(-3)} . \color{green}{(b)} + \color{orange}{(-3)} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{3}{5}x-3b+3.\frac{3}{5}& \text{Uitwerken } \\ & =bx-\frac{3}{5}x-3b+\frac{9}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{13}{9}-q)(\frac{11}{18}+a)& =(\color{red}{-q}+\color{orange}{\frac{13}{9}}).(\color{green}{a}+\color{blue}{\frac{11}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{11}{18})} + \color{orange}{(\frac{13}{9})} . \color{green}{(a)} + \color{orange}{(\frac{13}{9})} . \color{blue}{(\frac{11}{18})}& \text{Boogjes en uitschrijven} \\ & = -aq-\frac{11}{18}q+\frac{13}{9}a+\frac{13}{9}.\frac{11}{18}& \text{Uitwerken } \\ & =-aq-\frac{11}{18}q+\frac{13}{9}a+\frac{143}{162} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)