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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{20}{19}+a)(b-\frac{15}{18})& =(\color{red}{a}+\color{orange}{\frac{20}{19}}).(\color{green}{b}+\color{blue}{\frac{-5}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{6})} + \color{orange}{(\frac{20}{19})} . \color{green}{(b)} + \color{orange}{(\frac{20}{19})} . \color{blue}{(\frac{-5}{6})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{6}a+\frac{20}{19}b-\frac{20}{19}.\frac{5}{6}& \text{Uitwerken } \\ & =ab-\frac{5}{6}a+\frac{20}{19}b-\frac{100}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{5}{6}a+\frac{20}{19}b-\frac{50}{57} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-20}{16}+a)(x-\frac{15}{4})& =(\color{red}{a}+\color{orange}{\frac{-5}{4}}).(\color{green}{x}+\color{blue}{\frac{-15}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{4})} + \color{orange}{(\frac{-5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{4})} . \color{blue}{(\frac{-15}{4})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{15}{4}a-\frac{5}{4}x+\frac{5}{4}.\frac{15}{4}& \text{Uitwerken } \\ & =ax-\frac{15}{4}a-\frac{5}{4}x+\frac{75}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-10}{11}-a)(\frac{3}{4}+p)& =(\color{red}{-a}+\color{orange}{\frac{-10}{11}}).(\color{green}{p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{-10}{11})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{3}{4}a-\frac{10}{11}p-\frac{10}{11}.\frac{3}{4}& \text{Uitwerken } \\ & =-ap-\frac{3}{4}a-\frac{10}{11}p-\frac{30}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{3}{4}a-\frac{10}{11}p-\frac{15}{22} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{1}{15}+p)(\frac{-18}{19}-x)& =(\color{red}{p}+\color{orange}{\frac{1}{15}}).(\color{green}{-x}+\color{blue}{\frac{-18}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-18}{19})} + \color{orange}{(\frac{1}{15})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{15})} . \color{blue}{(\frac{-18}{19})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{18}{19}p-\frac{1}{15}x-\frac{1}{15}.\frac{18}{19}& \text{Uitwerken } \\ & =-px-\frac{18}{19}p-\frac{1}{15}x-\frac{18}{285} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{18}{19}p-\frac{1}{15}x-\frac{6}{95} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(x+\frac{-1}{7})(\frac{2}{2}+p)& =(\color{red}{x}+\color{orange}{\frac{-1}{7}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(\frac{-1}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = px+1x-\frac{1}{7}p-\frac{1}{7}.1& \text{Uitwerken } \\ & =px+1x-\frac{1}{7}p-\frac{1}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b+\frac{15}{5})(x+\frac{-17}{19})& =(\color{red}{b}+\color{orange}{3}).(\color{green}{x}+\color{blue}{\frac{-17}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-17}{19})} + \color{orange}{(3)} . \color{green}{(x)} + \color{orange}{(3)} . \color{blue}{(\frac{-17}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{17}{19}b+3x-3.\frac{17}{19}& \text{Uitwerken } \\ & =bx-\frac{17}{19}b+3x-\frac{51}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-3}{5}+q)(\frac{1}{2}-x)& =(\color{red}{q}+\color{orange}{\frac{-3}{5}}).(\color{green}{-x}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = -qx+\frac{1}{2}q+\frac{3}{5}x-\frac{3}{5}.\frac{1}{2}& \text{Uitwerken } \\ & =-qx+\frac{1}{2}q+\frac{3}{5}x-\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b+\frac{9}{9})(\frac{-2}{13}-a)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{-a}+\color{blue}{\frac{-2}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{13})} + \color{orange}{(1)} . \color{green}{(-a)} + \color{orange}{(1)} . \color{blue}{(\frac{-2}{13})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{2}{13}b-1a-1.\frac{2}{13}& \text{Uitwerken } \\ & =-ab-\frac{2}{13}b-1a-\frac{2}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p-\frac{4}{4})(q+\frac{2}{18})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{q}+\color{blue}{\frac{1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{9})} + \color{orange}{(-1)} . \color{green}{(q)} + \color{orange}{(-1)} . \color{blue}{(\frac{1}{9})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{9}p-1q-1.\frac{1}{9}& \text{Uitwerken } \\ & =pq+\frac{1}{9}p-1q-\frac{1}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{8}{18}-p)(x+\frac{-7}{9})& =(\color{red}{-p}+\color{orange}{\frac{4}{9}}).(\color{green}{x}+\color{blue}{\frac{-7}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-7}{9})} + \color{orange}{(\frac{4}{9})} . \color{green}{(x)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(\frac{-7}{9})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{7}{9}p+\frac{4}{9}x-\frac{4}{9}.\frac{7}{9}& \text{Uitwerken } \\ & =-px+\frac{7}{9}p+\frac{4}{9}x-\frac{28}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a+\frac{-18}{16})(\frac{-1}{10}-b)& =(\color{red}{a}+\color{orange}{\frac{-9}{8}}).(\color{green}{-b}+\color{blue}{\frac{-1}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{10})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(-b)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{-1}{10})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{10}a+\frac{9}{8}b+\frac{9}{8}.\frac{1}{10}& \text{Uitwerken } \\ & =-ab-\frac{1}{10}a+\frac{9}{8}b+\frac{9}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b+\frac{12}{20})(p+\frac{-20}{19})& =(\color{red}{b}+\color{orange}{\frac{3}{5}}).(\color{green}{p}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{3}{5})} . \color{green}{(p)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{20}{19}b+\frac{3}{5}p-\frac{3}{5}.\frac{20}{19}& \text{Uitwerken } \\ & =bp-\frac{20}{19}b+\frac{3}{5}p-\frac{60}{95} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{20}{19}b+\frac{3}{5}p-\frac{12}{19} & \text{Vereenvoudig} \\\end{align}\)