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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{1}{15})(q-\frac{-1}{19})& =(\color{red}{a}+\color{orange}{\frac{-1}{15}}).(\color{green}{q}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{19}a-\frac{1}{15}q-\frac{1}{15}.\frac{1}{19}& \text{Uitwerken } \\ & =aq+\frac{1}{19}a-\frac{1}{15}q-\frac{1}{285} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b-\frac{-20}{20})(p+\frac{-6}{17})& =(\color{red}{b}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-6}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-6}{17})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-6}{17})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{6}{17}b+1p-1.\frac{6}{17}& \text{Uitwerken } \\ & =bp-\frac{6}{17}b+1p-\frac{6}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-20}{7}-p)(\frac{9}{2}-b)& =(\color{red}{-p}+\color{orange}{\frac{-20}{7}}).(\color{green}{-b}+\color{blue}{\frac{9}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(\frac{9}{2})} + \color{orange}{(\frac{-20}{7})} . \color{green}{(-b)} + \color{orange}{(\frac{-20}{7})} . \color{blue}{(\frac{9}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{9}{2}p+\frac{20}{7}b-\frac{20}{7}.\frac{9}{2}& \text{Uitwerken } \\ & =bp-\frac{9}{2}p+\frac{20}{7}b-\frac{180}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{9}{2}p+\frac{20}{7}b-\frac{90}{7} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{2}{19}+x)(\frac{2}{9}-x)& =(\color{red}{x}+\color{orange}{\frac{2}{19}}).(\color{green}{-x}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{2}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{2}{19})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{2}{9}x-\frac{2}{19}x+\frac{2}{19}.\frac{2}{9}& \text{Uitwerken } \\ & =-x^2+(\frac{2}{9}+(\frac{-2}{19}))x+(\frac{-4}{171}) & \text{Neem samen} \\ &=-x^2+\frac{20}{171}x+(\frac{-4}{171}) & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(x-\frac{-3}{9})(a-\frac{-8}{2})& =(\color{red}{x}+\color{orange}{\frac{1}{3}}).(\color{green}{a}+\color{blue}{4})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(4)} + \color{orange}{(\frac{1}{3})} . \color{green}{(a)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = ax+4x+\frac{1}{3}a+\frac{1}{3}.4& \text{Uitwerken } \\ & =ax+4x+\frac{1}{3}a+\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b+\frac{-13}{9})(b+\frac{-3}{11})& =(\color{red}{b}+\color{orange}{\frac{-13}{9}}).(\color{green}{b}+\color{blue}{\frac{-3}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{11})} + \color{orange}{(\frac{-13}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{9})} . \color{blue}{(\frac{-3}{11})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{3}{11}b-\frac{13}{9}b+\frac{13}{9}.\frac{3}{11}& \text{Uitwerken } \\ & =b^2+((\frac{-3}{11})+(\frac{-13}{9}))b+\frac{39}{99} & \text{Neem samen} \\ &=b^2-\frac{170}{99}b+\frac{39}{99} & \text{Maak de som} \\ &=b^2-\frac{170}{99}b+\frac{13}{33} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
7. \(\begin{align}(\frac{18}{16}+x)(a+\frac{19}{2})& =(\color{red}{x}+\color{orange}{\frac{9}{8}}).(\color{green}{a}+\color{blue}{\frac{19}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{19}{2})} + \color{orange}{(\frac{9}{8})} . \color{green}{(a)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{19}{2})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{19}{2}x+\frac{9}{8}a+\frac{9}{8}.\frac{19}{2}& \text{Uitwerken } \\ & =ax+\frac{19}{2}x+\frac{9}{8}a+\frac{171}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p+\frac{-10}{7})(12+x)& =(\color{red}{p}+\color{orange}{\frac{-10}{7}}).(\color{green}{x}+\color{blue}{12})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(12)} + \color{orange}{(\frac{-10}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{7})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = px+12p-\frac{10}{7}x-\frac{10}{7}.12& \text{Uitwerken } \\ & =px+12p-\frac{10}{7}x-\frac{120}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+\frac{-8}{16})(\frac{-19}{16}+a)& =(\color{red}{x}+\color{orange}{\frac{-1}{2}}).(\color{green}{a}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{19}{16}x-\frac{1}{2}a+\frac{1}{2}.\frac{19}{16}& \text{Uitwerken } \\ & =ax-\frac{19}{16}x-\frac{1}{2}a+\frac{19}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{5}{4}+a)(q-\frac{14}{5})& =(\color{red}{a}+\color{orange}{\frac{5}{4}}).(\color{green}{q}+\color{blue}{\frac{-14}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-14}{5})} + \color{orange}{(\frac{5}{4})} . \color{green}{(q)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-14}{5})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{14}{5}a+\frac{5}{4}q-\frac{5}{4}.\frac{14}{5}& \text{Uitwerken } \\ & =aq-\frac{14}{5}a+\frac{5}{4}q-\frac{70}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{14}{5}a+\frac{5}{4}q-\frac{7}{2} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(x-\frac{10}{16})(a-\frac{13}{13})& =(\color{red}{x}+\color{orange}{\frac{-5}{8}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-5}{8})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{8})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1x-\frac{5}{8}a+\frac{5}{8}.1& \text{Uitwerken } \\ & =ax-1x-\frac{5}{8}a+\frac{5}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p+\frac{-20}{10})(\frac{-6}{7}+a)& =(\color{red}{p}+\color{orange}{(-2)}).(\color{green}{a}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(-2)} . \color{green}{(a)} + \color{orange}{(-2)} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{6}{7}p-2a+2.\frac{6}{7}& \text{Uitwerken } \\ & =ap-\frac{6}{7}p-2a+\frac{12}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)