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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{3}{3})(a+\frac{-5}{9})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-5}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{9})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-5}{9})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{5}{9}a+1a-1.\frac{5}{9}& \text{Uitwerken } \\ & =a^2+((\frac{-5}{9})+1)a-(\frac{-5}{9}) & \text{Neem samen} \\ &=a^2+\frac{4}{9}a-(\frac{-5}{9}) & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(\frac{-19}{12}-b)(\frac{12}{19}-a)& =(\color{red}{-b}+\color{orange}{\frac{-19}{12}}).(\color{green}{-a}+\color{blue}{\frac{12}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{12}{19})} + \color{orange}{(\frac{-19}{12})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{12})} . \color{blue}{(\frac{12}{19})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{12}{19}b+\frac{19}{12}a-\frac{19}{12}.\frac{12}{19}& \text{Uitwerken } \\ & =ab-\frac{12}{19}b+\frac{19}{12}a-\frac{228}{228} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{12}{19}b+\frac{19}{12}a-1 & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(b-\frac{-4}{11})(a-\frac{-5}{9})& =(\color{red}{b}+\color{orange}{\frac{4}{11}}).(\color{green}{a}+\color{blue}{\frac{5}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{5}{9})} + \color{orange}{(\frac{4}{11})} . \color{green}{(a)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(\frac{5}{9})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{9}b+\frac{4}{11}a+\frac{4}{11}.\frac{5}{9}& \text{Uitwerken } \\ & =ab+\frac{5}{9}b+\frac{4}{11}a+\frac{20}{99} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-7}{16}+p)(b+2)& =(\color{red}{p}+\color{orange}{\frac{-7}{16}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{-7}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{16})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bp+2p-\frac{7}{16}b-\frac{7}{16}.2& \text{Uitwerken } \\ & =bp+2p-\frac{7}{16}b-\frac{14}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+2p-\frac{7}{16}b-\frac{7}{8} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-11}{13}+q)(x+\frac{-12}{7})& =(\color{red}{q}+\color{orange}{\frac{-11}{13}}).(\color{green}{x}+\color{blue}{\frac{-12}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-12}{7})} + \color{orange}{(\frac{-11}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{13})} . \color{blue}{(\frac{-12}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{12}{7}q-\frac{11}{13}x+\frac{11}{13}.\frac{12}{7}& \text{Uitwerken } \\ & =qx-\frac{12}{7}q-\frac{11}{13}x+\frac{132}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{10}{8}-b)(\frac{16}{16}-x)& =(\color{red}{-b}+\color{orange}{\frac{5}{4}}).(\color{green}{-x}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(1)} + \color{orange}{(\frac{5}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx-1b-\frac{5}{4}x+\frac{5}{4}.1& \text{Uitwerken } \\ & =bx-1b-\frac{5}{4}x+\frac{5}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b+\frac{6}{14})(p-\frac{-2}{3})& =(\color{red}{b}+\color{orange}{\frac{3}{7}}).(\color{green}{p}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{3}{7})} . \color{green}{(p)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{2}{3}b+\frac{3}{7}p+\frac{3}{7}.\frac{2}{3}& \text{Uitwerken } \\ & =bp+\frac{2}{3}b+\frac{3}{7}p+\frac{6}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{2}{3}b+\frac{3}{7}p+\frac{2}{7} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(a-\frac{-11}{5})(\frac{6}{19}+x)& =(\color{red}{a}+\color{orange}{\frac{11}{5}}).(\color{green}{x}+\color{blue}{\frac{6}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{6}{19})} + \color{orange}{(\frac{11}{5})} . \color{green}{(x)} + \color{orange}{(\frac{11}{5})} . \color{blue}{(\frac{6}{19})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{6}{19}a+\frac{11}{5}x+\frac{11}{5}.\frac{6}{19}& \text{Uitwerken } \\ & =ax+\frac{6}{19}a+\frac{11}{5}x+\frac{66}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+(-11))(\frac{3}{17}-a)& =(\color{red}{x}+\color{orange}{(-11)}).(\color{green}{-a}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(-11)} . \color{green}{(-a)} + \color{orange}{(-11)} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{3}{17}x+11a-11.\frac{3}{17}& \text{Uitwerken } \\ & =-ax+\frac{3}{17}x+11a-\frac{33}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{7}{16}-x)(a+\frac{-19}{2})& =(\color{red}{-x}+\color{orange}{\frac{7}{16}}).(\color{green}{a}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(\frac{7}{16})} . \color{green}{(a)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{19}{2}x+\frac{7}{16}a-\frac{7}{16}.\frac{19}{2}& \text{Uitwerken } \\ & =-ax+\frac{19}{2}x+\frac{7}{16}a-\frac{133}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-3}{17}-q)(\frac{10}{3}-p)& =(\color{red}{-q}+\color{orange}{\frac{-3}{17}}).(\color{green}{-p}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{-3}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-3}{17})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{10}{3}q+\frac{3}{17}p-\frac{3}{17}.\frac{10}{3}& \text{Uitwerken } \\ & =pq-\frac{10}{3}q+\frac{3}{17}p-\frac{30}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{10}{3}q+\frac{3}{17}p-\frac{10}{17} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(q+\frac{3}{3})(\frac{-10}{8}+q)& =(\color{red}{q}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{-5}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{4})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{-5}{4})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{5}{4}q+1q-1.\frac{5}{4}& \text{Uitwerken } \\ & =q^2+((\frac{-5}{4})+1)q-(\frac{-5}{4}) & \text{Neem samen} \\ &=q^2-\frac{1}{4}q-(\frac{-5}{4}) & \text{Maak de som} \\\end{align}\)