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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{-7}{15})(x-\frac{-9}{11})& =(\color{red}{b}+\color{orange}{\frac{-7}{15}}).(\color{green}{x}+\color{blue}{\frac{9}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{9}{11})} + \color{orange}{(\frac{-7}{15})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{15})} . \color{blue}{(\frac{9}{11})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{9}{11}b-\frac{7}{15}x-\frac{7}{15}.\frac{9}{11}& \text{Uitwerken } \\ & =bx+\frac{9}{11}b-\frac{7}{15}x-\frac{63}{165} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{9}{11}b-\frac{7}{15}x-\frac{21}{55} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(p-\frac{-10}{8})(x-\frac{20}{15})& =(\color{red}{p}+\color{orange}{\frac{5}{4}}).(\color{green}{x}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{5}{4})} . \color{green}{(x)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{4}{3}p+\frac{5}{4}x-\frac{5}{4}.\frac{4}{3}& \text{Uitwerken } \\ & =px-\frac{4}{3}p+\frac{5}{4}x-\frac{20}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{4}{3}p+\frac{5}{4}x-\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(p-\frac{-15}{7})(\frac{4}{2}+b)& =(\color{red}{p}+\color{orange}{\frac{15}{7}}).(\color{green}{b}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{15}{7})} . \color{green}{(b)} + \color{orange}{(\frac{15}{7})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bp+2p+\frac{15}{7}b+\frac{15}{7}.2& \text{Uitwerken } \\ & =bp+2p+\frac{15}{7}b+\frac{30}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a-\frac{19}{17})(\frac{4}{4}-a)& =(\color{red}{a}+\color{orange}{\frac{-19}{17}}).(\color{green}{-a}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{-19}{17})} . \color{green}{(-a)} + \color{orange}{(\frac{-19}{17})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -aa+1a+\frac{19}{17}a-\frac{19}{17}.1& \text{Uitwerken } \\ & =-a^2+(1+\frac{19}{17})a-\frac{19}{17} & \text{Neem samen} \\ &=-a^2+\frac{36}{17}a-\frac{19}{17} & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(a-\frac{19}{17})(p+\frac{6}{15})& =(\color{red}{a}+\color{orange}{\frac{-19}{17}}).(\color{green}{p}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-19}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{17})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{2}{5}a-\frac{19}{17}p-\frac{19}{17}.\frac{2}{5}& \text{Uitwerken } \\ & =ap+\frac{2}{5}a-\frac{19}{17}p-\frac{38}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{4}{11}-q)(\frac{-15}{8}-p)& =(\color{red}{-q}+\color{orange}{\frac{4}{11}}).(\color{green}{-p}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-p)} + \color{red}{(-q)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{4}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{15}{8}q-\frac{4}{11}p-\frac{4}{11}.\frac{15}{8}& \text{Uitwerken } \\ & =pq+\frac{15}{8}q-\frac{4}{11}p-\frac{60}{88} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{15}{8}q-\frac{4}{11}p-\frac{15}{22} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(x+\frac{-9}{5})((-12)-a)& =(\color{red}{x}+\color{orange}{\frac{-9}{5}}).(\color{green}{-a}+\color{blue}{(-12)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-a)} + \color{red}{(x)} . \color{blue}{(-12)} + \color{orange}{(\frac{-9}{5})} . \color{green}{(-a)} + \color{orange}{(\frac{-9}{5})} . \color{blue}{(-12)}& \text{Boogjes en uitschrijven} \\ & = -ax-12x+\frac{9}{5}a+\frac{9}{5}.12& \text{Uitwerken } \\ & =-ax-12x+\frac{9}{5}a+\frac{108}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{5}{15}-x)(b+\frac{15}{20})& =(\color{red}{-x}+\color{orange}{\frac{1}{3}}).(\color{green}{b}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{3}{4}x+\frac{1}{3}b+\frac{1}{3}.\frac{3}{4}& \text{Uitwerken } \\ & =-bx-\frac{3}{4}x+\frac{1}{3}b+\frac{3}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{3}{4}x+\frac{1}{3}b+\frac{1}{4} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(q-\frac{-16}{17})(\frac{-16}{6}+a)& =(\color{red}{q}+\color{orange}{\frac{16}{17}}).(\color{green}{a}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{16}{17})} . \color{green}{(a)} + \color{orange}{(\frac{16}{17})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{8}{3}q+\frac{16}{17}a-\frac{16}{17}.\frac{8}{3}& \text{Uitwerken } \\ & =aq-\frac{8}{3}q+\frac{16}{17}a-\frac{128}{51} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{6}{3}-a)(\frac{7}{12}-q)& =(\color{red}{-a}+\color{orange}{2}).(\color{green}{-q}+\color{blue}{\frac{7}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{12})} + \color{orange}{(2)} . \color{green}{(-q)} + \color{orange}{(2)} . \color{blue}{(\frac{7}{12})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{7}{12}a-2q+2.\frac{7}{12}& \text{Uitwerken } \\ & =aq-\frac{7}{12}a-2q+\frac{14}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{7}{12}a-2q+\frac{7}{6} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(p+\frac{-5}{2})(q-\frac{-16}{8})& =(\color{red}{p}+\color{orange}{\frac{-5}{2}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{-5}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = pq+2p-\frac{5}{2}q-\frac{5}{2}.2& \text{Uitwerken } \\ & =pq+2p-\frac{5}{2}q-\frac{10}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+2p-\frac{5}{2}q-5 & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{1}{10}-x)(p+\frac{20}{19})& =(\color{red}{-x}+\color{orange}{\frac{1}{10}}).(\color{green}{p}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{1}{10})} . \color{green}{(p)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{20}{19}x+\frac{1}{10}p+\frac{1}{10}.\frac{20}{19}& \text{Uitwerken } \\ & =-px-\frac{20}{19}x+\frac{1}{10}p+\frac{20}{190} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{20}{19}x+\frac{1}{10}p+\frac{2}{19} & \text{Vereenvoudig} \\\end{align}\)