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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{-15}{17})(q+\frac{17}{17})& =(\color{red}{b}+\color{orange}{\frac{-15}{17}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-15}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{17})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bq+1b-\frac{15}{17}q-\frac{15}{17}.1& \text{Uitwerken } \\ & =bq+1b-\frac{15}{17}q-\frac{15}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{1}{10}+x)(p+\frac{-13}{3})& =(\color{red}{x}+\color{orange}{\frac{1}{10}}).(\color{green}{p}+\color{blue}{\frac{-13}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-13}{3})} + \color{orange}{(\frac{1}{10})} . \color{green}{(p)} + \color{orange}{(\frac{1}{10})} . \color{blue}{(\frac{-13}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{13}{3}x+\frac{1}{10}p-\frac{1}{10}.\frac{13}{3}& \text{Uitwerken } \\ & =px-\frac{13}{3}x+\frac{1}{10}p-\frac{13}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(a-\frac{16}{7})(\frac{19}{19}+q)& =(\color{red}{a}+\color{orange}{\frac{-16}{7}}).(\color{green}{q}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{-16}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = aq+1a-\frac{16}{7}q-\frac{16}{7}.1& \text{Uitwerken } \\ & =aq+1a-\frac{16}{7}q-\frac{16}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{9}{7}-b)(q+12)& =(\color{red}{-b}+\color{orange}{\frac{9}{7}}).(\color{green}{q}+\color{blue}{12})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(12)} + \color{orange}{(\frac{9}{7})} . \color{green}{(q)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = -bq-12b+\frac{9}{7}q+\frac{9}{7}.12& \text{Uitwerken } \\ & =-bq-12b+\frac{9}{7}q+\frac{108}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-20}{7}-b)(a-\frac{7}{2})& =(\color{red}{-b}+\color{orange}{\frac{-20}{7}}).(\color{green}{a}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{-20}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-20}{7})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{7}{2}b-\frac{20}{7}a+\frac{20}{7}.\frac{7}{2}& \text{Uitwerken } \\ & =-ab+\frac{7}{2}b-\frac{20}{7}a+\frac{140}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+\frac{7}{2}b-\frac{20}{7}a+10 & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{1}{13}-a)(\frac{-4}{6}+b)& =(\color{red}{-a}+\color{orange}{\frac{1}{13}}).(\color{green}{b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{1}{13})} . \color{green}{(b)} + \color{orange}{(\frac{1}{13})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{2}{3}a+\frac{1}{13}b-\frac{1}{13}.\frac{2}{3}& \text{Uitwerken } \\ & =-ab+\frac{2}{3}a+\frac{1}{13}b-\frac{2}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{7}{3}-a)(\frac{-13}{10}-q)& =(\color{red}{-a}+\color{orange}{\frac{7}{3}}).(\color{green}{-q}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(\frac{7}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{13}{10}a-\frac{7}{3}q-\frac{7}{3}.\frac{13}{10}& \text{Uitwerken } \\ & =aq+\frac{13}{10}a-\frac{7}{3}q-\frac{91}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b-\frac{1}{15})(\frac{7}{19}+p)& =(\color{red}{b}+\color{orange}{\frac{-1}{15}}).(\color{green}{p}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(\frac{-1}{15})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{15})} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{7}{19}b-\frac{1}{15}p-\frac{1}{15}.\frac{7}{19}& \text{Uitwerken } \\ & =bp+\frac{7}{19}b-\frac{1}{15}p-\frac{7}{285} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p-\frac{-18}{11})(\frac{-15}{20}+q)& =(\color{red}{p}+\color{orange}{\frac{18}{11}}).(\color{green}{q}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{18}{11})} . \color{green}{(q)} + \color{orange}{(\frac{18}{11})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{3}{4}p+\frac{18}{11}q-\frac{18}{11}.\frac{3}{4}& \text{Uitwerken } \\ & =pq-\frac{3}{4}p+\frac{18}{11}q-\frac{54}{44} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{3}{4}p+\frac{18}{11}q-\frac{27}{22} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(b+\frac{12}{6})(p-\frac{9}{4})& =(\color{red}{b}+\color{orange}{2}).(\color{green}{p}+\color{blue}{\frac{-9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{4})} + \color{orange}{(2)} . \color{green}{(p)} + \color{orange}{(2)} . \color{blue}{(\frac{-9}{4})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{9}{4}b+2p-2.\frac{9}{4}& \text{Uitwerken } \\ & =bp-\frac{9}{4}b+2p-\frac{18}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{9}{4}b+2p-\frac{9}{2} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{3}{17}-q)(\frac{9}{19}+q)& =(\color{red}{-q}+\color{orange}{\frac{3}{17}}).(\color{green}{q}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(\frac{3}{17})} . \color{green}{(q)} + \color{orange}{(\frac{3}{17})} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{9}{19}q+\frac{3}{17}q+\frac{3}{17}.\frac{9}{19}& \text{Uitwerken } \\ & =-q^2+((\frac{-9}{19})+\frac{3}{17})q+(\frac{-27}{323}) & \text{Neem samen} \\ &=-q^2-\frac{96}{323}q+(\frac{-27}{323}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(x-\frac{18}{3})(\frac{11}{12}+q)& =(\color{red}{x}+\color{orange}{(-6)}).(\color{green}{q}+\color{blue}{\frac{11}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{11}{12})} + \color{orange}{(-6)} . \color{green}{(q)} + \color{orange}{(-6)} . \color{blue}{(\frac{11}{12})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{11}{12}x-6q-6.\frac{11}{12}& \text{Uitwerken } \\ & =qx+\frac{11}{12}x-6q-\frac{66}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{11}{12}x-6q-\frac{11}{2} & \text{Vereenvoudig} \\\end{align}\)