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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b-\frac{20}{3})(a+\frac{7}{6})& =(\color{red}{b}+\color{orange}{\frac{-20}{3}}).(\color{green}{a}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(\frac{-20}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{7}{6}b-\frac{20}{3}a-\frac{20}{3}.\frac{7}{6}& \text{Uitwerken } \\ & =ab+\frac{7}{6}b-\frac{20}{3}a-\frac{140}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{7}{6}b-\frac{20}{3}a-\frac{70}{9} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(x-\frac{-13}{19})(q+\frac{-8}{14})& =(\color{red}{x}+\color{orange}{\frac{13}{19}}).(\color{green}{q}+\color{blue}{\frac{-4}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{7})} + \color{orange}{(\frac{13}{19})} . \color{green}{(q)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{-4}{7})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{4}{7}x+\frac{13}{19}q-\frac{13}{19}.\frac{4}{7}& \text{Uitwerken } \\ & =qx-\frac{4}{7}x+\frac{13}{19}q-\frac{52}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q-\frac{20}{8})(p+\frac{-18}{6})& =(\color{red}{q}+\color{orange}{\frac{-5}{2}}).(\color{green}{p}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(-3)} + \color{orange}{(\frac{-5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = pq-3q-\frac{5}{2}p+\frac{5}{2}.3& \text{Uitwerken } \\ & =pq-3q-\frac{5}{2}p+\frac{15}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-3}{12}-b)(b+\frac{1}{10})& =(\color{red}{-b}+\color{orange}{\frac{-1}{4}}).(\color{green}{b}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{1}{10}b-\frac{1}{4}b-\frac{1}{4}.\frac{1}{10}& \text{Uitwerken } \\ & =-b^2+((\frac{-1}{10})+(\frac{-1}{4}))b-\frac{1}{40} & \text{Neem samen} \\ &=-b^2-\frac{7}{20}b-\frac{1}{40} & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(x+\frac{-8}{5})(\frac{-11}{19}+b)& =(\color{red}{x}+\color{orange}{\frac{-8}{5}}).(\color{green}{b}+\color{blue}{\frac{-11}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-11}{19})} + \color{orange}{(\frac{-8}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{5})} . \color{blue}{(\frac{-11}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{11}{19}x-\frac{8}{5}b+\frac{8}{5}.\frac{11}{19}& \text{Uitwerken } \\ & =bx-\frac{11}{19}x-\frac{8}{5}b+\frac{88}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{2}{17}-b)(q+\frac{-14}{4})& =(\color{red}{-b}+\color{orange}{\frac{2}{17}}).(\color{green}{q}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{2}{17})} . \color{green}{(q)} + \color{orange}{(\frac{2}{17})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{7}{2}b+\frac{2}{17}q-\frac{2}{17}.\frac{7}{2}& \text{Uitwerken } \\ & =-bq+\frac{7}{2}b+\frac{2}{17}q-\frac{14}{34} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{7}{2}b+\frac{2}{17}q-\frac{7}{17} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(q-\frac{4}{18})(\frac{-8}{12}-q)& =(\color{red}{q}+\color{orange}{\frac{-2}{9}}).(\color{green}{-q}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{2}{3}q+\frac{2}{9}q+\frac{2}{9}.\frac{2}{3}& \text{Uitwerken } \\ & =-q^2+((\frac{-2}{3})+\frac{2}{9})q+(\frac{-4}{27}) & \text{Neem samen} \\ &=-q^2-\frac{4}{9}q+(\frac{-4}{27}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(x+\frac{14}{6})(\frac{-10}{19}-b)& =(\color{red}{x}+\color{orange}{\frac{7}{3}}).(\color{green}{-b}+\color{blue}{\frac{-10}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-10}{19})} + \color{orange}{(\frac{7}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{-10}{19})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{10}{19}x-\frac{7}{3}b-\frac{7}{3}.\frac{10}{19}& \text{Uitwerken } \\ & =-bx-\frac{10}{19}x-\frac{7}{3}b-\frac{70}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{13}{12}+x)(q+(-7))& =(\color{red}{x}+\color{orange}{\frac{13}{12}}).(\color{green}{q}+\color{blue}{(-7)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(-7)} + \color{orange}{(\frac{13}{12})} . \color{green}{(q)} + \color{orange}{(\frac{13}{12})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = qx-7x+\frac{13}{12}q-\frac{13}{12}.7& \text{Uitwerken } \\ & =qx-7x+\frac{13}{12}q-\frac{91}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-7}{18}+p)(\frac{-13}{18}-b)& =(\color{red}{p}+\color{orange}{\frac{-7}{18}}).(\color{green}{-b}+\color{blue}{\frac{-13}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{18})} + \color{orange}{(\frac{-7}{18})} . \color{green}{(-b)} + \color{orange}{(\frac{-7}{18})} . \color{blue}{(\frac{-13}{18})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{13}{18}p+\frac{7}{18}b+\frac{7}{18}.\frac{13}{18}& \text{Uitwerken } \\ & =-bp-\frac{13}{18}p+\frac{7}{18}b+\frac{91}{324} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p+\frac{-4}{12})(4-q)& =(\color{red}{p}+\color{orange}{\frac{-1}{3}}).(\color{green}{-q}+\color{blue}{4})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(4)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = -pq+4p+\frac{1}{3}q-\frac{1}{3}.4& \text{Uitwerken } \\ & =-pq+4p+\frac{1}{3}q-\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{13}{19}+a)(\frac{3}{15}+a)& =(\color{red}{a}+\color{orange}{\frac{13}{19}}).(\color{green}{a}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{13}{19})} . \color{green}{(a)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{1}{5}a+\frac{13}{19}a+\frac{13}{19}.\frac{1}{5}& \text{Uitwerken } \\ & =a^2+(\frac{1}{5}+\frac{13}{19})a+\frac{13}{95} & \text{Neem samen} \\ &=a^2+\frac{84}{95}a+\frac{13}{95} & \text{Maak de som} \\\end{align}\)