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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{8}{13})(\frac{-20}{19}-a)& =(\color{red}{a}+\color{orange}{\frac{8}{13}}).(\color{green}{-a}+\color{blue}{\frac{-20}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-20}{19})} + \color{orange}{(\frac{8}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{-20}{19})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{20}{19}a-\frac{8}{13}a-\frac{8}{13}.\frac{20}{19}& \text{Uitwerken } \\ & =-a^2+((\frac{-20}{19})+(\frac{-8}{13}))a-\frac{160}{247} & \text{Neem samen} \\ &=-a^2-\frac{412}{247}a-\frac{160}{247} & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(\frac{5}{13}-b)(\frac{-9}{12}-a)& =(\color{red}{-b}+\color{orange}{\frac{5}{13}}).(\color{green}{-a}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-a)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{5}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{3}{4}b-\frac{5}{13}a-\frac{5}{13}.\frac{3}{4}& \text{Uitwerken } \\ & =ab+\frac{3}{4}b-\frac{5}{13}a-\frac{15}{52} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{16}{2}-a)(b+\frac{-8}{17})& =(\color{red}{-a}+\color{orange}{8}).(\color{green}{b}+\color{blue}{\frac{-8}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(\frac{-8}{17})} + \color{orange}{(8)} . \color{green}{(b)} + \color{orange}{(8)} . \color{blue}{(\frac{-8}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{8}{17}a+8b-8.\frac{8}{17}& \text{Uitwerken } \\ & =-ab+\frac{8}{17}a+8b-\frac{64}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-5}{9}-p)(\frac{-1}{18}-a)& =(\color{red}{-p}+\color{orange}{\frac{-5}{9}}).(\color{green}{-a}+\color{blue}{\frac{-1}{18}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{18})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-1}{18})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{1}{18}p+\frac{5}{9}a+\frac{5}{9}.\frac{1}{18}& \text{Uitwerken } \\ & =ap+\frac{1}{18}p+\frac{5}{9}a+\frac{5}{162} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-4}{14}-a)(x+\frac{18}{19})& =(\color{red}{-a}+\color{orange}{\frac{-2}{7}}).(\color{green}{x}+\color{blue}{\frac{18}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{18}{19})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{18}{19})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{18}{19}a-\frac{2}{7}x-\frac{2}{7}.\frac{18}{19}& \text{Uitwerken } \\ & =-ax-\frac{18}{19}a-\frac{2}{7}x-\frac{36}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{-5}{17})(x-\frac{-2}{8})& =(\color{red}{a}+\color{orange}{\frac{-5}{17}}).(\color{green}{x}+\color{blue}{\frac{1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{1}{4})} + \color{orange}{(\frac{-5}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-5}{17})} . \color{blue}{(\frac{1}{4})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{1}{4}a-\frac{5}{17}x-\frac{5}{17}.\frac{1}{4}& \text{Uitwerken } \\ & =ax+\frac{1}{4}a-\frac{5}{17}x-\frac{5}{68} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-20}{10}+x)(q+\frac{-4}{5})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{4}{5}x-2q+2.\frac{4}{5}& \text{Uitwerken } \\ & =qx-\frac{4}{5}x-2q+\frac{8}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b+\frac{-16}{18})((-6)-a)& =(\color{red}{b}+\color{orange}{\frac{-8}{9}}).(\color{green}{-a}+\color{blue}{(-6)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(-6)} + \color{orange}{(\frac{-8}{9})} . \color{green}{(-a)} + \color{orange}{(\frac{-8}{9})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = -ab-6b+\frac{8}{9}a+\frac{8}{9}.6& \text{Uitwerken } \\ & =-ab-6b+\frac{8}{9}a+\frac{48}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-6b+\frac{8}{9}a+\frac{16}{3} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(a+\frac{3}{14})(\frac{2}{16}+b)& =(\color{red}{a}+\color{orange}{\frac{3}{14}}).(\color{green}{b}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{3}{14})} . \color{green}{(b)} + \color{orange}{(\frac{3}{14})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{1}{8}a+\frac{3}{14}b+\frac{3}{14}.\frac{1}{8}& \text{Uitwerken } \\ & =ab+\frac{1}{8}a+\frac{3}{14}b+\frac{3}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{7}{11}+a)(q-\frac{-17}{19})& =(\color{red}{a}+\color{orange}{\frac{7}{11}}).(\color{green}{q}+\color{blue}{\frac{17}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{17}{19})} + \color{orange}{(\frac{7}{11})} . \color{green}{(q)} + \color{orange}{(\frac{7}{11})} . \color{blue}{(\frac{17}{19})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{17}{19}a+\frac{7}{11}q+\frac{7}{11}.\frac{17}{19}& \text{Uitwerken } \\ & =aq+\frac{17}{19}a+\frac{7}{11}q+\frac{119}{209} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x+\frac{-5}{7})(b+\frac{3}{7})& =(\color{red}{x}+\color{orange}{\frac{-5}{7}}).(\color{green}{b}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{-5}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{7})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{7}x-\frac{5}{7}b-\frac{5}{7}.\frac{3}{7}& \text{Uitwerken } \\ & =bx+\frac{3}{7}x-\frac{5}{7}b-\frac{15}{49} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q-\frac{-14}{4})(\frac{2}{7}+x)& =(\color{red}{q}+\color{orange}{\frac{7}{2}}).(\color{green}{x}+\color{blue}{\frac{2}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{2}{7})} + \color{orange}{(\frac{7}{2})} . \color{green}{(x)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{2}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{2}{7}q+\frac{7}{2}x+\frac{7}{2}.\frac{2}{7}& \text{Uitwerken } \\ & =qx+\frac{2}{7}q+\frac{7}{2}x+\frac{14}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{2}{7}q+\frac{7}{2}x+1 & \text{Vereenvoudig} \\\end{align}\)