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

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1. \((p+\frac{20}{19})(\frac{-3}{7}+b)\)
2. \((\frac{1}{18}+b)(q-\frac{5}{8})\)
3. \((\frac{-9}{18}-x)(x-\frac{-12}{4})\)
4. \((\frac{-2}{14}+p)(\frac{-6}{3}+q)\)
5. \((\frac{-15}{20}-x)(x-\frac{3}{14})\)
6. \((\frac{-17}{9}-a)(q-\frac{5}{13})\)
7. \((\frac{-18}{9}+b)(b-\frac{-20}{17})\)
8. \((x+\frac{-20}{12})(\frac{14}{6}+a)\)
9. \((a+\frac{-13}{12})(\frac{11}{9}-x)\)
10. \((q-\frac{9}{4})(b-\frac{-20}{16})\)
11. \((x-\frac{-7}{9})(x+\frac{6}{13})\)
12. \((\frac{16}{20}+q)(b+\frac{-10}{17})\)

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{20}{19})(\frac{-3}{7}+b)& =(\color{red}{p}+\color{orange}{\frac{20}{19}}).(\color{green}{b}+\color{blue}{\frac{-3}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{7})} + \color{orange}{(\frac{20}{19})} . \color{green}{(b)} + \color{orange}{(\frac{20}{19})} . \color{blue}{(\frac{-3}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{7}p+\frac{20}{19}b-\frac{20}{19}.\frac{3}{7}& \text{Uitwerken } \\ & =bp-\frac{3}{7}p+\frac{20}{19}b-\frac{60}{133} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{1}{18}+b)(q-\frac{5}{8})& =(\color{red}{b}+\color{orange}{\frac{1}{18}}).(\color{green}{q}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{1}{18})} . \color{green}{(q)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{5}{8}b+\frac{1}{18}q-\frac{1}{18}.\frac{5}{8}& \text{Uitwerken } \\ & =bq-\frac{5}{8}b+\frac{1}{18}q-\frac{5}{144} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-9}{18}-x)(x-\frac{-12}{4})& =(\color{red}{-x}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(3)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -xx-3x-\frac{1}{2}x-\frac{1}{2}.3& \text{Uitwerken } \\ & =-x^2+((-3)+(\frac{-1}{2}))x-\frac{3}{2} & \text{Neem samen} \\ &=-x^2-\frac{7}{2}x-\frac{3}{2} & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{-2}{14}+p)(\frac{-6}{3}+q)& =(\color{red}{p}+\color{orange}{\frac{-1}{7}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(-2)} + \color{orange}{(\frac{-1}{7})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = pq-2p-\frac{1}{7}q+\frac{1}{7}.2& \text{Uitwerken } \\ & =pq-2p-\frac{1}{7}q+\frac{2}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-15}{20}-x)(x-\frac{3}{14})& =(\color{red}{-x}+\color{orange}{\frac{-3}{4}}).(\color{green}{x}+\color{blue}{\frac{-3}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-3}{14})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-3}{14})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{3}{14}x-\frac{3}{4}x+\frac{3}{4}.\frac{3}{14}& \text{Uitwerken } \\ & =-x^2+(\frac{3}{14}+(\frac{-3}{4}))x+(\frac{-9}{56}) & \text{Neem samen} \\ &=-x^2-\frac{15}{28}x+(\frac{-9}{56}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{-17}{9}-a)(q-\frac{5}{13})& =(\color{red}{-a}+\color{orange}{\frac{-17}{9}}).(\color{green}{q}+\color{blue}{\frac{-5}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(\frac{-5}{13})} + \color{orange}{(\frac{-17}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-17}{9})} . \color{blue}{(\frac{-5}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{5}{13}a-\frac{17}{9}q+\frac{17}{9}.\frac{5}{13}& \text{Uitwerken } \\ & =-aq+\frac{5}{13}a-\frac{17}{9}q+\frac{85}{117} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-18}{9}+b)(b-\frac{-20}{17})& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{20}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{20}{17})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{20}{17})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{20}{17}b-2b-2.\frac{20}{17}& \text{Uitwerken } \\ & =b^2+(\frac{20}{17}+(-2))b-(\frac{-40}{17}) & \text{Neem samen} \\ &=b^2-\frac{14}{17}b-(\frac{-40}{17}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(x+\frac{-20}{12})(\frac{14}{6}+a)& =(\color{red}{x}+\color{orange}{\frac{-5}{3}}).(\color{green}{a}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{7}{3}x-\frac{5}{3}a-\frac{5}{3}.\frac{7}{3}& \text{Uitwerken } \\ & =ax+\frac{7}{3}x-\frac{5}{3}a-\frac{35}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a+\frac{-13}{12})(\frac{11}{9}-x)& =(\color{red}{a}+\color{orange}{\frac{-13}{12}}).(\color{green}{-x}+\color{blue}{\frac{11}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{11}{9})} + \color{orange}{(\frac{-13}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{-13}{12})} . \color{blue}{(\frac{11}{9})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{11}{9}a+\frac{13}{12}x-\frac{13}{12}.\frac{11}{9}& \text{Uitwerken } \\ & =-ax+\frac{11}{9}a+\frac{13}{12}x-\frac{143}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(q-\frac{9}{4})(b-\frac{-20}{16})& =(\color{red}{q}+\color{orange}{\frac{-9}{4}}).(\color{green}{b}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{5}{4}q-\frac{9}{4}b-\frac{9}{4}.\frac{5}{4}& \text{Uitwerken } \\ & =bq+\frac{5}{4}q-\frac{9}{4}b-\frac{45}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x-\frac{-7}{9})(x+\frac{6}{13})& =(\color{red}{x}+\color{orange}{\frac{7}{9}}).(\color{green}{x}+\color{blue}{\frac{6}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{6}{13})} + \color{orange}{(\frac{7}{9})} . \color{green}{(x)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{6}{13})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{6}{13}x+\frac{7}{9}x+\frac{7}{9}.\frac{6}{13}& \text{Uitwerken } \\ & =x^2+(\frac{6}{13}+\frac{7}{9})x+\frac{42}{117} & \text{Neem samen} \\ &=x^2+\frac{145}{117}x+\frac{42}{117} & \text{Maak de som} \\ &=x^2+\frac{145}{117}x+\frac{14}{39} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
12. \(\begin{align}(\frac{16}{20}+q)(b+\frac{-10}{17})& =(\color{red}{q}+\color{orange}{\frac{4}{5}}).(\color{green}{b}+\color{blue}{\frac{-10}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{17})} + \color{orange}{(\frac{4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-10}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{10}{17}q+\frac{4}{5}b-\frac{4}{5}.\frac{10}{17}& \text{Uitwerken } \\ & =bq-\frac{10}{17}q+\frac{4}{5}b-\frac{40}{85} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-\frac{10}{17}q+\frac{4}{5}b-\frac{8}{17} & \text{Vereenvoudig} \\\end{align}\)