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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{14}{20})(q-\frac{16}{14})& =(\color{red}{p}+\color{orange}{\frac{-7}{10}}).(\color{green}{q}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{-7}{10})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{10})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{8}{7}p-\frac{7}{10}q+\frac{7}{10}.\frac{8}{7}& \text{Uitwerken } \\ & =pq-\frac{8}{7}p-\frac{7}{10}q+\frac{56}{70} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{8}{7}p-\frac{7}{10}q+\frac{4}{5} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(q+\frac{5}{13})(a+\frac{7}{3})& =(\color{red}{q}+\color{orange}{\frac{5}{13}}).(\color{green}{a}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{5}{13})} . \color{green}{(a)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{3}q+\frac{5}{13}a+\frac{5}{13}.\frac{7}{3}& \text{Uitwerken } \\ & =aq+\frac{7}{3}q+\frac{5}{13}a+\frac{35}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b+\frac{-1}{17})(\frac{3}{8}-p)& =(\color{red}{b}+\color{orange}{\frac{-1}{17}}).(\color{green}{-p}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{-1}{17})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{3}{8}b+\frac{1}{17}p-\frac{1}{17}.\frac{3}{8}& \text{Uitwerken } \\ & =-bp+\frac{3}{8}b+\frac{1}{17}p-\frac{3}{136} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q-\frac{15}{9})(\frac{-12}{8}-p)& =(\color{red}{q}+\color{orange}{\frac{-5}{3}}).(\color{green}{-p}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{3}{2}q+\frac{5}{3}p+\frac{5}{3}.\frac{3}{2}& \text{Uitwerken } \\ & =-pq-\frac{3}{2}q+\frac{5}{3}p+\frac{15}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{3}{2}q+\frac{5}{3}p+\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(p+\frac{-5}{17})(b-\frac{-18}{20})& =(\color{red}{p}+\color{orange}{\frac{-5}{17}}).(\color{green}{b}+\color{blue}{\frac{9}{10}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{10})} + \color{orange}{(\frac{-5}{17})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{17})} . \color{blue}{(\frac{9}{10})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{10}p-\frac{5}{17}b-\frac{5}{17}.\frac{9}{10}& \text{Uitwerken } \\ & =bp+\frac{9}{10}p-\frac{5}{17}b-\frac{45}{170} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{9}{10}p-\frac{5}{17}b-\frac{9}{34} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(x+\frac{-12}{6})(p+\frac{16}{20})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{4}{5}x-2p-2.\frac{4}{5}& \text{Uitwerken } \\ & =px+\frac{4}{5}x-2p-\frac{8}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{9}{10}+q)(p-\frac{-7}{13})& =(\color{red}{q}+\color{orange}{\frac{9}{10}}).(\color{green}{p}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(\frac{9}{10})} . \color{green}{(p)} + \color{orange}{(\frac{9}{10})} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{7}{13}q+\frac{9}{10}p+\frac{9}{10}.\frac{7}{13}& \text{Uitwerken } \\ & =pq+\frac{7}{13}q+\frac{9}{10}p+\frac{63}{130} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-10}{4}-p)(a+\frac{10}{3})& =(\color{red}{-p}+\color{orange}{\frac{-5}{2}}).(\color{green}{a}+\color{blue}{\frac{10}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{10}{3})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{10}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{10}{3}p-\frac{5}{2}a-\frac{5}{2}.\frac{10}{3}& \text{Uitwerken } \\ & =-ap-\frac{10}{3}p-\frac{5}{2}a-\frac{50}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{10}{3}p-\frac{5}{2}a-\frac{25}{3} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(a-\frac{2}{3})(\frac{-15}{6}+b)& =(\color{red}{a}+\color{orange}{\frac{-2}{3}}).(\color{green}{b}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{2}a-\frac{2}{3}b+\frac{2}{3}.\frac{5}{2}& \text{Uitwerken } \\ & =ab-\frac{5}{2}a-\frac{2}{3}b+\frac{10}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{5}{2}a-\frac{2}{3}b+\frac{5}{3} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-11}{16}-x)(\frac{20}{14}+b)& =(\color{red}{-x}+\color{orange}{\frac{-11}{16}}).(\color{green}{b}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(b)} + \color{red}{(-x)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{-11}{16})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{16})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{10}{7}x-\frac{11}{16}b-\frac{11}{16}.\frac{10}{7}& \text{Uitwerken } \\ & =-bx-\frac{10}{7}x-\frac{11}{16}b-\frac{110}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{10}{7}x-\frac{11}{16}b-\frac{55}{56} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(a-\frac{16}{9})(\frac{15}{2}+b)& =(\color{red}{a}+\color{orange}{\frac{-16}{9}}).(\color{green}{b}+\color{blue}{\frac{15}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{15}{2})} + \color{orange}{(\frac{-16}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{9})} . \color{blue}{(\frac{15}{2})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{15}{2}a-\frac{16}{9}b-\frac{16}{9}.\frac{15}{2}& \text{Uitwerken } \\ & =ab+\frac{15}{2}a-\frac{16}{9}b-\frac{240}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{15}{2}a-\frac{16}{9}b-\frac{40}{3} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-10}{9}+b)((-20)+a)& =(\color{red}{b}+\color{orange}{\frac{-10}{9}}).(\color{green}{a}+\color{blue}{(-20)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-20)} + \color{orange}{(\frac{-10}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(-20)}& \text{Boogjes en uitschrijven} \\ & = ab-20b-\frac{10}{9}a+\frac{10}{9}.20& \text{Uitwerken } \\ & =ab-20b-\frac{10}{9}a+\frac{200}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)