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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b-\frac{-7}{14})(a-\frac{15}{14})& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{-15}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{14})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-15}{14})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{15}{14}b+\frac{1}{2}a-\frac{1}{2}.\frac{15}{14}& \text{Uitwerken } \\ & =ab-\frac{15}{14}b+\frac{1}{2}a-\frac{15}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a+\frac{15}{13})(p+\frac{-5}{17})& =(\color{red}{a}+\color{orange}{\frac{15}{13}}).(\color{green}{p}+\color{blue}{\frac{-5}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{17})} + \color{orange}{(\frac{15}{13})} . \color{green}{(p)} + \color{orange}{(\frac{15}{13})} . \color{blue}{(\frac{-5}{17})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{5}{17}a+\frac{15}{13}p-\frac{15}{13}.\frac{5}{17}& \text{Uitwerken } \\ & =ap-\frac{5}{17}a+\frac{15}{13}p-\frac{75}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p+\frac{-1}{9})(q-\frac{8}{17})& =(\color{red}{p}+\color{orange}{\frac{-1}{9}}).(\color{green}{q}+\color{blue}{\frac{-8}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{17})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{-8}{17})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{8}{17}p-\frac{1}{9}q+\frac{1}{9}.\frac{8}{17}& \text{Uitwerken } \\ & =pq-\frac{8}{17}p-\frac{1}{9}q+\frac{8}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(p-\frac{4}{3})(\frac{-5}{8}-q)& =(\color{red}{p}+\color{orange}{\frac{-4}{3}}).(\color{green}{-q}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{5}{8}p+\frac{4}{3}q+\frac{4}{3}.\frac{5}{8}& \text{Uitwerken } \\ & =-pq-\frac{5}{8}p+\frac{4}{3}q+\frac{20}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{5}{8}p+\frac{4}{3}q+\frac{5}{6} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(b-\frac{12}{20})(p-\frac{-5}{7})& =(\color{red}{b}+\color{orange}{\frac{-3}{5}}).(\color{green}{p}+\color{blue}{\frac{5}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{5}{7})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{5}{7})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{7}b-\frac{3}{5}p-\frac{3}{5}.\frac{5}{7}& \text{Uitwerken } \\ & =bp+\frac{5}{7}b-\frac{3}{5}p-\frac{15}{35} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{5}{7}b-\frac{3}{5}p-\frac{3}{7} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-13}{6}-b)(\frac{8}{19}+a)& =(\color{red}{-b}+\color{orange}{\frac{-13}{6}}).(\color{green}{a}+\color{blue}{\frac{8}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{8}{19})} + \color{orange}{(\frac{-13}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{6})} . \color{blue}{(\frac{8}{19})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{8}{19}b-\frac{13}{6}a-\frac{13}{6}.\frac{8}{19}& \text{Uitwerken } \\ & =-ab-\frac{8}{19}b-\frac{13}{6}a-\frac{104}{114} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{8}{19}b-\frac{13}{6}a-\frac{52}{57} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-10}{11}+b)(\frac{-7}{16}-p)& =(\color{red}{b}+\color{orange}{\frac{-10}{11}}).(\color{green}{-p}+\color{blue}{\frac{-7}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{16})} + \color{orange}{(\frac{-10}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(\frac{-7}{16})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{7}{16}b+\frac{10}{11}p+\frac{10}{11}.\frac{7}{16}& \text{Uitwerken } \\ & =-bp-\frac{7}{16}b+\frac{10}{11}p+\frac{70}{176} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{7}{16}b+\frac{10}{11}p+\frac{35}{88} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(p+\frac{10}{7})(\frac{-10}{20}-q)& =(\color{red}{p}+\color{orange}{\frac{10}{7}}).(\color{green}{-q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{10}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{10}{7})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{2}p-\frac{10}{7}q-\frac{10}{7}.\frac{1}{2}& \text{Uitwerken } \\ & =-pq-\frac{1}{2}p-\frac{10}{7}q-\frac{10}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{1}{2}p-\frac{10}{7}q-\frac{5}{7} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{18}{2}+a)(b+\frac{11}{8})& =(\color{red}{a}+\color{orange}{9}).(\color{green}{b}+\color{blue}{\frac{11}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{11}{8})} + \color{orange}{(9)} . \color{green}{(b)} + \color{orange}{(9)} . \color{blue}{(\frac{11}{8})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{11}{8}a+9b+9.\frac{11}{8}& \text{Uitwerken } \\ & =ab+\frac{11}{8}a+9b+\frac{99}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(p-\frac{-18}{14})(b+\frac{8}{8})& =(\color{red}{p}+\color{orange}{\frac{9}{7}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{9}{7})} . \color{green}{(b)} + \color{orange}{(\frac{9}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bp+1p+\frac{9}{7}b+\frac{9}{7}.1& \text{Uitwerken } \\ & =bp+1p+\frac{9}{7}b+\frac{9}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x-\frac{2}{3})(\frac{-16}{5}+p)& =(\color{red}{x}+\color{orange}{\frac{-2}{3}}).(\color{green}{p}+\color{blue}{\frac{-16}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{5})} + \color{orange}{(\frac{-2}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-2}{3})} . \color{blue}{(\frac{-16}{5})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{16}{5}x-\frac{2}{3}p+\frac{2}{3}.\frac{16}{5}& \text{Uitwerken } \\ & =px-\frac{16}{5}x-\frac{2}{3}p+\frac{32}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{19}{14}-x)(q+\frac{-13}{13})& =(\color{red}{-x}+\color{orange}{\frac{19}{14}}).(\color{green}{q}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(q)} + \color{red}{(-x)} . \color{blue}{(-1)} + \color{orange}{(\frac{19}{14})} . \color{green}{(q)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qx+1x+\frac{19}{14}q-\frac{19}{14}.1& \text{Uitwerken } \\ & =-qx+1x+\frac{19}{14}q-\frac{19}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)