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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{-3}{20})(\frac{-2}{14}+q)& =(\color{red}{p}+\color{orange}{\frac{-3}{20}}).(\color{green}{q}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(\frac{-3}{20})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{20})} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{7}p-\frac{3}{20}q+\frac{3}{20}.\frac{1}{7}& \text{Uitwerken } \\ & =pq-\frac{1}{7}p-\frac{3}{20}q+\frac{3}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{7}{3}-b)(p-\frac{-11}{12})& =(\color{red}{-b}+\color{orange}{\frac{7}{3}}).(\color{green}{p}+\color{blue}{\frac{11}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{12})} + \color{orange}{(\frac{7}{3})} . \color{green}{(p)} + \color{orange}{(\frac{7}{3})} . \color{blue}{(\frac{11}{12})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{11}{12}b+\frac{7}{3}p+\frac{7}{3}.\frac{11}{12}& \text{Uitwerken } \\ & =-bp-\frac{11}{12}b+\frac{7}{3}p+\frac{77}{36} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{12}{16}-q)(b-\frac{10}{17})& =(\color{red}{-q}+\color{orange}{\frac{3}{4}}).(\color{green}{b}+\color{blue}{\frac{-10}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-10}{17})} + \color{orange}{(\frac{3}{4})} . \color{green}{(b)} + \color{orange}{(\frac{3}{4})} . \color{blue}{(\frac{-10}{17})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{10}{17}q+\frac{3}{4}b-\frac{3}{4}.\frac{10}{17}& \text{Uitwerken } \\ & =-bq+\frac{10}{17}q+\frac{3}{4}b-\frac{30}{68} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{10}{17}q+\frac{3}{4}b-\frac{15}{34} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(b+\frac{9}{8})(\frac{-16}{20}-a)& =(\color{red}{b}+\color{orange}{\frac{9}{8}}).(\color{green}{-a}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{9}{8})} . \color{green}{(-a)} + \color{orange}{(\frac{9}{8})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{4}{5}b-\frac{9}{8}a-\frac{9}{8}.\frac{4}{5}& \text{Uitwerken } \\ & =-ab-\frac{4}{5}b-\frac{9}{8}a-\frac{36}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{4}{5}b-\frac{9}{8}a-\frac{9}{10} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(p-\frac{-5}{7})(x-\frac{-9}{12})& =(\color{red}{p}+\color{orange}{\frac{5}{7}}).(\color{green}{x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{5}{7})} . \color{green}{(x)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{4}p+\frac{5}{7}x+\frac{5}{7}.\frac{3}{4}& \text{Uitwerken } \\ & =px+\frac{3}{4}p+\frac{5}{7}x+\frac{15}{28} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b-\frac{-5}{18})(x-\frac{-11}{19})& =(\color{red}{b}+\color{orange}{\frac{5}{18}}).(\color{green}{x}+\color{blue}{\frac{11}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{11}{19})} + \color{orange}{(\frac{5}{18})} . \color{green}{(x)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{11}{19})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{11}{19}b+\frac{5}{18}x+\frac{5}{18}.\frac{11}{19}& \text{Uitwerken } \\ & =bx+\frac{11}{19}b+\frac{5}{18}x+\frac{55}{342} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p-\frac{9}{13})(\frac{3}{10}+x)& =(\color{red}{p}+\color{orange}{\frac{-9}{13}}).(\color{green}{x}+\color{blue}{\frac{3}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{3}{10})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{3}{10})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{10}p-\frac{9}{13}x-\frac{9}{13}.\frac{3}{10}& \text{Uitwerken } \\ & =px+\frac{3}{10}p-\frac{9}{13}x-\frac{27}{130} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a-\frac{18}{18})(p-\frac{7}{15})& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{\frac{-7}{15}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{15})} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(\frac{-7}{15})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{15}a-1p+1.\frac{7}{15}& \text{Uitwerken } \\ & =ap-\frac{7}{15}a-1p+\frac{7}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{10}{3}-p)(b+\frac{11}{19})& =(\color{red}{-p}+\color{orange}{\frac{10}{3}}).(\color{green}{b}+\color{blue}{\frac{11}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{11}{19})} + \color{orange}{(\frac{10}{3})} . \color{green}{(b)} + \color{orange}{(\frac{10}{3})} . \color{blue}{(\frac{11}{19})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{11}{19}p+\frac{10}{3}b+\frac{10}{3}.\frac{11}{19}& \text{Uitwerken } \\ & =-bp-\frac{11}{19}p+\frac{10}{3}b+\frac{110}{57} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(a+(-16))(\frac{-18}{7}+q)& =(\color{red}{a}+\color{orange}{(-16)}).(\color{green}{q}+\color{blue}{\frac{-18}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{-18}{7})} + \color{orange}{(-16)} . \color{green}{(q)} + \color{orange}{(-16)} . \color{blue}{(\frac{-18}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{18}{7}a-16q+16.\frac{18}{7}& \text{Uitwerken } \\ & =aq-\frac{18}{7}a-16q+\frac{288}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{16}{15}-q)(\frac{-12}{7}-b)& =(\color{red}{-q}+\color{orange}{\frac{16}{15}}).(\color{green}{-b}+\color{blue}{\frac{-12}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(\frac{-12}{7})} + \color{orange}{(\frac{16}{15})} . \color{green}{(-b)} + \color{orange}{(\frac{16}{15})} . \color{blue}{(\frac{-12}{7})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{12}{7}q-\frac{16}{15}b-\frac{16}{15}.\frac{12}{7}& \text{Uitwerken } \\ & =bq+\frac{12}{7}q-\frac{16}{15}b-\frac{192}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{12}{7}q-\frac{16}{15}b-\frac{64}{35} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{15}{7}+b)(q+\frac{11}{20})& =(\color{red}{b}+\color{orange}{\frac{15}{7}}).(\color{green}{q}+\color{blue}{\frac{11}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{11}{20})} + \color{orange}{(\frac{15}{7})} . \color{green}{(q)} + \color{orange}{(\frac{15}{7})} . \color{blue}{(\frac{11}{20})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{11}{20}b+\frac{15}{7}q+\frac{15}{7}.\frac{11}{20}& \text{Uitwerken } \\ & =bq+\frac{11}{20}b+\frac{15}{7}q+\frac{165}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+\frac{11}{20}b+\frac{15}{7}q+\frac{33}{28} & \text{Vereenvoudig} \\\end{align}\)