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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-11}{2}-p)(\frac{4}{15}+b)& =(\color{red}{-p}+\color{orange}{\frac{-11}{2}}).(\color{green}{b}+\color{blue}{\frac{4}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{4}{15})} + \color{orange}{(\frac{-11}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{2})} . \color{blue}{(\frac{4}{15})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{4}{15}p-\frac{11}{2}b-\frac{11}{2}.\frac{4}{15}& \text{Uitwerken } \\ & =-bp-\frac{4}{15}p-\frac{11}{2}b-\frac{44}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{4}{15}p-\frac{11}{2}b-\frac{22}{15} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(a-\frac{-17}{10})(a+\frac{-6}{4})& =(\color{red}{a}+\color{orange}{\frac{17}{10}}).(\color{green}{a}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{17}{10})} . \color{green}{(a)} + \color{orange}{(\frac{17}{10})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{3}{2}a+\frac{17}{10}a-\frac{17}{10}.\frac{3}{2}& \text{Uitwerken } \\ & =a^2+((\frac{-3}{2})+\frac{17}{10})a-(\frac{-51}{20}) & \text{Neem samen} \\ &=a^2+\frac{2}{10}a-(\frac{-51}{20}) & \text{Maak de som} \\ &=a^2+\frac{1}{5}a+\frac{51}{20} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
3. \(\begin{align}(p-\frac{-16}{8})(\frac{-17}{9}-a)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{-a}+\color{blue}{\frac{-17}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-17}{9})} + \color{orange}{(2)} . \color{green}{(-a)} + \color{orange}{(2)} . \color{blue}{(\frac{-17}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{17}{9}p-2a-2.\frac{17}{9}& \text{Uitwerken } \\ & =-ap-\frac{17}{9}p-2a-\frac{34}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a-\frac{13}{20})(b+\frac{8}{7})& =(\color{red}{a}+\color{orange}{\frac{-13}{20}}).(\color{green}{b}+\color{blue}{\frac{8}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{8}{7})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{8}{7})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{8}{7}a-\frac{13}{20}b-\frac{13}{20}.\frac{8}{7}& \text{Uitwerken } \\ & =ab+\frac{8}{7}a-\frac{13}{20}b-\frac{104}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{8}{7}a-\frac{13}{20}b-\frac{26}{35} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-12}{20}+a)(\frac{7}{19}-q)& =(\color{red}{a}+\color{orange}{\frac{-3}{5}}).(\color{green}{-q}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-q)} + \color{red}{(a)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(\frac{-3}{5})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{5})} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{7}{19}a+\frac{3}{5}q-\frac{3}{5}.\frac{7}{19}& \text{Uitwerken } \\ & =-aq+\frac{7}{19}a+\frac{3}{5}q-\frac{21}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-5}{6}+q)(a-\frac{-7}{3})& =(\color{red}{q}+\color{orange}{\frac{-5}{6}}).(\color{green}{a}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{3}q-\frac{5}{6}a-\frac{5}{6}.\frac{7}{3}& \text{Uitwerken } \\ & =aq+\frac{7}{3}q-\frac{5}{6}a-\frac{35}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b-\frac{16}{2})(a+\frac{-7}{14})& =(\color{red}{b}+\color{orange}{(-8)}).(\color{green}{a}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(-8)} . \color{green}{(a)} + \color{orange}{(-8)} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{2}b-8a+8.\frac{1}{2}& \text{Uitwerken } \\ & =ab-\frac{1}{2}b-8a+\frac{8}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{1}{2}b-8a+4 & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{8}{13}+a)(p+\frac{-17}{17})& =(\color{red}{a}+\color{orange}{\frac{8}{13}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{8}{13})} . \color{green}{(p)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ap-1a+\frac{8}{13}p-\frac{8}{13}.1& \text{Uitwerken } \\ & =ap-1a+\frac{8}{13}p-\frac{8}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(b-\frac{5}{16})(\frac{-13}{2}-a)& =(\color{red}{b}+\color{orange}{\frac{-5}{16}}).(\color{green}{-a}+\color{blue}{\frac{-13}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{2})} + \color{orange}{(\frac{-5}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{16})} . \color{blue}{(\frac{-13}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{13}{2}b+\frac{5}{16}a+\frac{5}{16}.\frac{13}{2}& \text{Uitwerken } \\ & =-ab-\frac{13}{2}b+\frac{5}{16}a+\frac{65}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(q-\frac{9}{14})(q-\frac{-17}{12})& =(\color{red}{q}+\color{orange}{\frac{-9}{14}}).(\color{green}{q}+\color{blue}{\frac{17}{12}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{17}{12})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{17}{12})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{17}{12}q-\frac{9}{14}q-\frac{9}{14}.\frac{17}{12}& \text{Uitwerken } \\ & =q^2+(\frac{17}{12}+(\frac{-9}{14}))q-(\frac{-153}{168}) & \text{Neem samen} \\ &=q^2+\frac{65}{84}q-(\frac{-153}{168}) & \text{Maak de som} \\ &=q^2+\frac{65}{84}q+\frac{51}{56} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
11. \(\begin{align}(\frac{-2}{13}+p)(\frac{-6}{13}+b)& =(\color{red}{p}+\color{orange}{\frac{-2}{13}}).(\color{green}{b}+\color{blue}{\frac{-6}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{13})} + \color{orange}{(\frac{-2}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(\frac{-6}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{6}{13}p-\frac{2}{13}b+\frac{2}{13}.\frac{6}{13}& \text{Uitwerken } \\ & =bp-\frac{6}{13}p-\frac{2}{13}b+\frac{12}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b+\frac{16}{19})(b+\frac{-3}{12})& =(\color{red}{b}+\color{orange}{\frac{16}{19}}).(\color{green}{b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{16}{19})} . \color{green}{(b)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{1}{4}b+\frac{16}{19}b-\frac{16}{19}.\frac{1}{4}& \text{Uitwerken } \\ & =b^2+((\frac{-1}{4})+\frac{16}{19})b-(\frac{-16}{76}) & \text{Neem samen} \\ &=b^2+\frac{45}{76}b-(\frac{-16}{76}) & \text{Maak de som} \\ &=b^2+\frac{45}{76}b+\frac{4}{19} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)