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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x+\frac{13}{16})(\frac{-12}{17}+b)& =(\color{red}{x}+\color{orange}{\frac{13}{16}}).(\color{green}{b}+\color{blue}{\frac{-12}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-12}{17})} + \color{orange}{(\frac{13}{16})} . \color{green}{(b)} + \color{orange}{(\frac{13}{16})} . \color{blue}{(\frac{-12}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{12}{17}x+\frac{13}{16}b-\frac{13}{16}.\frac{12}{17}& \text{Uitwerken } \\ & =bx-\frac{12}{17}x+\frac{13}{16}b-\frac{156}{272} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{12}{17}x+\frac{13}{16}b-\frac{39}{68} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(p-\frac{4}{13})(b+\frac{-19}{3})& =(\color{red}{p}+\color{orange}{\frac{-4}{13}}).(\color{green}{b}+\color{blue}{\frac{-19}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{3})} + \color{orange}{(\frac{-4}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{13})} . \color{blue}{(\frac{-19}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{19}{3}p-\frac{4}{13}b+\frac{4}{13}.\frac{19}{3}& \text{Uitwerken } \\ & =bp-\frac{19}{3}p-\frac{4}{13}b+\frac{76}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b-\frac{11}{2})(\frac{19}{7}-a)& =(\color{red}{b}+\color{orange}{\frac{-11}{2}}).(\color{green}{-a}+\color{blue}{\frac{19}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{19}{7})} + \color{orange}{(\frac{-11}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-11}{2})} . \color{blue}{(\frac{19}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{19}{7}b+\frac{11}{2}a-\frac{11}{2}.\frac{19}{7}& \text{Uitwerken } \\ & =-ab+\frac{19}{7}b+\frac{11}{2}a-\frac{209}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x-\frac{-12}{2})(\frac{14}{19}-p)& =(\color{red}{x}+\color{orange}{6}).(\color{green}{-p}+\color{blue}{\frac{14}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{14}{19})} + \color{orange}{(6)} . \color{green}{(-p)} + \color{orange}{(6)} . \color{blue}{(\frac{14}{19})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{14}{19}x-6p+6.\frac{14}{19}& \text{Uitwerken } \\ & =-px+\frac{14}{19}x-6p+\frac{84}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b+13)(\frac{-18}{7}+b)& =(\color{red}{b}+\color{orange}{13}).(\color{green}{b}+\color{blue}{\frac{-18}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{7})} + \color{orange}{(13)} . \color{green}{(b)} + \color{orange}{(13)} . \color{blue}{(\frac{-18}{7})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{18}{7}b+13b-13.\frac{18}{7}& \text{Uitwerken } \\ & =b^2+((\frac{-18}{7})+13)b-(\frac{-234}{7}) & \text{Neem samen} \\ &=b^2+\frac{73}{7}b-(\frac{-234}{7}) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(\frac{-2}{18}+p)(12+b)& =(\color{red}{p}+\color{orange}{\frac{-1}{9}}).(\color{green}{b}+\color{blue}{12})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(12)} + \color{orange}{(\frac{-1}{9})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(12)}& \text{Boogjes en uitschrijven} \\ & = bp+12p-\frac{1}{9}b-\frac{1}{9}.12& \text{Uitwerken } \\ & =bp+12p-\frac{1}{9}b-\frac{12}{9} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+12p-\frac{1}{9}b-\frac{4}{3} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-12}{8}-b)(q+\frac{-19}{15})& =(\color{red}{-b}+\color{orange}{\frac{-3}{2}}).(\color{green}{q}+\color{blue}{\frac{-19}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{-19}{15})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-19}{15})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{19}{15}b-\frac{3}{2}q+\frac{3}{2}.\frac{19}{15}& \text{Uitwerken } \\ & =-bq+\frac{19}{15}b-\frac{3}{2}q+\frac{57}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{19}{15}b-\frac{3}{2}q+\frac{19}{10} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(x-\frac{1}{6})(\frac{-3}{4}-q)& =(\color{red}{x}+\color{orange}{\frac{-1}{6}}).(\color{green}{-q}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(-q)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{3}{4}x+\frac{1}{6}q+\frac{1}{6}.\frac{3}{4}& \text{Uitwerken } \\ & =-qx-\frac{3}{4}x+\frac{1}{6}q+\frac{3}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -qx-\frac{3}{4}x+\frac{1}{6}q+\frac{1}{8} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(q-\frac{-4}{8})(a-\frac{4}{14})& =(\color{red}{q}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{\frac{-2}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{7})} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-2}{7})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{2}{7}q+\frac{1}{2}a-\frac{1}{2}.\frac{2}{7}& \text{Uitwerken } \\ & =aq-\frac{2}{7}q+\frac{1}{2}a-\frac{2}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq-\frac{2}{7}q+\frac{1}{2}a-\frac{1}{7} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{16}{8}-x)(\frac{4}{17}-b)& =(\color{red}{-x}+\color{orange}{2}).(\color{green}{-b}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(2)} . \color{green}{(-b)} + \color{orange}{(2)} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{4}{17}x-2b+2.\frac{4}{17}& \text{Uitwerken } \\ & =bx-\frac{4}{17}x-2b+\frac{8}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-\frac{16}{14})(\frac{13}{16}+p)& =(\color{red}{a}+\color{orange}{\frac{-8}{7}}).(\color{green}{p}+\color{blue}{\frac{13}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{13}{16})} + \color{orange}{(\frac{-8}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-8}{7})} . \color{blue}{(\frac{13}{16})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{13}{16}a-\frac{8}{7}p-\frac{8}{7}.\frac{13}{16}& \text{Uitwerken } \\ & =ap+\frac{13}{16}a-\frac{8}{7}p-\frac{104}{112} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{13}{16}a-\frac{8}{7}p-\frac{13}{14} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(x-\frac{3}{20})((-4)+b)& =(\color{red}{x}+\color{orange}{\frac{-3}{20}}).(\color{green}{b}+\color{blue}{(-4)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(-4)} + \color{orange}{(\frac{-3}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{20})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = bx-4x-\frac{3}{20}b+\frac{3}{20}.4& \text{Uitwerken } \\ & =bx-4x-\frac{3}{20}b+\frac{12}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-4x-\frac{3}{20}b+\frac{3}{5} & \text{Vereenvoudig} \\\end{align}\)