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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{-4}{14})(b+\frac{-5}{2})& =(\color{red}{p}+\color{orange}{\frac{-2}{7}}).(\color{green}{b}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{-2}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{7})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{5}{2}p-\frac{2}{7}b+\frac{2}{7}.\frac{5}{2}& \text{Uitwerken } \\ & =bp-\frac{5}{2}p-\frac{2}{7}b+\frac{10}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{5}{2}p-\frac{2}{7}b+\frac{5}{7} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(x-(-20))(\frac{-1}{4}-b)& =(\color{red}{x}+\color{orange}{20}).(\color{green}{-b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-b)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(20)} . \color{green}{(-b)} + \color{orange}{(20)} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bx-\frac{1}{4}x-20b-20.\frac{1}{4}& \text{Uitwerken } \\ & =-bx-\frac{1}{4}x-20b-\frac{20}{4} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bx-\frac{1}{4}x-20b-5 & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(b+\frac{-15}{2})(x+\frac{1}{19})& =(\color{red}{b}+\color{orange}{\frac{-15}{2}}).(\color{green}{x}+\color{blue}{\frac{1}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{1}{19})} + \color{orange}{(\frac{-15}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(\frac{1}{19})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{19}b-\frac{15}{2}x-\frac{15}{2}.\frac{1}{19}& \text{Uitwerken } \\ & =bx+\frac{1}{19}b-\frac{15}{2}x-\frac{15}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(a+\frac{8}{11})((-19)-a)& =(\color{red}{a}+\color{orange}{\frac{8}{11}}).(\color{green}{-a}+\color{blue}{(-19)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(-19)} + \color{orange}{(\frac{8}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{8}{11})} . \color{blue}{(-19)}& \text{Boogjes en uitschrijven} \\ & = -aa-19a-\frac{8}{11}a-\frac{8}{11}.19& \text{Uitwerken } \\ & =-a^2+((-19)+(\frac{-8}{11}))a-\frac{152}{11} & \text{Neem samen} \\ &=-a^2-\frac{217}{11}a-\frac{152}{11} & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(a+\frac{-18}{16})(b+\frac{8}{3})& =(\color{red}{a}+\color{orange}{\frac{-9}{8}}).(\color{green}{b}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(\frac{-9}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{8}{3}a-\frac{9}{8}b-\frac{9}{8}.\frac{8}{3}& \text{Uitwerken } \\ & =ab+\frac{8}{3}a-\frac{9}{8}b-\frac{72}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{8}{3}a-\frac{9}{8}b-3 & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(p+\frac{-2}{10})(x-\frac{2}{12})& =(\color{red}{p}+\color{orange}{\frac{-1}{5}}).(\color{green}{x}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-1}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{5})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{6}p-\frac{1}{5}x+\frac{1}{5}.\frac{1}{6}& \text{Uitwerken } \\ & =px-\frac{1}{6}p-\frac{1}{5}x+\frac{1}{30} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b+\frac{-10}{13})(\frac{16}{6}-x)& =(\color{red}{b}+\color{orange}{\frac{-10}{13}}).(\color{green}{-x}+\color{blue}{\frac{8}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-x)} + \color{red}{(b)} . \color{blue}{(\frac{8}{3})} + \color{orange}{(\frac{-10}{13})} . \color{green}{(-x)} + \color{orange}{(\frac{-10}{13})} . \color{blue}{(\frac{8}{3})}& \text{Boogjes en uitschrijven} \\ & = -bx+\frac{8}{3}b+\frac{10}{13}x-\frac{10}{13}.\frac{8}{3}& \text{Uitwerken } \\ & =-bx+\frac{8}{3}b+\frac{10}{13}x-\frac{80}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p-\frac{-3}{16})(\frac{-13}{12}-a)& =(\color{red}{p}+\color{orange}{\frac{3}{16}}).(\color{green}{-a}+\color{blue}{\frac{-13}{12}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{12})} + \color{orange}{(\frac{3}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{3}{16})} . \color{blue}{(\frac{-13}{12})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{13}{12}p-\frac{3}{16}a-\frac{3}{16}.\frac{13}{12}& \text{Uitwerken } \\ & =-ap-\frac{13}{12}p-\frac{3}{16}a-\frac{39}{192} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{13}{12}p-\frac{3}{16}a-\frac{13}{64} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(a+\frac{-19}{11})(\frac{5}{15}-p)& =(\color{red}{a}+\color{orange}{\frac{-19}{11}}).(\color{green}{-p}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-19}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-19}{11})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{1}{3}a+\frac{19}{11}p-\frac{19}{11}.\frac{1}{3}& \text{Uitwerken } \\ & =-ap+\frac{1}{3}a+\frac{19}{11}p-\frac{19}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-16}{16}-q)(8-b)& =(\color{red}{-q}+\color{orange}{(-1)}).(\color{green}{-b}+\color{blue}{8})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-b)} + \color{red}{(-q)} . \color{blue}{(8)} + \color{orange}{(-1)} . \color{green}{(-b)} + \color{orange}{(-1)} . \color{blue}{(8)}& \text{Boogjes en uitschrijven} \\ & = bq-8q+1b-1.8& \text{Uitwerken } \\ & =bq-8q+1b-8 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{16}{8}+b)(\frac{4}{6}+x)& =(\color{red}{b}+\color{orange}{2}).(\color{green}{x}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(2)} . \color{green}{(x)} + \color{orange}{(2)} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{2}{3}b+2x+2.\frac{2}{3}& \text{Uitwerken } \\ & =bx+\frac{2}{3}b+2x+\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-1}{7}-b)(\frac{-11}{7}+b)& =(\color{red}{-b}+\color{orange}{\frac{-1}{7}}).(\color{green}{b}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(\frac{-1}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{7})} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{11}{7}b-\frac{1}{7}b+\frac{1}{7}.\frac{11}{7}& \text{Uitwerken } \\ & =-b^2+(\frac{11}{7}+(\frac{-1}{7}))b+(\frac{-11}{49}) & \text{Neem samen} \\ &=-b^2+\frac{10}{7}b+(\frac{-11}{49}) & \text{Maak de som} \\\end{align}\)