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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-19}{19}-b)(p+(-14))& =(\color{red}{-b}+\color{orange}{(-1)}).(\color{green}{p}+\color{blue}{(-14)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(-14)} + \color{orange}{(-1)} . \color{green}{(p)} + \color{orange}{(-1)} . \color{blue}{(-14)}& \text{Boogjes en uitschrijven} \\ & = -bp+14b-1p+1.14& \text{Uitwerken } \\ & =-bp+14b-1p+14 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-20}{15}+p)(\frac{-1}{8}+q)& =(\color{red}{p}+\color{orange}{\frac{-4}{3}}).(\color{green}{q}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{8}p-\frac{4}{3}q+\frac{4}{3}.\frac{1}{8}& \text{Uitwerken } \\ & =pq-\frac{1}{8}p-\frac{4}{3}q+\frac{4}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{1}{8}p-\frac{4}{3}q+\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(x-\frac{-13}{5})(p-\frac{2}{18})& =(\color{red}{x}+\color{orange}{\frac{13}{5}}).(\color{green}{p}+\color{blue}{\frac{-1}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-1}{9})} + \color{orange}{(\frac{13}{5})} . \color{green}{(p)} + \color{orange}{(\frac{13}{5})} . \color{blue}{(\frac{-1}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{9}x+\frac{13}{5}p-\frac{13}{5}.\frac{1}{9}& \text{Uitwerken } \\ & =px-\frac{1}{9}x+\frac{13}{5}p-\frac{13}{45} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{2}{12}-b)(\frac{15}{4}-p)& =(\color{red}{-b}+\color{orange}{\frac{1}{6}}).(\color{green}{-p}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{1}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{1}{6})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{15}{4}b-\frac{1}{6}p+\frac{1}{6}.\frac{15}{4}& \text{Uitwerken } \\ & =bp-\frac{15}{4}b-\frac{1}{6}p+\frac{15}{24} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{15}{4}b-\frac{1}{6}p+\frac{5}{8} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-13}{20}+x)(14-p)& =(\color{red}{x}+\color{orange}{\frac{-13}{20}}).(\color{green}{-p}+\color{blue}{14})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(14)} + \color{orange}{(\frac{-13}{20})} . \color{green}{(-p)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(14)}& \text{Boogjes en uitschrijven} \\ & = -px+14x+\frac{13}{20}p-\frac{13}{20}.14& \text{Uitwerken } \\ & =-px+14x+\frac{13}{20}p-\frac{182}{20} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+14x+\frac{13}{20}p-\frac{91}{10} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{16}{20}+x)(p-11)& =(\color{red}{x}+\color{orange}{\frac{4}{5}}).(\color{green}{p}+\color{blue}{(-11)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(-11)} + \color{orange}{(\frac{4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(-11)}& \text{Boogjes en uitschrijven} \\ & = px-11x+\frac{4}{5}p-\frac{4}{5}.11& \text{Uitwerken } \\ & =px-11x+\frac{4}{5}p-\frac{44}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{14}{20}+p)(x+\frac{4}{5})& =(\color{red}{p}+\color{orange}{\frac{7}{10}}).(\color{green}{x}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{7}{10})} . \color{green}{(x)} + \color{orange}{(\frac{7}{10})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{4}{5}p+\frac{7}{10}x+\frac{7}{10}.\frac{4}{5}& \text{Uitwerken } \\ & =px+\frac{4}{5}p+\frac{7}{10}x+\frac{28}{50} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{4}{5}p+\frac{7}{10}x+\frac{14}{25} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{16}{14}-p)(\frac{7}{7}-x)& =(\color{red}{-p}+\color{orange}{\frac{8}{7}}).(\color{green}{-x}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(1)} + \color{orange}{(\frac{8}{7})} . \color{green}{(-x)} + \color{orange}{(\frac{8}{7})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = px-1p-\frac{8}{7}x+\frac{8}{7}.1& \text{Uitwerken } \\ & =px-1p-\frac{8}{7}x+\frac{8}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x-\frac{17}{19})(p-\frac{16}{19})& =(\color{red}{x}+\color{orange}{\frac{-17}{19}}).(\color{green}{p}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{-17}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-17}{19})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{16}{19}x-\frac{17}{19}p+\frac{17}{19}.\frac{16}{19}& \text{Uitwerken } \\ & =px-\frac{16}{19}x-\frac{17}{19}p+\frac{272}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(p-\frac{7}{20})(a+\frac{6}{17})& =(\color{red}{p}+\color{orange}{\frac{-7}{20}}).(\color{green}{a}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(\frac{-7}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{6}{17}p-\frac{7}{20}a-\frac{7}{20}.\frac{6}{17}& \text{Uitwerken } \\ & =ap+\frac{6}{17}p-\frac{7}{20}a-\frac{42}{340} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{6}{17}p-\frac{7}{20}a-\frac{21}{170} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(b-\frac{-5}{13})(\frac{13}{13}+b)& =(\color{red}{b}+\color{orange}{\frac{5}{13}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{5}{13})} . \color{green}{(b)} + \color{orange}{(\frac{5}{13})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bb+1b+\frac{5}{13}b+\frac{5}{13}.1& \text{Uitwerken } \\ & =b^2+(1+\frac{5}{13})b+\frac{5}{13} & \text{Neem samen} \\ &=b^2+\frac{18}{13}b+\frac{5}{13} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(p+\frac{-19}{17})(\frac{-6}{12}+x)& =(\color{red}{p}+\color{orange}{\frac{-19}{17}}).(\color{green}{x}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-19}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-19}{17})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{1}{2}p-\frac{19}{17}x+\frac{19}{17}.\frac{1}{2}& \text{Uitwerken } \\ & =px-\frac{1}{2}p-\frac{19}{17}x+\frac{19}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)