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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{12}{2}+x)(p+\frac{-12}{12})& =(\color{red}{x}+\color{orange}{6}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(6)} . \color{green}{(p)} + \color{orange}{(6)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = px-1x+6p-6.1& \text{Uitwerken } \\ & =px-1x+6p-6 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{4}{12}-b)(p-\frac{-12}{12})& =(\color{red}{-b}+\color{orange}{\frac{1}{3}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(1)} + \color{orange}{(\frac{1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bp-1b+\frac{1}{3}p+\frac{1}{3}.1& \text{Uitwerken } \\ & =-bp-1b+\frac{1}{3}p+\frac{1}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}((-15)+b)(\frac{14}{17}-a)& =(\color{red}{b}+\color{orange}{(-15)}).(\color{green}{-a}+\color{blue}{\frac{14}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{14}{17})} + \color{orange}{(-15)} . \color{green}{(-a)} + \color{orange}{(-15)} . \color{blue}{(\frac{14}{17})}& \text{Boogjes en uitschrijven} \\ & = -ab+\frac{14}{17}b+15a-15.\frac{14}{17}& \text{Uitwerken } \\ & =-ab+\frac{14}{17}b+15a-\frac{210}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{8}{19}-q)(\frac{20}{18}-a)& =(\color{red}{-q}+\color{orange}{\frac{8}{19}}).(\color{green}{-a}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-a)} + \color{red}{(-q)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(\frac{8}{19})} . \color{green}{(-a)} + \color{orange}{(\frac{8}{19})} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{10}{9}q-\frac{8}{19}a+\frac{8}{19}.\frac{10}{9}& \text{Uitwerken } \\ & =aq-\frac{10}{9}q-\frac{8}{19}a+\frac{80}{171} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p+\frac{-12}{15})(x-\frac{-1}{8})& =(\color{red}{p}+\color{orange}{\frac{-4}{5}}).(\color{green}{x}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{-4}{5})} . \color{green}{(x)} + \color{orange}{(\frac{-4}{5})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{1}{8}p-\frac{4}{5}x-\frac{4}{5}.\frac{1}{8}& \text{Uitwerken } \\ & =px+\frac{1}{8}p-\frac{4}{5}x-\frac{4}{40} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{1}{8}p-\frac{4}{5}x-\frac{1}{10} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{19}{7}+a)(\frac{-11}{2}+p)& =(\color{red}{a}+\color{orange}{\frac{19}{7}}).(\color{green}{p}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(\frac{19}{7})} . \color{green}{(p)} + \color{orange}{(\frac{19}{7})} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{11}{2}a+\frac{19}{7}p-\frac{19}{7}.\frac{11}{2}& \text{Uitwerken } \\ & =ap-\frac{11}{2}a+\frac{19}{7}p-\frac{209}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p-\frac{-4}{11})(\frac{-12}{2}+x)& =(\color{red}{p}+\color{orange}{\frac{4}{11}}).(\color{green}{x}+\color{blue}{(-6)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-6)} + \color{orange}{(\frac{4}{11})} . \color{green}{(x)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = px-6p+\frac{4}{11}x-\frac{4}{11}.6& \text{Uitwerken } \\ & =px-6p+\frac{4}{11}x-\frac{24}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{15}{12}+a)(\frac{-4}{8}-b)& =(\color{red}{a}+\color{orange}{\frac{5}{4}}).(\color{green}{-b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{5}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{5}{4})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{1}{2}a-\frac{5}{4}b-\frac{5}{4}.\frac{1}{2}& \text{Uitwerken } \\ & =-ab-\frac{1}{2}a-\frac{5}{4}b-\frac{5}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-9}{4}-b)(\frac{15}{9}+q)& =(\color{red}{-b}+\color{orange}{\frac{-9}{4}}).(\color{green}{q}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{5}{3}b-\frac{9}{4}q-\frac{9}{4}.\frac{5}{3}& \text{Uitwerken } \\ & =-bq-\frac{5}{3}b-\frac{9}{4}q-\frac{45}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{5}{3}b-\frac{9}{4}q-\frac{15}{4} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p-\frac{9}{10})(x-\frac{-18}{9})& =(\color{red}{p}+\color{orange}{\frac{-9}{10}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{-9}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = px+2p-\frac{9}{10}x-\frac{9}{10}.2& \text{Uitwerken } \\ & =px+2p-\frac{9}{10}x-\frac{18}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+2p-\frac{9}{10}x-\frac{9}{5} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-2}{11}-b)(b-\frac{16}{16})& =(\color{red}{-b}+\color{orange}{\frac{-2}{11}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(-1)} + \color{orange}{(\frac{-2}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -bb+1b-\frac{2}{11}b+\frac{2}{11}.1& \text{Uitwerken } \\ & =-b^2+(1+(\frac{-2}{11}))b+(\frac{-2}{11}) & \text{Neem samen} \\ &=-b^2+\frac{9}{11}b+(\frac{-2}{11}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(p+\frac{-2}{9})(\frac{-14}{15}+a)& =(\color{red}{p}+\color{orange}{\frac{-2}{9}}).(\color{green}{a}+\color{blue}{\frac{-14}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{15})} + \color{orange}{(\frac{-2}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{9})} . \color{blue}{(\frac{-14}{15})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{14}{15}p-\frac{2}{9}a+\frac{2}{9}.\frac{14}{15}& \text{Uitwerken } \\ & =ap-\frac{14}{15}p-\frac{2}{9}a+\frac{28}{135} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)