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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x+\frac{-10}{18})(\frac{-18}{4}-p)& =(\color{red}{x}+\color{orange}{\frac{-5}{9}}).(\color{green}{-p}+\color{blue}{\frac{-9}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{2})} + \color{orange}{(\frac{-5}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{-5}{9})} . \color{blue}{(\frac{-9}{2})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{9}{2}x+\frac{5}{9}p+\frac{5}{9}.\frac{9}{2}& \text{Uitwerken } \\ & =-px-\frac{9}{2}x+\frac{5}{9}p+\frac{45}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px-\frac{9}{2}x+\frac{5}{9}p+\frac{5}{2} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(b-\frac{-1}{17})(\frac{4}{20}-b)& =(\color{red}{b}+\color{orange}{\frac{1}{17}}).(\color{green}{-b}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{1}{17})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{17})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -bb+\frac{1}{5}b-\frac{1}{17}b+\frac{1}{17}.\frac{1}{5}& \text{Uitwerken } \\ & =-b^2+(\frac{1}{5}+(\frac{-1}{17}))b+(\frac{-1}{85}) & \text{Neem samen} \\ &=-b^2+\frac{12}{85}b+(\frac{-1}{85}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(q+\frac{-7}{7})(a+\frac{7}{13})& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{7}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{7}{13})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{7}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{13}q-1a-1.\frac{7}{13}& \text{Uitwerken } \\ & =aq+\frac{7}{13}q-1a-\frac{7}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{19}{5}+q)(\frac{-8}{18}+q)& =(\color{red}{q}+\color{orange}{\frac{19}{5}}).(\color{green}{q}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{19}{5})} . \color{green}{(q)} + \color{orange}{(\frac{19}{5})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{4}{9}q+\frac{19}{5}q-\frac{19}{5}.\frac{4}{9}& \text{Uitwerken } \\ & =q^2+((\frac{-4}{9})+\frac{19}{5})q-(\frac{-76}{45}) & \text{Neem samen} \\ &=q^2+\frac{151}{45}q-(\frac{-76}{45}) & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(b+\frac{-15}{2})(\frac{-15}{2}-p)& =(\color{red}{b}+\color{orange}{\frac{-15}{2}}).(\color{green}{-p}+\color{blue}{\frac{-15}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{2})} + \color{orange}{(\frac{-15}{2})} . \color{green}{(-p)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(\frac{-15}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{15}{2}b+\frac{15}{2}p+\frac{15}{2}.\frac{15}{2}& \text{Uitwerken } \\ & =-bp-\frac{15}{2}b+\frac{15}{2}p+\frac{225}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a-(-19))(\frac{-12}{18}-p)& =(\color{red}{a}+\color{orange}{19}).(\color{green}{-p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(19)} . \color{green}{(-p)} + \color{orange}{(19)} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{2}{3}a-19p-19.\frac{2}{3}& \text{Uitwerken } \\ & =-ap-\frac{2}{3}a-19p-\frac{38}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a-\frac{3}{20})(\frac{-4}{5}-a)& =(\color{red}{a}+\color{orange}{\frac{-3}{20}}).(\color{green}{-a}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-3}{20})} . \color{green}{(-a)} + \color{orange}{(\frac{-3}{20})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -aa-\frac{4}{5}a+\frac{3}{20}a+\frac{3}{20}.\frac{4}{5}& \text{Uitwerken } \\ & =-a^2+((\frac{-4}{5})+\frac{3}{20})a+(\frac{-12}{100}) & \text{Neem samen} \\ &=-a^2-\frac{13}{20}a+(\frac{-12}{100}) & \text{Maak de som} \\ &=-a^2-\frac{13}{20}a+(\frac{-3}{25}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
8. \(\begin{align}(a-\frac{6}{20})(x-\frac{10}{2})& =(\color{red}{a}+\color{orange}{\frac{-3}{10}}).(\color{green}{x}+\color{blue}{(-5)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(-5)} + \color{orange}{(\frac{-3}{10})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(-5)}& \text{Boogjes en uitschrijven} \\ & = ax-5a-\frac{3}{10}x+\frac{3}{10}.5& \text{Uitwerken } \\ & =ax-5a-\frac{3}{10}x+\frac{15}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-5a-\frac{3}{10}x+\frac{3}{2} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{13}{13}+x)(a-\frac{9}{5})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{9}{5}x+1a-1.\frac{9}{5}& \text{Uitwerken } \\ & =ax-\frac{9}{5}x+1a-\frac{9}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-19}{10}+a)(p+\frac{-19}{2})& =(\color{red}{a}+\color{orange}{\frac{-19}{10}}).(\color{green}{p}+\color{blue}{\frac{-19}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{2})} + \color{orange}{(\frac{-19}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{10})} . \color{blue}{(\frac{-19}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{19}{2}a-\frac{19}{10}p+\frac{19}{10}.\frac{19}{2}& \text{Uitwerken } \\ & =ap-\frac{19}{2}a-\frac{19}{10}p+\frac{361}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p+\frac{1}{18})(b+\frac{5}{6})& =(\color{red}{p}+\color{orange}{\frac{1}{18}}).(\color{green}{b}+\color{blue}{\frac{5}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{5}{6})} + \color{orange}{(\frac{1}{18})} . \color{green}{(b)} + \color{orange}{(\frac{1}{18})} . \color{blue}{(\frac{5}{6})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{6}p+\frac{1}{18}b+\frac{1}{18}.\frac{5}{6}& \text{Uitwerken } \\ & =bp+\frac{5}{6}p+\frac{1}{18}b+\frac{5}{108} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{10}{20}+b)(\frac{10}{2}+a)& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{a}+\color{blue}{5})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(5)} + \color{orange}{(\frac{1}{2})} . \color{green}{(a)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = ab+5b+\frac{1}{2}a+\frac{1}{2}.5& \text{Uitwerken } \\ & =ab+5b+\frac{1}{2}a+\frac{5}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)