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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+\frac{1}{20})(q-\frac{-20}{9})& =(\color{red}{a}+\color{orange}{\frac{1}{20}}).(\color{green}{q}+\color{blue}{\frac{20}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{20}{9})} + \color{orange}{(\frac{1}{20})} . \color{green}{(q)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(\frac{20}{9})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{20}{9}a+\frac{1}{20}q+\frac{1}{20}.\frac{20}{9}& \text{Uitwerken } \\ & =aq+\frac{20}{9}a+\frac{1}{20}q+\frac{20}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{20}{9}a+\frac{1}{20}q+\frac{1}{9} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(x-\frac{-12}{12})(\frac{-8}{19}-q)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{-q}+\color{blue}{\frac{-8}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-q)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{19})} + \color{orange}{(1)} . \color{green}{(-q)} + \color{orange}{(1)} . \color{blue}{(\frac{-8}{19})}& \text{Boogjes en uitschrijven} \\ & = -qx-\frac{8}{19}x-1q-1.\frac{8}{19}& \text{Uitwerken } \\ & =-qx-\frac{8}{19}x-1q-\frac{8}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-13}{20}+p)(b+\frac{-20}{14})& =(\color{red}{p}+\color{orange}{\frac{-13}{20}}).(\color{green}{b}+\color{blue}{\frac{-10}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-10}{7})} + \color{orange}{(\frac{-13}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-13}{20})} . \color{blue}{(\frac{-10}{7})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{10}{7}p-\frac{13}{20}b+\frac{13}{20}.\frac{10}{7}& \text{Uitwerken } \\ & =bp-\frac{10}{7}p-\frac{13}{20}b+\frac{130}{140} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{10}{7}p-\frac{13}{20}b+\frac{13}{14} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(q-\frac{-4}{18})(x+\frac{20}{14})& =(\color{red}{q}+\color{orange}{\frac{2}{9}}).(\color{green}{x}+\color{blue}{\frac{10}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{10}{7})} + \color{orange}{(\frac{2}{9})} . \color{green}{(x)} + \color{orange}{(\frac{2}{9})} . \color{blue}{(\frac{10}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{10}{7}q+\frac{2}{9}x+\frac{2}{9}.\frac{10}{7}& \text{Uitwerken } \\ & =qx+\frac{10}{7}q+\frac{2}{9}x+\frac{20}{63} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{11}{10}+a)(x+\frac{10}{5})& =(\color{red}{a}+\color{orange}{\frac{11}{10}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(2)} + \color{orange}{(\frac{11}{10})} . \color{green}{(x)} + \color{orange}{(\frac{11}{10})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ax+2a+\frac{11}{10}x+\frac{11}{10}.2& \text{Uitwerken } \\ & =ax+2a+\frac{11}{10}x+\frac{22}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+2a+\frac{11}{10}x+\frac{11}{5} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(b-(-20))(\frac{-15}{19}-a)& =(\color{red}{b}+\color{orange}{20}).(\color{green}{-a}+\color{blue}{\frac{-15}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-15}{19})} + \color{orange}{(20)} . \color{green}{(-a)} + \color{orange}{(20)} . \color{blue}{(\frac{-15}{19})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{15}{19}b-20a-20.\frac{15}{19}& \text{Uitwerken } \\ & =-ab-\frac{15}{19}b-20a-\frac{300}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a+\frac{-15}{5})(\frac{12}{4}-p)& =(\color{red}{a}+\color{orange}{(-3)}).(\color{green}{-p}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(3)} + \color{orange}{(-3)} . \color{green}{(-p)} + \color{orange}{(-3)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -ap+3a+3p-3.3& \text{Uitwerken } \\ & =-ap+3a+3p-9 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{12}{7}-b)(p-\frac{-10}{8})& =(\color{red}{-b}+\color{orange}{\frac{12}{7}}).(\color{green}{p}+\color{blue}{\frac{5}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{5}{4})} + \color{orange}{(\frac{12}{7})} . \color{green}{(p)} + \color{orange}{(\frac{12}{7})} . \color{blue}{(\frac{5}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{5}{4}b+\frac{12}{7}p+\frac{12}{7}.\frac{5}{4}& \text{Uitwerken } \\ & =-bp-\frac{5}{4}b+\frac{12}{7}p+\frac{60}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{5}{4}b+\frac{12}{7}p+\frac{15}{7} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(p+\frac{9}{9})(\frac{13}{9}-a)& =(\color{red}{p}+\color{orange}{1}).(\color{green}{-a}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(1)} . \color{green}{(-a)} + \color{orange}{(1)} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{13}{9}p-1a+1.\frac{13}{9}& \text{Uitwerken } \\ & =-ap+\frac{13}{9}p-1a+\frac{13}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x-\frac{-20}{4})(\frac{-16}{11}+q)& =(\color{red}{x}+\color{orange}{5}).(\color{green}{q}+\color{blue}{\frac{-16}{11}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{11})} + \color{orange}{(5)} . \color{green}{(q)} + \color{orange}{(5)} . \color{blue}{(\frac{-16}{11})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{16}{11}x+5q-5.\frac{16}{11}& \text{Uitwerken } \\ & =qx-\frac{16}{11}x+5q-\frac{80}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{11}{20}-x)(p+\frac{3}{3})& =(\color{red}{-x}+\color{orange}{\frac{11}{20}}).(\color{green}{p}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(1)} + \color{orange}{(\frac{11}{20})} . \color{green}{(p)} + \color{orange}{(\frac{11}{20})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -px-1x+\frac{11}{20}p+\frac{11}{20}.1& \text{Uitwerken } \\ & =-px-1x+\frac{11}{20}p+\frac{11}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-1}{9}+x)(\frac{-4}{6}+p)& =(\color{red}{x}+\color{orange}{\frac{-1}{9}}).(\color{green}{p}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-1}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{9})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{2}{3}x-\frac{1}{9}p+\frac{1}{9}.\frac{2}{3}& \text{Uitwerken } \\ & =px-\frac{2}{3}x-\frac{1}{9}p+\frac{2}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)