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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b-\frac{-13}{6})(\frac{-6}{18}-q)& =(\color{red}{b}+\color{orange}{\frac{13}{6}}).(\color{green}{-q}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{13}{6})} . \color{green}{(-q)} + \color{orange}{(\frac{13}{6})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{1}{3}b-\frac{13}{6}q-\frac{13}{6}.\frac{1}{3}& \text{Uitwerken } \\ & =-bq-\frac{1}{3}b-\frac{13}{6}q-\frac{13}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{1}{11}+b)(\frac{-16}{7}+q)& =(\color{red}{b}+\color{orange}{\frac{1}{11}}).(\color{green}{q}+\color{blue}{\frac{-16}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{7})} + \color{orange}{(\frac{1}{11})} . \color{green}{(q)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(\frac{-16}{7})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{16}{7}b+\frac{1}{11}q-\frac{1}{11}.\frac{16}{7}& \text{Uitwerken } \\ & =bq-\frac{16}{7}b+\frac{1}{11}q-\frac{16}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{20}{4}+q)(q+\frac{-18}{7})& =(\color{red}{q}+\color{orange}{5}).(\color{green}{q}+\color{blue}{\frac{-18}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-18}{7})} + \color{orange}{(5)} . \color{green}{(q)} + \color{orange}{(5)} . \color{blue}{(\frac{-18}{7})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{18}{7}q+5q-5.\frac{18}{7}& \text{Uitwerken } \\ & =q^2+((\frac{-18}{7})+5)q-(\frac{-90}{7}) & \text{Neem samen} \\ &=q^2+\frac{17}{7}q-(\frac{-90}{7}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(b+\frac{-2}{11})(\frac{18}{18}-p)& =(\color{red}{b}+\color{orange}{\frac{-2}{11}}).(\color{green}{-p}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{-2}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{-2}{11})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bp+1b+\frac{2}{11}p-\frac{2}{11}.1& \text{Uitwerken } \\ & =-bp+1b+\frac{2}{11}p-\frac{2}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-12}{10}-b)(a+\frac{18}{14})& =(\color{red}{-b}+\color{orange}{\frac{-6}{5}}).(\color{green}{a}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{9}{7}b-\frac{6}{5}a-\frac{6}{5}.\frac{9}{7}& \text{Uitwerken } \\ & =-ab-\frac{9}{7}b-\frac{6}{5}a-\frac{54}{35} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p-\frac{-6}{4})(\frac{16}{5}-x)& =(\color{red}{p}+\color{orange}{\frac{3}{2}}).(\color{green}{-x}+\color{blue}{\frac{16}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{16}{5})} + \color{orange}{(\frac{3}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{16}{5})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{16}{5}p-\frac{3}{2}x+\frac{3}{2}.\frac{16}{5}& \text{Uitwerken } \\ & =-px+\frac{16}{5}p-\frac{3}{2}x+\frac{48}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{16}{5}p-\frac{3}{2}x+\frac{24}{5} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(\frac{-5}{2}+p)(\frac{6}{14}-a)& =(\color{red}{p}+\color{orange}{\frac{-5}{2}}).(\color{green}{-a}+\color{blue}{\frac{3}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{3}{7})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{3}{7})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{3}{7}p+\frac{5}{2}a-\frac{5}{2}.\frac{3}{7}& \text{Uitwerken } \\ & =-ap+\frac{3}{7}p+\frac{5}{2}a-\frac{15}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}((-10)+b)(p+\frac{-18}{13})& =(\color{red}{b}+\color{orange}{(-10)}).(\color{green}{p}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(-10)} . \color{green}{(p)} + \color{orange}{(-10)} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{18}{13}b-10p+10.\frac{18}{13}& \text{Uitwerken } \\ & =bp-\frac{18}{13}b-10p+\frac{180}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-17}{20}-p)(a+\frac{19}{4})& =(\color{red}{-p}+\color{orange}{\frac{-17}{20}}).(\color{green}{a}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{-17}{20})} . \color{green}{(a)} + \color{orange}{(\frac{-17}{20})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{19}{4}p-\frac{17}{20}a-\frac{17}{20}.\frac{19}{4}& \text{Uitwerken } \\ & =-ap-\frac{19}{4}p-\frac{17}{20}a-\frac{323}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(x-\frac{-10}{18})(a-\frac{-2}{17})& =(\color{red}{x}+\color{orange}{\frac{5}{9}}).(\color{green}{a}+\color{blue}{\frac{2}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{2}{17})} + \color{orange}{(\frac{5}{9})} . \color{green}{(a)} + \color{orange}{(\frac{5}{9})} . \color{blue}{(\frac{2}{17})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{2}{17}x+\frac{5}{9}a+\frac{5}{9}.\frac{2}{17}& \text{Uitwerken } \\ & =ax+\frac{2}{17}x+\frac{5}{9}a+\frac{10}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(b+\frac{-2}{13})(\frac{4}{10}+x)& =(\color{red}{b}+\color{orange}{\frac{-2}{13}}).(\color{green}{x}+\color{blue}{\frac{2}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{2}{5})} + \color{orange}{(\frac{-2}{13})} . \color{green}{(x)} + \color{orange}{(\frac{-2}{13})} . \color{blue}{(\frac{2}{5})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{2}{5}b-\frac{2}{13}x-\frac{2}{13}.\frac{2}{5}& \text{Uitwerken } \\ & =bx+\frac{2}{5}b-\frac{2}{13}x-\frac{4}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{-13}{16}-x)(p+\frac{-18}{11})& =(\color{red}{-x}+\color{orange}{\frac{-13}{16}}).(\color{green}{p}+\color{blue}{\frac{-18}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(\frac{-18}{11})} + \color{orange}{(\frac{-13}{16})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{16})} . \color{blue}{(\frac{-18}{11})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{18}{11}x-\frac{13}{16}p+\frac{13}{16}.\frac{18}{11}& \text{Uitwerken } \\ & =-px+\frac{18}{11}x-\frac{13}{16}p+\frac{234}{176} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -px+\frac{18}{11}x-\frac{13}{16}p+\frac{117}{88} & \text{Vereenvoudig} \\\end{align}\)