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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b-\frac{-1}{14})(a+\frac{-11}{14})& =(\color{red}{b}+\color{orange}{\frac{1}{14}}).(\color{green}{a}+\color{blue}{\frac{-11}{14}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-11}{14})} + \color{orange}{(\frac{1}{14})} . \color{green}{(a)} + \color{orange}{(\frac{1}{14})} . \color{blue}{(\frac{-11}{14})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{11}{14}b+\frac{1}{14}a-\frac{1}{14}.\frac{11}{14}& \text{Uitwerken } \\ & =ab-\frac{11}{14}b+\frac{1}{14}a-\frac{11}{196} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{3}{7}-b)(a+\frac{11}{3})& =(\color{red}{-b}+\color{orange}{\frac{3}{7}}).(\color{green}{a}+\color{blue}{\frac{11}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(a)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{3})} + \color{orange}{(\frac{3}{7})} . \color{green}{(a)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(\frac{11}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{11}{3}b+\frac{3}{7}a+\frac{3}{7}.\frac{11}{3}& \text{Uitwerken } \\ & =-ab-\frac{11}{3}b+\frac{3}{7}a+\frac{33}{21} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab-\frac{11}{3}b+\frac{3}{7}a+\frac{11}{7} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(p-\frac{16}{15})(b-\frac{-10}{20})& =(\color{red}{p}+\color{orange}{\frac{-16}{15}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-16}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-16}{15})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{2}p-\frac{16}{15}b-\frac{16}{15}.\frac{1}{2}& \text{Uitwerken } \\ & =bp+\frac{1}{2}p-\frac{16}{15}b-\frac{16}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{1}{2}p-\frac{16}{15}b-\frac{8}{15} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{19}{19}-a)(b-13)& =(\color{red}{-a}+\color{orange}{1}).(\color{green}{b}+\color{blue}{(-13)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(-13)} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = -ab+13a+1b-1.13& \text{Uitwerken } \\ & =-ab+13a+1b-13 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{20}{10}+p)(b+\frac{19}{2})& =(\color{red}{p}+\color{orange}{2}).(\color{green}{b}+\color{blue}{\frac{19}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{19}{2})} + \color{orange}{(2)} . \color{green}{(b)} + \color{orange}{(2)} . \color{blue}{(\frac{19}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{2}p+2b+2.\frac{19}{2}& \text{Uitwerken } \\ & =bp+\frac{19}{2}p+2b+\frac{38}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{19}{2}p+2b+19 & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{12}{3}+q)(x+\frac{-15}{5})& =(\color{red}{q}+\color{orange}{4}).(\color{green}{x}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-3)} + \color{orange}{(4)} . \color{green}{(x)} + \color{orange}{(4)} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = qx-3q+4x-4.3& \text{Uitwerken } \\ & =qx-3q+4x-12 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-1}{14}+b)(p-\frac{-17}{10})& =(\color{red}{b}+\color{orange}{\frac{-1}{14}}).(\color{green}{p}+\color{blue}{\frac{17}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{17}{10})} + \color{orange}{(\frac{-1}{14})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{14})} . \color{blue}{(\frac{17}{10})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{17}{10}b-\frac{1}{14}p-\frac{1}{14}.\frac{17}{10}& \text{Uitwerken } \\ & =bp+\frac{17}{10}b-\frac{1}{14}p-\frac{17}{140} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-13}{2}+x)(\frac{-17}{9}+x)& =(\color{red}{x}+\color{orange}{\frac{-13}{2}}).(\color{green}{x}+\color{blue}{\frac{-17}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-17}{9})} + \color{orange}{(\frac{-13}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-13}{2})} . \color{blue}{(\frac{-17}{9})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{17}{9}x-\frac{13}{2}x+\frac{13}{2}.\frac{17}{9}& \text{Uitwerken } \\ & =x^2+((\frac{-17}{9})+(\frac{-13}{2}))x+\frac{221}{18} & \text{Neem samen} \\ &=x^2-\frac{151}{18}x+\frac{221}{18} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(p+\frac{-15}{3})(\frac{18}{10}+b)& =(\color{red}{p}+\color{orange}{(-5)}).(\color{green}{b}+\color{blue}{\frac{9}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{9}{5})} + \color{orange}{(-5)} . \color{green}{(b)} + \color{orange}{(-5)} . \color{blue}{(\frac{9}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{5}p-5b-5.\frac{9}{5}& \text{Uitwerken } \\ & =bp+\frac{9}{5}p-5b-\frac{45}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{9}{5}p-5b-9 & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p+\frac{11}{12})(3+q)& =(\color{red}{p}+\color{orange}{\frac{11}{12}}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(\frac{11}{12})} . \color{green}{(q)} + \color{orange}{(\frac{11}{12})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = pq+3p+\frac{11}{12}q+\frac{11}{12}.3& \text{Uitwerken } \\ & =pq+3p+\frac{11}{12}q+\frac{33}{12} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+3p+\frac{11}{12}q+\frac{11}{4} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(a+\frac{20}{4})(p+\frac{5}{3})& =(\color{red}{a}+\color{orange}{5}).(\color{green}{p}+\color{blue}{\frac{5}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{5}{3})} + \color{orange}{(5)} . \color{green}{(p)} + \color{orange}{(5)} . \color{blue}{(\frac{5}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{5}{3}a+5p+5.\frac{5}{3}& \text{Uitwerken } \\ & =ap+\frac{5}{3}a+5p+\frac{25}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(a-\frac{3}{10})(18-x)& =(\color{red}{a}+\color{orange}{\frac{-3}{10}}).(\color{green}{-x}+\color{blue}{18})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(18)} + \color{orange}{(\frac{-3}{10})} . \color{green}{(-x)} + \color{orange}{(\frac{-3}{10})} . \color{blue}{(18)}& \text{Boogjes en uitschrijven} \\ & = -ax+18a+\frac{3}{10}x-\frac{3}{10}.18& \text{Uitwerken } \\ & =-ax+18a+\frac{3}{10}x-\frac{54}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax+18a+\frac{3}{10}x-\frac{27}{5} & \text{Vereenvoudig} \\\end{align}\)