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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{5}{12}+b)(\frac{-13}{15}+a)& =(\color{red}{b}+\color{orange}{\frac{5}{12}}).(\color{green}{a}+\color{blue}{\frac{-13}{15}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{15})} + \color{orange}{(\frac{5}{12})} . \color{green}{(a)} + \color{orange}{(\frac{5}{12})} . \color{blue}{(\frac{-13}{15})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{15}b+\frac{5}{12}a-\frac{5}{12}.\frac{13}{15}& \text{Uitwerken } \\ & =ab-\frac{13}{15}b+\frac{5}{12}a-\frac{65}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{13}{15}b+\frac{5}{12}a-\frac{13}{36} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{13}{16}-p)(\frac{5}{5}-q)& =(\color{red}{-p}+\color{orange}{\frac{13}{16}}).(\color{green}{-q}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-q)} + \color{red}{(-p)} . \color{blue}{(1)} + \color{orange}{(\frac{13}{16})} . \color{green}{(-q)} + \color{orange}{(\frac{13}{16})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = pq-1p-\frac{13}{16}q+\frac{13}{16}.1& \text{Uitwerken } \\ & =pq-1p-\frac{13}{16}q+\frac{13}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-10}{10}-p)(\frac{-9}{3}-b)& =(\color{red}{-p}+\color{orange}{(-1)}).(\color{green}{-b}+\color{blue}{(-3)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-b)} + \color{red}{(-p)} . \color{blue}{(-3)} + \color{orange}{(-1)} . \color{green}{(-b)} + \color{orange}{(-1)} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bp+3p+1b+1.3& \text{Uitwerken } \\ & =bp+3p+1b+3 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(b+\frac{-12}{19})(p-\frac{-3}{15})& =(\color{red}{b}+\color{orange}{\frac{-12}{19}}).(\color{green}{p}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{-12}{19})} . \color{green}{(p)} + \color{orange}{(\frac{-12}{19})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{1}{5}b-\frac{12}{19}p-\frac{12}{19}.\frac{1}{5}& \text{Uitwerken } \\ & =bp+\frac{1}{5}b-\frac{12}{19}p-\frac{12}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p-\frac{2}{8})(\frac{-1}{16}-x)& =(\color{red}{p}+\color{orange}{\frac{-1}{4}}).(\color{green}{-x}+\color{blue}{\frac{-1}{16}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{16})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-1}{16})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{1}{16}p+\frac{1}{4}x+\frac{1}{4}.\frac{1}{16}& \text{Uitwerken } \\ & =-px-\frac{1}{16}p+\frac{1}{4}x+\frac{1}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b+\frac{-11}{18})(b-\frac{-8}{14})& =(\color{red}{b}+\color{orange}{\frac{-11}{18}}).(\color{green}{b}+\color{blue}{\frac{4}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{4}{7})} + \color{orange}{(\frac{-11}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{18})} . \color{blue}{(\frac{4}{7})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{4}{7}b-\frac{11}{18}b-\frac{11}{18}.\frac{4}{7}& \text{Uitwerken } \\ & =b^2+(\frac{4}{7}+(\frac{-11}{18}))b-(\frac{-44}{126}) & \text{Neem samen} \\ &=b^2-\frac{5}{126}b-(\frac{-44}{126}) & \text{Maak de som} \\ &=b^2-\frac{5}{126}b+\frac{22}{63} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
7. \(\begin{align}(q-\frac{11}{11})(\frac{-16}{19}-q)& =(\color{red}{q}+\color{orange}{(-1)}).(\color{green}{-q}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(-1)} . \color{green}{(-q)} + \color{orange}{(-1)} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{16}{19}q+1q+1.\frac{16}{19}& \text{Uitwerken } \\ & =-q^2+((\frac{-16}{19})+1)q+(\frac{-16}{19}) & \text{Neem samen} \\ &=-q^2+\frac{3}{19}q+(\frac{-16}{19}) & \text{Maak de som} \\\end{align}\)
8. \(\begin{align}(4-p)(x+\frac{10}{9})& =(\color{red}{-p}+\color{orange}{4}).(\color{green}{x}+\color{blue}{\frac{10}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{10}{9})} + \color{orange}{(4)} . \color{green}{(x)} + \color{orange}{(4)} . \color{blue}{(\frac{10}{9})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{10}{9}p+4x+4.\frac{10}{9}& \text{Uitwerken } \\ & =-px-\frac{10}{9}p+4x+\frac{40}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(b+\frac{-18}{6})(x+\frac{-20}{13})& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{x}+\color{blue}{\frac{-20}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-20}{13})} + \color{orange}{(-3)} . \color{green}{(x)} + \color{orange}{(-3)} . \color{blue}{(\frac{-20}{13})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{20}{13}b-3x+3.\frac{20}{13}& \text{Uitwerken } \\ & =bx-\frac{20}{13}b-3x+\frac{60}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{16}{17}+a)(x+\frac{14}{14})& =(\color{red}{a}+\color{orange}{\frac{16}{17}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(1)} + \color{orange}{(\frac{16}{17})} . \color{green}{(x)} + \color{orange}{(\frac{16}{17})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ax+1a+\frac{16}{17}x+\frac{16}{17}.1& \text{Uitwerken } \\ & =ax+1a+\frac{16}{17}x+\frac{16}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-9}{11}-a)(\frac{5}{12}-x)& =(\color{red}{-a}+\color{orange}{\frac{-9}{11}}).(\color{green}{-x}+\color{blue}{\frac{5}{12}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(\frac{5}{12})} + \color{orange}{(\frac{-9}{11})} . \color{green}{(-x)} + \color{orange}{(\frac{-9}{11})} . \color{blue}{(\frac{5}{12})}& \text{Boogjes en uitschrijven} \\ & = ax-\frac{5}{12}a+\frac{9}{11}x-\frac{9}{11}.\frac{5}{12}& \text{Uitwerken } \\ & =ax-\frac{5}{12}a+\frac{9}{11}x-\frac{45}{132} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax-\frac{5}{12}a+\frac{9}{11}x-\frac{15}{44} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(b-\frac{18}{9})(b+\frac{18}{14})& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{9}{7}b-2b-2.\frac{9}{7}& \text{Uitwerken } \\ & =b^2+(\frac{9}{7}+(-2))b-(\frac{-18}{7}) & \text{Neem samen} \\ &=b^2-\frac{5}{7}b-(\frac{-18}{7}) & \text{Maak de som} \\\end{align}\)