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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-7}{9}-p)(p+\frac{6}{19})& =(\color{red}{-p}+\color{orange}{\frac{-7}{9}}).(\color{green}{p}+\color{blue}{\frac{6}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{6}{19})} + \color{orange}{(\frac{-7}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{9})} . \color{blue}{(\frac{6}{19})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{6}{19}p-\frac{7}{9}p-\frac{7}{9}.\frac{6}{19}& \text{Uitwerken } \\ & =-p^2+((\frac{-6}{19})+(\frac{-7}{9}))p-\frac{42}{171} & \text{Neem samen} \\ &=-p^2-\frac{187}{171}p-\frac{42}{171} & \text{Maak de som} \\ &=-p^2-\frac{187}{171}p-\frac{14}{57} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
2. \(\begin{align}(\frac{-13}{9}-q)(\frac{-9}{19}+a)& =(\color{red}{-q}+\color{orange}{\frac{-13}{9}}).(\color{green}{a}+\color{blue}{\frac{-9}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-9}{19})} + \color{orange}{(\frac{-13}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{9})} . \color{blue}{(\frac{-9}{19})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{9}{19}q-\frac{13}{9}a+\frac{13}{9}.\frac{9}{19}& \text{Uitwerken } \\ & =-aq+\frac{9}{19}q-\frac{13}{9}a+\frac{117}{171} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+\frac{9}{19}q-\frac{13}{9}a+\frac{13}{19} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(x-19)(x+\frac{-17}{17})& =(\color{red}{x}+\color{orange}{(-19)}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(-19)} . \color{green}{(x)} + \color{orange}{(-19)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = xx-1x-19x+19.1& \text{Uitwerken } \\ & =x^2+((-1)+(-19))x+19 & \text{Neem samen} \\ &=x^2-20x+19 & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(\frac{10}{12}+p)(\frac{13}{9}-x)& =(\color{red}{p}+\color{orange}{\frac{5}{6}}).(\color{green}{-x}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{5}{6})} . \color{green}{(-x)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{13}{9}p-\frac{5}{6}x+\frac{5}{6}.\frac{13}{9}& \text{Uitwerken } \\ & =-px+\frac{13}{9}p-\frac{5}{6}x+\frac{65}{54} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p+\frac{6}{6})(a-\frac{7}{18})& =(\color{red}{p}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-7}{18}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{18})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-7}{18})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{7}{18}p+1a-1.\frac{7}{18}& \text{Uitwerken } \\ & =ap-\frac{7}{18}p+1a-\frac{7}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-2}{12}-b)(\frac{9}{20}-p)& =(\color{red}{-b}+\color{orange}{\frac{-1}{6}}).(\color{green}{-p}+\color{blue}{\frac{9}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-p)} + \color{red}{(-b)} . \color{blue}{(\frac{9}{20})} + \color{orange}{(\frac{-1}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{6})} . \color{blue}{(\frac{9}{20})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{9}{20}b+\frac{1}{6}p-\frac{1}{6}.\frac{9}{20}& \text{Uitwerken } \\ & =bp-\frac{9}{20}b+\frac{1}{6}p-\frac{9}{120} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{9}{20}b+\frac{1}{6}p-\frac{3}{40} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(a+\frac{-3}{4})(p-\frac{11}{2})& =(\color{red}{a}+\color{orange}{\frac{-3}{4}}).(\color{green}{p}+\color{blue}{\frac{-11}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-11}{2})} + \color{orange}{(\frac{-3}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(\frac{-11}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{11}{2}a-\frac{3}{4}p+\frac{3}{4}.\frac{11}{2}& \text{Uitwerken } \\ & =ap-\frac{11}{2}a-\frac{3}{4}p+\frac{33}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(x+\frac{6}{6})(x+\frac{-12}{12})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{x}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(1)} . \color{green}{(x)} + \color{orange}{(1)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = xx-1x+1x-1.1& \text{Uitwerken } \\ & =x^2+((-1)+1)x-(-1) & \text{Neem samen} \\ &=x^2+0x-(-1) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(b-\frac{6}{7})(p+\frac{9}{4})& =(\color{red}{b}+\color{orange}{\frac{-6}{7}}).(\color{green}{p}+\color{blue}{\frac{9}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{9}{4})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{9}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{9}{4}b-\frac{6}{7}p-\frac{6}{7}.\frac{9}{4}& \text{Uitwerken } \\ & =bp+\frac{9}{4}b-\frac{6}{7}p-\frac{54}{28} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{9}{4}b-\frac{6}{7}p-\frac{27}{14} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{9}{15}+b)(\frac{-6}{9}-b)& =(\color{red}{b}+\color{orange}{\frac{3}{5}}).(\color{green}{-b}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{3}{5})} . \color{green}{(-b)} + \color{orange}{(\frac{3}{5})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -bb-\frac{2}{3}b-\frac{3}{5}b-\frac{3}{5}.\frac{2}{3}& \text{Uitwerken } \\ & =-b^2+((\frac{-2}{3})+(\frac{-3}{5}))b-\frac{6}{15} & \text{Neem samen} \\ &=-b^2-\frac{19}{15}b-\frac{6}{15} & \text{Maak de som} \\ &=-b^2-\frac{19}{15}b-\frac{2}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
11. \(\begin{align}(q-\frac{-4}{15})(p-\frac{-2}{13})& =(\color{red}{q}+\color{orange}{\frac{4}{15}}).(\color{green}{p}+\color{blue}{\frac{2}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{2}{13})} + \color{orange}{(\frac{4}{15})} . \color{green}{(p)} + \color{orange}{(\frac{4}{15})} . \color{blue}{(\frac{2}{13})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{2}{13}q+\frac{4}{15}p+\frac{4}{15}.\frac{2}{13}& \text{Uitwerken } \\ & =pq+\frac{2}{13}q+\frac{4}{15}p+\frac{8}{195} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(b+\frac{4}{5})(\frac{-9}{7}+b)& =(\color{red}{b}+\color{orange}{\frac{4}{5}}).(\color{green}{b}+\color{blue}{\frac{-9}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-9}{7})} + \color{orange}{(\frac{4}{5})} . \color{green}{(b)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{-9}{7})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{9}{7}b+\frac{4}{5}b-\frac{4}{5}.\frac{9}{7}& \text{Uitwerken } \\ & =b^2+((\frac{-9}{7})+\frac{4}{5})b-(\frac{-36}{35}) & \text{Neem samen} \\ &=b^2-\frac{17}{35}b-(\frac{-36}{35}) & \text{Maak de som} \\\end{align}\)