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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{9}{14}+b)((-13)+a)& =(\color{red}{b}+\color{orange}{\frac{9}{14}}).(\color{green}{a}+\color{blue}{(-13)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-13)} + \color{orange}{(\frac{9}{14})} . \color{green}{(a)} + \color{orange}{(\frac{9}{14})} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = ab-13b+\frac{9}{14}a-\frac{9}{14}.13& \text{Uitwerken } \\ & =ab-13b+\frac{9}{14}a-\frac{117}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{14}{2}+x)(\frac{7}{19}-x)& =(\color{red}{x}+\color{orange}{7}).(\color{green}{-x}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(7)} . \color{green}{(-x)} + \color{orange}{(7)} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{7}{19}x-7x+7.\frac{7}{19}& \text{Uitwerken } \\ & =-x^2+(\frac{7}{19}+(-7))x+(\frac{-49}{19}) & \text{Neem samen} \\ &=-x^2-\frac{126}{19}x+(\frac{-49}{19}) & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(\frac{-4}{8}-q)(\frac{-1}{8}+b)& =(\color{red}{-q}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{-1}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-1}{8})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-1}{8})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{1}{8}q-\frac{1}{2}b+\frac{1}{2}.\frac{1}{8}& \text{Uitwerken } \\ & =-bq+\frac{1}{8}q-\frac{1}{2}b+\frac{1}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-9}{9}+x)(\frac{2}{2}+b)& =(\color{red}{x}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(1)} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bx+1x-1b-1.1& \text{Uitwerken } \\ & =bx+1x-1b-1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{7}{2}-a)(\frac{-2}{10}-q)& =(\color{red}{-a}+\color{orange}{\frac{7}{2}}).(\color{green}{-q}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-q)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{7}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{7}{2})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{5}a-\frac{7}{2}q-\frac{7}{2}.\frac{1}{5}& \text{Uitwerken } \\ & =aq+\frac{1}{5}a-\frac{7}{2}q-\frac{7}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{7}{16})(q+\frac{15}{4})& =(\color{red}{a}+\color{orange}{\frac{7}{16}}).(\color{green}{q}+\color{blue}{\frac{15}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{15}{4})} + \color{orange}{(\frac{7}{16})} . \color{green}{(q)} + \color{orange}{(\frac{7}{16})} . \color{blue}{(\frac{15}{4})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{15}{4}a+\frac{7}{16}q+\frac{7}{16}.\frac{15}{4}& \text{Uitwerken } \\ & =aq+\frac{15}{4}a+\frac{7}{16}q+\frac{105}{64} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p-\frac{-14}{12})(x-\frac{16}{17})& =(\color{red}{p}+\color{orange}{\frac{7}{6}}).(\color{green}{x}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(\frac{7}{6})} . \color{green}{(x)} + \color{orange}{(\frac{7}{6})} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{16}{17}p+\frac{7}{6}x-\frac{7}{6}.\frac{16}{17}& \text{Uitwerken } \\ & =px-\frac{16}{17}p+\frac{7}{6}x-\frac{112}{102} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px-\frac{16}{17}p+\frac{7}{6}x-\frac{56}{51} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(x+\frac{-15}{16})(\frac{11}{13}-x)& =(\color{red}{x}+\color{orange}{\frac{-15}{16}}).(\color{green}{-x}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(\frac{-15}{16})} . \color{green}{(-x)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{11}{13}x+\frac{15}{16}x-\frac{15}{16}.\frac{11}{13}& \text{Uitwerken } \\ & =-x^2+(\frac{11}{13}+\frac{15}{16})x-\frac{165}{208} & \text{Neem samen} \\ &=-x^2+\frac{371}{208}x-\frac{165}{208} & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(\frac{-18}{20}+b)(\frac{-12}{9}+p)& =(\color{red}{b}+\color{orange}{\frac{-9}{10}}).(\color{green}{p}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(\frac{-9}{10})} . \color{green}{(p)} + \color{orange}{(\frac{-9}{10})} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{4}{3}b-\frac{9}{10}p+\frac{9}{10}.\frac{4}{3}& \text{Uitwerken } \\ & =bp-\frac{4}{3}b-\frac{9}{10}p+\frac{36}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{4}{3}b-\frac{9}{10}p+\frac{6}{5} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(q+\frac{-15}{2})(3-a)& =(\color{red}{q}+\color{orange}{\frac{-15}{2}}).(\color{green}{-a}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-a)} + \color{red}{(q)} . \color{blue}{(3)} + \color{orange}{(\frac{-15}{2})} . \color{green}{(-a)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -aq+3q+\frac{15}{2}a-\frac{15}{2}.3& \text{Uitwerken } \\ & =-aq+3q+\frac{15}{2}a-\frac{45}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}((-3)+b)(\frac{14}{6}+x)& =(\color{red}{b}+\color{orange}{(-3)}).(\color{green}{x}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(-3)} . \color{green}{(x)} + \color{orange}{(-3)} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{7}{3}b-3x-3.\frac{7}{3}& \text{Uitwerken } \\ & =bx+\frac{7}{3}b-3x-\frac{21}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{7}{3}b-3x-7 & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-19}{15}+b)(b+\frac{-13}{9})& =(\color{red}{b}+\color{orange}{\frac{-19}{15}}).(\color{green}{b}+\color{blue}{\frac{-13}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{9})} + \color{orange}{(\frac{-19}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-19}{15})} . \color{blue}{(\frac{-13}{9})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{13}{9}b-\frac{19}{15}b+\frac{19}{15}.\frac{13}{9}& \text{Uitwerken } \\ & =b^2+((\frac{-13}{9})+(\frac{-19}{15}))b+\frac{247}{135} & \text{Neem samen} \\ &=b^2-\frac{122}{45}b+\frac{247}{135} & \text{Maak de som} \\\end{align}\)