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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-14}{14}+p)(a+\frac{17}{5})& =(\color{red}{p}+\color{orange}{(-1)}).(\color{green}{a}+\color{blue}{\frac{17}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{17}{5})} + \color{orange}{(-1)} . \color{green}{(a)} + \color{orange}{(-1)} . \color{blue}{(\frac{17}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{17}{5}p-1a-1.\frac{17}{5}& \text{Uitwerken } \\ & =ap+\frac{17}{5}p-1a-\frac{17}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{4}{11}+q)(\frac{-17}{16}-p)& =(\color{red}{q}+\color{orange}{\frac{4}{11}}).(\color{green}{-p}+\color{blue}{\frac{-17}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-p)} + \color{red}{(q)} . \color{blue}{(\frac{-17}{16})} + \color{orange}{(\frac{4}{11})} . \color{green}{(-p)} + \color{orange}{(\frac{4}{11})} . \color{blue}{(\frac{-17}{16})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{17}{16}q-\frac{4}{11}p-\frac{4}{11}.\frac{17}{16}& \text{Uitwerken } \\ & =-pq-\frac{17}{16}q-\frac{4}{11}p-\frac{68}{176} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{17}{16}q-\frac{4}{11}p-\frac{17}{44} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{9}{6}+p)(a-\frac{-20}{19})& =(\color{red}{p}+\color{orange}{\frac{3}{2}}).(\color{green}{a}+\color{blue}{\frac{20}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{20}{19})} + \color{orange}{(\frac{3}{2})} . \color{green}{(a)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{20}{19})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{20}{19}p+\frac{3}{2}a+\frac{3}{2}.\frac{20}{19}& \text{Uitwerken } \\ & =ap+\frac{20}{19}p+\frac{3}{2}a+\frac{60}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{20}{19}p+\frac{3}{2}a+\frac{30}{19} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{3}{17}+p)(\frac{-3}{15}+q)& =(\color{red}{p}+\color{orange}{\frac{3}{17}}).(\color{green}{q}+\color{blue}{\frac{-1}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{5})} + \color{orange}{(\frac{3}{17})} . \color{green}{(q)} + \color{orange}{(\frac{3}{17})} . \color{blue}{(\frac{-1}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{5}p+\frac{3}{17}q-\frac{3}{17}.\frac{1}{5}& \text{Uitwerken } \\ & =pq-\frac{1}{5}p+\frac{3}{17}q-\frac{3}{85} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(p+\frac{-2}{17})(q+\frac{-8}{9})& =(\color{red}{p}+\color{orange}{\frac{-2}{17}}).(\color{green}{q}+\color{blue}{\frac{-8}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{9})} + \color{orange}{(\frac{-2}{17})} . \color{green}{(q)} + \color{orange}{(\frac{-2}{17})} . \color{blue}{(\frac{-8}{9})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{8}{9}p-\frac{2}{17}q+\frac{2}{17}.\frac{8}{9}& \text{Uitwerken } \\ & =pq-\frac{8}{9}p-\frac{2}{17}q+\frac{16}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(p+\frac{12}{11})(\frac{8}{8}+a)& =(\color{red}{p}+\color{orange}{\frac{12}{11}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{12}{11})} . \color{green}{(a)} + \color{orange}{(\frac{12}{11})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ap+1p+\frac{12}{11}a+\frac{12}{11}.1& \text{Uitwerken } \\ & =ap+1p+\frac{12}{11}a+\frac{12}{11} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{2}{16}-a)(p-\frac{-11}{17})& =(\color{red}{-a}+\color{orange}{\frac{1}{8}}).(\color{green}{p}+\color{blue}{\frac{11}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{11}{17})} + \color{orange}{(\frac{1}{8})} . \color{green}{(p)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{11}{17})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{11}{17}a+\frac{1}{8}p+\frac{1}{8}.\frac{11}{17}& \text{Uitwerken } \\ & =-ap-\frac{11}{17}a+\frac{1}{8}p+\frac{11}{136} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(q+\frac{15}{9})(q+\frac{-1}{2})& =(\color{red}{q}+\color{orange}{\frac{5}{3}}).(\color{green}{q}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{5}{3})} . \color{green}{(q)} + \color{orange}{(\frac{5}{3})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{1}{2}q+\frac{5}{3}q-\frac{5}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =q^2+((\frac{-1}{2})+\frac{5}{3})q-(\frac{-5}{6}) & \text{Neem samen} \\ &=q^2+\frac{7}{6}q-(\frac{-5}{6}) & \text{Maak de som} \\\end{align}\)
9. \(\begin{align}(\frac{-5}{11}-b)(\frac{-16}{4}+b)& =(\color{red}{-b}+\color{orange}{\frac{-5}{11}}).(\color{green}{b}+\color{blue}{(-4)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(b)} + \color{red}{(-b)} . \color{blue}{(-4)} + \color{orange}{(\frac{-5}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{11})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -bb+4b-\frac{5}{11}b+\frac{5}{11}.4& \text{Uitwerken } \\ & =-b^2+(4+(\frac{-5}{11}))b+(\frac{-20}{11}) & \text{Neem samen} \\ &=-b^2+\frac{39}{11}b+(\frac{-20}{11}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(\frac{-19}{2}+a)(\frac{-15}{8}-x)& =(\color{red}{a}+\color{orange}{\frac{-19}{2}}).(\color{green}{-x}+\color{blue}{\frac{-15}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{8})} + \color{orange}{(\frac{-19}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{2})} . \color{blue}{(\frac{-15}{8})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{15}{8}a+\frac{19}{2}x+\frac{19}{2}.\frac{15}{8}& \text{Uitwerken } \\ & =-ax-\frac{15}{8}a+\frac{19}{2}x+\frac{285}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p+(-4))(\frac{14}{15}-q)& =(\color{red}{p}+\color{orange}{(-4)}).(\color{green}{-q}+\color{blue}{\frac{14}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{14}{15})} + \color{orange}{(-4)} . \color{green}{(-q)} + \color{orange}{(-4)} . \color{blue}{(\frac{14}{15})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{14}{15}p+4q-4.\frac{14}{15}& \text{Uitwerken } \\ & =-pq+\frac{14}{15}p+4q-\frac{56}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q-\frac{6}{15})(\frac{-6}{19}+b)& =(\color{red}{q}+\color{orange}{\frac{-2}{5}}).(\color{green}{b}+\color{blue}{\frac{-6}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-6}{19})} + \color{orange}{(\frac{-2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(\frac{-6}{19})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{6}{19}q-\frac{2}{5}b+\frac{2}{5}.\frac{6}{19}& \text{Uitwerken } \\ & =bq-\frac{6}{19}q-\frac{2}{5}b+\frac{12}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)