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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-11}{9}+x)(a+\frac{17}{9})& =(\color{red}{x}+\color{orange}{\frac{-11}{9}}).(\color{green}{a}+\color{blue}{\frac{17}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{17}{9})} + \color{orange}{(\frac{-11}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(\frac{17}{9})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{17}{9}x-\frac{11}{9}a-\frac{11}{9}.\frac{17}{9}& \text{Uitwerken } \\ & =ax+\frac{17}{9}x-\frac{11}{9}a-\frac{187}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-16}{11}+q)(x+\frac{18}{7})& =(\color{red}{q}+\color{orange}{\frac{-16}{11}}).(\color{green}{x}+\color{blue}{\frac{18}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{18}{7})} + \color{orange}{(\frac{-16}{11})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{11})} . \color{blue}{(\frac{18}{7})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{18}{7}q-\frac{16}{11}x-\frac{16}{11}.\frac{18}{7}& \text{Uitwerken } \\ & =qx+\frac{18}{7}q-\frac{16}{11}x-\frac{288}{77} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p-\frac{9}{13})(\frac{19}{13}-b)& =(\color{red}{p}+\color{orange}{\frac{-9}{13}}).(\color{green}{-b}+\color{blue}{\frac{19}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{19}{13})} + \color{orange}{(\frac{-9}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-9}{13})} . \color{blue}{(\frac{19}{13})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{19}{13}p+\frac{9}{13}b-\frac{9}{13}.\frac{19}{13}& \text{Uitwerken } \\ & =-bp+\frac{19}{13}p+\frac{9}{13}b-\frac{171}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{7}{9}+x)(\frac{8}{2}+p)& =(\color{red}{x}+\color{orange}{\frac{7}{9}}).(\color{green}{p}+\color{blue}{4})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(4)} + \color{orange}{(\frac{7}{9})} . \color{green}{(p)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = px+4x+\frac{7}{9}p+\frac{7}{9}.4& \text{Uitwerken } \\ & =px+4x+\frac{7}{9}p+\frac{28}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(x+\frac{12}{12})(\frac{4}{17}-p)& =(\color{red}{x}+\color{orange}{1}).(\color{green}{-p}+\color{blue}{\frac{4}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-p)} + \color{red}{(x)} . \color{blue}{(\frac{4}{17})} + \color{orange}{(1)} . \color{green}{(-p)} + \color{orange}{(1)} . \color{blue}{(\frac{4}{17})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{4}{17}x-1p+1.\frac{4}{17}& \text{Uitwerken } \\ & =-px+\frac{4}{17}x-1p+\frac{4}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a+\frac{17}{17})(\frac{-12}{15}-p)& =(\color{red}{a}+\color{orange}{1}).(\color{green}{-p}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(1)} . \color{green}{(-p)} + \color{orange}{(1)} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{4}{5}a-1p-1.\frac{4}{5}& \text{Uitwerken } \\ & =-ap-\frac{4}{5}a-1p-\frac{4}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{1}{15}+b)(q+\frac{-16}{19})& =(\color{red}{b}+\color{orange}{\frac{1}{15}}).(\color{green}{q}+\color{blue}{\frac{-16}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-16}{19})} + \color{orange}{(\frac{1}{15})} . \color{green}{(q)} + \color{orange}{(\frac{1}{15})} . \color{blue}{(\frac{-16}{19})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{16}{19}b+\frac{1}{15}q-\frac{1}{15}.\frac{16}{19}& \text{Uitwerken } \\ & =bq-\frac{16}{19}b+\frac{1}{15}q-\frac{16}{285} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-20}{10}+q)(\frac{-5}{16}+q)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{q}+\color{blue}{\frac{-5}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-5}{16})} + \color{orange}{(-2)} . \color{green}{(q)} + \color{orange}{(-2)} . \color{blue}{(\frac{-5}{16})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{5}{16}q-2q+2.\frac{5}{16}& \text{Uitwerken } \\ & =q^2+((\frac{-5}{16})+(-2))q+\frac{10}{16} & \text{Neem samen} \\ &=q^2-\frac{37}{16}q+\frac{10}{16} & \text{Maak de som} \\ &=q^2-\frac{37}{16}q+\frac{5}{8} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
9. \(\begin{align}(a-\frac{-20}{9})(p-\frac{-18}{5})& =(\color{red}{a}+\color{orange}{\frac{20}{9}}).(\color{green}{p}+\color{blue}{\frac{18}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{18}{5})} + \color{orange}{(\frac{20}{9})} . \color{green}{(p)} + \color{orange}{(\frac{20}{9})} . \color{blue}{(\frac{18}{5})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{18}{5}a+\frac{20}{9}p+\frac{20}{9}.\frac{18}{5}& \text{Uitwerken } \\ & =ap+\frac{18}{5}a+\frac{20}{9}p+\frac{360}{45} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{18}{5}a+\frac{20}{9}p+8 & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-3}{7}+a)(p-\frac{6}{12})& =(\color{red}{a}+\color{orange}{\frac{-3}{7}}).(\color{green}{p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-3}{7})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{7})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{1}{2}a-\frac{3}{7}p+\frac{3}{7}.\frac{1}{2}& \text{Uitwerken } \\ & =ap-\frac{1}{2}a-\frac{3}{7}p+\frac{3}{14} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{4}{4}+x)(q-\frac{-3}{6})& =(\color{red}{x}+\color{orange}{1}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(1)} . \color{green}{(q)} + \color{orange}{(1)} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{2}x+1q+1.\frac{1}{2}& \text{Uitwerken } \\ & =qx+\frac{1}{2}x+1q+\frac{1}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p+\frac{15}{8})(\frac{-14}{2}+x)& =(\color{red}{p}+\color{orange}{\frac{15}{8}}).(\color{green}{x}+\color{blue}{(-7)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(-7)} + \color{orange}{(\frac{15}{8})} . \color{green}{(x)} + \color{orange}{(\frac{15}{8})} . \color{blue}{(-7)}& \text{Boogjes en uitschrijven} \\ & = px-7p+\frac{15}{8}x-\frac{15}{8}.7& \text{Uitwerken } \\ & =px-7p+\frac{15}{8}x-\frac{105}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)