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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{17}{5}+x)(\frac{-16}{17}-x)& =(\color{red}{x}+\color{orange}{\frac{17}{5}}).(\color{green}{-x}+\color{blue}{\frac{-16}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{-16}{17})} + \color{orange}{(\frac{17}{5})} . \color{green}{(-x)} + \color{orange}{(\frac{17}{5})} . \color{blue}{(\frac{-16}{17})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{16}{17}x-\frac{17}{5}x-\frac{17}{5}.\frac{16}{17}& \text{Uitwerken } \\ & =-x^2+((\frac{-16}{17})+(\frac{-17}{5}))x-\frac{272}{85} & \text{Neem samen} \\ &=-x^2-\frac{369}{85}x-\frac{272}{85} & \text{Maak de som} \\ &=-x^2-\frac{369}{85}x-\frac{16}{5} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
2. \(\begin{align}(a+\frac{-7}{19})(\frac{1}{8}+q)& =(\color{red}{a}+\color{orange}{\frac{-7}{19}}).(\color{green}{q}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{-7}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-7}{19})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{1}{8}a-\frac{7}{19}q-\frac{7}{19}.\frac{1}{8}& \text{Uitwerken } \\ & =aq+\frac{1}{8}a-\frac{7}{19}q-\frac{7}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}((-15)+a)(\frac{17}{16}-p)& =(\color{red}{a}+\color{orange}{(-15)}).(\color{green}{-p}+\color{blue}{\frac{17}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{17}{16})} + \color{orange}{(-15)} . \color{green}{(-p)} + \color{orange}{(-15)} . \color{blue}{(\frac{17}{16})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{17}{16}a+15p-15.\frac{17}{16}& \text{Uitwerken } \\ & =-ap+\frac{17}{16}a+15p-\frac{255}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q-\frac{-6}{20})(q+\frac{-10}{13})& =(\color{red}{q}+\color{orange}{\frac{3}{10}}).(\color{green}{q}+\color{blue}{\frac{-10}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-10}{13})} + \color{orange}{(\frac{3}{10})} . \color{green}{(q)} + \color{orange}{(\frac{3}{10})} . \color{blue}{(\frac{-10}{13})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{10}{13}q+\frac{3}{10}q-\frac{3}{10}.\frac{10}{13}& \text{Uitwerken } \\ & =q^2+((\frac{-10}{13})+\frac{3}{10})q-(\frac{-30}{130}) & \text{Neem samen} \\ &=q^2-\frac{61}{130}q-(\frac{-30}{130}) & \text{Maak de som} \\ &=q^2-\frac{61}{130}q+\frac{3}{13} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
5. \(\begin{align}(\frac{-14}{2}+p)(\frac{10}{5}+p)& =(\color{red}{p}+\color{orange}{(-7)}).(\color{green}{p}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(-7)} . \color{green}{(p)} + \color{orange}{(-7)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = pp+2p-7p-7.2& \text{Uitwerken } \\ & =p^2+(2+(-7))p-(-14) & \text{Neem samen} \\ &=p^2-5p-(-14) & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(a+\frac{8}{18})(b-\frac{6}{6})& =(\color{red}{a}+\color{orange}{\frac{4}{9}}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{4}{9})} . \color{green}{(b)} + \color{orange}{(\frac{4}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab-1a+\frac{4}{9}b-\frac{4}{9}.1& \text{Uitwerken } \\ & =ab-1a+\frac{4}{9}b-\frac{4}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p+\frac{7}{12})(\frac{2}{10}-x)& =(\color{red}{p}+\color{orange}{\frac{7}{12}}).(\color{green}{-x}+\color{blue}{\frac{1}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{1}{5})} + \color{orange}{(\frac{7}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{7}{12})} . \color{blue}{(\frac{1}{5})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{1}{5}p-\frac{7}{12}x+\frac{7}{12}.\frac{1}{5}& \text{Uitwerken } \\ & =-px+\frac{1}{5}p-\frac{7}{12}x+\frac{7}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{16}{15}-p)(a-\frac{-11}{12})& =(\color{red}{-p}+\color{orange}{\frac{16}{15}}).(\color{green}{a}+\color{blue}{\frac{11}{12}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{11}{12})} + \color{orange}{(\frac{16}{15})} . \color{green}{(a)} + \color{orange}{(\frac{16}{15})} . \color{blue}{(\frac{11}{12})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{11}{12}p+\frac{16}{15}a+\frac{16}{15}.\frac{11}{12}& \text{Uitwerken } \\ & =-ap-\frac{11}{12}p+\frac{16}{15}a+\frac{176}{180} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{11}{12}p+\frac{16}{15}a+\frac{44}{45} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{1}{11}+p)(p-\frac{12}{13})& =(\color{red}{p}+\color{orange}{\frac{1}{11}}).(\color{green}{p}+\color{blue}{\frac{-12}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-12}{13})} + \color{orange}{(\frac{1}{11})} . \color{green}{(p)} + \color{orange}{(\frac{1}{11})} . \color{blue}{(\frac{-12}{13})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{12}{13}p+\frac{1}{11}p-\frac{1}{11}.\frac{12}{13}& \text{Uitwerken } \\ & =p^2+((\frac{-12}{13})+\frac{1}{11})p-(\frac{-12}{143}) & \text{Neem samen} \\ &=p^2-\frac{119}{143}p-(\frac{-12}{143}) & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(\frac{-8}{11}+b)(b-\frac{2}{11})& =(\color{red}{b}+\color{orange}{\frac{-8}{11}}).(\color{green}{b}+\color{blue}{\frac{-2}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{11})} + \color{orange}{(\frac{-8}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-8}{11})} . \color{blue}{(\frac{-2}{11})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{2}{11}b-\frac{8}{11}b+\frac{8}{11}.\frac{2}{11}& \text{Uitwerken } \\ & =b^2+((\frac{-2}{11})+(\frac{-8}{11}))b+\frac{16}{121} & \text{Neem samen} \\ &=b^2-\frac{10}{11}b+\frac{16}{121} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(\frac{-20}{13}-x)(\frac{-6}{18}-b)& =(\color{red}{-x}+\color{orange}{\frac{-20}{13}}).(\color{green}{-b}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(-b)} + \color{red}{(-x)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-20}{13})} . \color{green}{(-b)} + \color{orange}{(\frac{-20}{13})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{3}x+\frac{20}{13}b+\frac{20}{13}.\frac{1}{3}& \text{Uitwerken } \\ & =bx+\frac{1}{3}x+\frac{20}{13}b+\frac{20}{39} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q+\frac{6}{14})(x-\frac{18}{9})& =(\color{red}{q}+\color{orange}{\frac{3}{7}}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(\frac{3}{7})} . \color{green}{(x)} + \color{orange}{(\frac{3}{7})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = qx-2q+\frac{3}{7}x-\frac{3}{7}.2& \text{Uitwerken } \\ & =qx-2q+\frac{3}{7}x-\frac{6}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)