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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-14}{13}+p)(\frac{-4}{5}+p)& =(\color{red}{p}+\color{orange}{\frac{-14}{13}}).(\color{green}{p}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(\frac{-14}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-14}{13})} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{4}{5}p-\frac{14}{13}p+\frac{14}{13}.\frac{4}{5}& \text{Uitwerken } \\ & =p^2+((\frac{-4}{5})+(\frac{-14}{13}))p+\frac{56}{65} & \text{Neem samen} \\ &=p^2-\frac{122}{65}p+\frac{56}{65} & \text{Maak de som} \\\end{align}\)
2. \(\begin{align}(\frac{-20}{6}+p)(x-\frac{4}{9})& =(\color{red}{p}+\color{orange}{\frac{-10}{3}}).(\color{green}{x}+\color{blue}{\frac{-4}{9}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-4}{9})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{-4}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{4}{9}p-\frac{10}{3}x+\frac{10}{3}.\frac{4}{9}& \text{Uitwerken } \\ & =px-\frac{4}{9}p-\frac{10}{3}x+\frac{40}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q-\frac{10}{11})(b-\frac{-18}{17})& =(\color{red}{q}+\color{orange}{\frac{-10}{11}}).(\color{green}{b}+\color{blue}{\frac{18}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{18}{17})} + \color{orange}{(\frac{-10}{11})} . \color{green}{(b)} + \color{orange}{(\frac{-10}{11})} . \color{blue}{(\frac{18}{17})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{18}{17}q-\frac{10}{11}b-\frac{10}{11}.\frac{18}{17}& \text{Uitwerken } \\ & =bq+\frac{18}{17}q-\frac{10}{11}b-\frac{180}{187} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x-\frac{-11}{12})(\frac{12}{16}-x)& =(\color{red}{x}+\color{orange}{\frac{11}{12}}).(\color{green}{-x}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{11}{12})} . \color{green}{(-x)} + \color{orange}{(\frac{11}{12})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{3}{4}x-\frac{11}{12}x+\frac{11}{12}.\frac{3}{4}& \text{Uitwerken } \\ & =-x^2+(\frac{3}{4}+(\frac{-11}{12}))x+(\frac{-33}{48}) & \text{Neem samen} \\ &=-x^2-\frac{2}{12}x+(\frac{-33}{48}) & \text{Maak de som} \\ &=-x^2-\frac{1}{6}x+(\frac{-11}{16}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
5. \(\begin{align}(p-\frac{-15}{5})(b-\frac{5}{5})& =(\color{red}{p}+\color{orange}{3}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(3)} . \color{green}{(b)} + \color{orange}{(3)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = bp-1p+3b-3.1& \text{Uitwerken } \\ & =bp-1p+3b-3 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(a-\frac{-7}{17})(\frac{18}{3}+p)& =(\color{red}{a}+\color{orange}{\frac{7}{17}}).(\color{green}{p}+\color{blue}{6})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(6)} + \color{orange}{(\frac{7}{17})} . \color{green}{(p)} + \color{orange}{(\frac{7}{17})} . \color{blue}{(6)}& \text{Boogjes en uitschrijven} \\ & = ap+6a+\frac{7}{17}p+\frac{7}{17}.6& \text{Uitwerken } \\ & =ap+6a+\frac{7}{17}p+\frac{42}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a-\frac{10}{3})(\frac{20}{9}-p)& =(\color{red}{a}+\color{orange}{\frac{-10}{3}}).(\color{green}{-p}+\color{blue}{\frac{20}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{20}{9})} + \color{orange}{(\frac{-10}{3})} . \color{green}{(-p)} + \color{orange}{(\frac{-10}{3})} . \color{blue}{(\frac{20}{9})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{20}{9}a+\frac{10}{3}p-\frac{10}{3}.\frac{20}{9}& \text{Uitwerken } \\ & =-ap+\frac{20}{9}a+\frac{10}{3}p-\frac{200}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(b-\frac{-2}{19})(p-13)& =(\color{red}{b}+\color{orange}{\frac{2}{19}}).(\color{green}{p}+\color{blue}{(-13)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-13)} + \color{orange}{(\frac{2}{19})} . \color{green}{(p)} + \color{orange}{(\frac{2}{19})} . \color{blue}{(-13)}& \text{Boogjes en uitschrijven} \\ & = bp-13b+\frac{2}{19}p-\frac{2}{19}.13& \text{Uitwerken } \\ & =bp-13b+\frac{2}{19}p-\frac{26}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(p-\frac{-14}{19})(\frac{1}{2}+q)& =(\color{red}{p}+\color{orange}{\frac{14}{19}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{14}{19})} . \color{green}{(q)} + \color{orange}{(\frac{14}{19})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{2}p+\frac{14}{19}q+\frac{14}{19}.\frac{1}{2}& \text{Uitwerken } \\ & =pq+\frac{1}{2}p+\frac{14}{19}q+\frac{14}{38} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq+\frac{1}{2}p+\frac{14}{19}q+\frac{7}{19} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{6}{17}-a)(\frac{19}{16}+x)& =(\color{red}{-a}+\color{orange}{\frac{6}{17}}).(\color{green}{x}+\color{blue}{\frac{19}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(x)} + \color{red}{(-a)} . \color{blue}{(\frac{19}{16})} + \color{orange}{(\frac{6}{17})} . \color{green}{(x)} + \color{orange}{(\frac{6}{17})} . \color{blue}{(\frac{19}{16})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{19}{16}a+\frac{6}{17}x+\frac{6}{17}.\frac{19}{16}& \text{Uitwerken } \\ & =-ax-\frac{19}{16}a+\frac{6}{17}x+\frac{114}{272} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ax-\frac{19}{16}a+\frac{6}{17}x+\frac{57}{136} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(p+\frac{20}{7})(b+\frac{15}{13})& =(\color{red}{p}+\color{orange}{\frac{20}{7}}).(\color{green}{b}+\color{blue}{\frac{15}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{15}{13})} + \color{orange}{(\frac{20}{7})} . \color{green}{(b)} + \color{orange}{(\frac{20}{7})} . \color{blue}{(\frac{15}{13})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{15}{13}p+\frac{20}{7}b+\frac{20}{7}.\frac{15}{13}& \text{Uitwerken } \\ & =bp+\frac{15}{13}p+\frac{20}{7}b+\frac{300}{91} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(q-\frac{7}{13})(b-\frac{2}{5})& =(\color{red}{q}+\color{orange}{\frac{-7}{13}}).(\color{green}{b}+\color{blue}{\frac{-2}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-2}{5})} + \color{orange}{(\frac{-7}{13})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{13})} . \color{blue}{(\frac{-2}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{2}{5}q-\frac{7}{13}b+\frac{7}{13}.\frac{2}{5}& \text{Uitwerken } \\ & =bq-\frac{2}{5}q-\frac{7}{13}b+\frac{14}{65} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)