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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{13}{14})(\frac{-12}{14}+q)& =(\color{red}{p}+\color{orange}{\frac{13}{14}}).(\color{green}{q}+\color{blue}{\frac{-6}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-6}{7})} + \color{orange}{(\frac{13}{14})} . \color{green}{(q)} + \color{orange}{(\frac{13}{14})} . \color{blue}{(\frac{-6}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{6}{7}p+\frac{13}{14}q-\frac{13}{14}.\frac{6}{7}& \text{Uitwerken } \\ & =pq-\frac{6}{7}p+\frac{13}{14}q-\frac{78}{98} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{6}{7}p+\frac{13}{14}q-\frac{39}{49} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(a-\frac{9}{7})(a-\frac{-14}{2})& =(\color{red}{a}+\color{orange}{\frac{-9}{7}}).(\color{green}{a}+\color{blue}{7})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(7)} + \color{orange}{(\frac{-9}{7})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{7})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = aa+7a-\frac{9}{7}a-\frac{9}{7}.7& \text{Uitwerken } \\ & =a^2+(7+(\frac{-9}{7}))a-(\frac{-63}{7}) & \text{Neem samen} \\ &=a^2+\frac{40}{7}a-(\frac{-63}{7}) & \text{Maak de som} \\ &=a^2+\frac{40}{7}a+9 & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
3. \(\begin{align}(x-\frac{-16}{4})(\frac{7}{3}-x)& =(\color{red}{x}+\color{orange}{4}).(\color{green}{-x}+\color{blue}{\frac{7}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{7}{3})} + \color{orange}{(4)} . \color{green}{(-x)} + \color{orange}{(4)} . \color{blue}{(\frac{7}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{7}{3}x-4x+4.\frac{7}{3}& \text{Uitwerken } \\ & =-x^2+(\frac{7}{3}+(-4))x+(\frac{-28}{3}) & \text{Neem samen} \\ &=-x^2-\frac{5}{3}x+(\frac{-28}{3}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(a+\frac{16}{19})(\frac{-15}{13}+b)& =(\color{red}{a}+\color{orange}{\frac{16}{19}}).(\color{green}{b}+\color{blue}{\frac{-15}{13}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-15}{13})} + \color{orange}{(\frac{16}{19})} . \color{green}{(b)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(\frac{-15}{13})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{15}{13}a+\frac{16}{19}b-\frac{16}{19}.\frac{15}{13}& \text{Uitwerken } \\ & =ab-\frac{15}{13}a+\frac{16}{19}b-\frac{240}{247} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{2}{2}-x)(\frac{-14}{14}+a)& =(\color{red}{-x}+\color{orange}{1}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(-1)} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ax+1x+1a-1.1& \text{Uitwerken } \\ & =-ax+1x+1a-1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b+\frac{8}{3})(\frac{2}{2}+b)& =(\color{red}{b}+\color{orange}{\frac{8}{3}}).(\color{green}{b}+\color{blue}{1})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{8}{3})} . \color{green}{(b)} + \color{orange}{(\frac{8}{3})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = bb+1b+\frac{8}{3}b+\frac{8}{3}.1& \text{Uitwerken } \\ & =b^2+(1+\frac{8}{3})b+\frac{8}{3} & \text{Neem samen} \\ &=b^2+\frac{11}{3}b+\frac{8}{3} & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(x+\frac{-16}{6})(\frac{7}{18}-x)& =(\color{red}{x}+\color{orange}{\frac{-8}{3}}).(\color{green}{-x}+\color{blue}{\frac{7}{18}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(-x)} + \color{red}{(x)} . \color{blue}{(\frac{7}{18})} + \color{orange}{(\frac{-8}{3})} . \color{green}{(-x)} + \color{orange}{(\frac{-8}{3})} . \color{blue}{(\frac{7}{18})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{7}{18}x+\frac{8}{3}x-\frac{8}{3}.\frac{7}{18}& \text{Uitwerken } \\ & =-x^2+(\frac{7}{18}+\frac{8}{3})x-\frac{56}{54} & \text{Neem samen} \\ &=-x^2+\frac{55}{18}x-\frac{56}{54} & \text{Maak de som} \\ &=-x^2+\frac{55}{18}x-\frac{28}{27} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
8. \(\begin{align}(b+\frac{-20}{4})(\frac{-13}{7}+x)& =(\color{red}{b}+\color{orange}{(-5)}).(\color{green}{x}+\color{blue}{\frac{-13}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{7})} + \color{orange}{(-5)} . \color{green}{(x)} + \color{orange}{(-5)} . \color{blue}{(\frac{-13}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{13}{7}b-5x+5.\frac{13}{7}& \text{Uitwerken } \\ & =bx-\frac{13}{7}b-5x+\frac{65}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(10-b)(p-\frac{19}{16})& =(\color{red}{-b}+\color{orange}{10}).(\color{green}{p}+\color{blue}{\frac{-19}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-19}{16})} + \color{orange}{(10)} . \color{green}{(p)} + \color{orange}{(10)} . \color{blue}{(\frac{-19}{16})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{19}{16}b+10p-10.\frac{19}{16}& \text{Uitwerken } \\ & =-bp+\frac{19}{16}b+10p-\frac{190}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{19}{16}b+10p-\frac{95}{8} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{9}{9}+b)(\frac{-7}{5}+p)& =(\color{red}{b}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{7}{5}b+1p-1.\frac{7}{5}& \text{Uitwerken } \\ & =bp-\frac{7}{5}b+1p-\frac{7}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(\frac{-15}{16}+a)(\frac{-16}{13}+a)& =(\color{red}{a}+\color{orange}{\frac{-15}{16}}).(\color{green}{a}+\color{blue}{\frac{-16}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-16}{13})} + \color{orange}{(\frac{-15}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{16})} . \color{blue}{(\frac{-16}{13})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{16}{13}a-\frac{15}{16}a+\frac{15}{16}.\frac{16}{13}& \text{Uitwerken } \\ & =a^2+((\frac{-16}{13})+(\frac{-15}{16}))a+\frac{240}{208} & \text{Neem samen} \\ &=a^2-\frac{451}{208}a+\frac{240}{208} & \text{Maak de som} \\ &=a^2-\frac{451}{208}a+\frac{15}{13} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
12. \(\begin{align}(\frac{13}{2}+a)(\frac{-20}{8}-x)& =(\color{red}{a}+\color{orange}{\frac{13}{2}}).(\color{green}{-x}+\color{blue}{\frac{-5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-x)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{2})} + \color{orange}{(\frac{13}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{13}{2})} . \color{blue}{(\frac{-5}{2})}& \text{Boogjes en uitschrijven} \\ & = -ax-\frac{5}{2}a-\frac{13}{2}x-\frac{13}{2}.\frac{5}{2}& \text{Uitwerken } \\ & =-ax-\frac{5}{2}a-\frac{13}{2}x-\frac{65}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)