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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{9}{3}+q)(p+\frac{18}{2})& =(\color{red}{q}+\color{orange}{3}).(\color{green}{p}+\color{blue}{9})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(9)} + \color{orange}{(3)} . \color{green}{(p)} + \color{orange}{(3)} . \color{blue}{(9)}& \text{Boogjes en uitschrijven} \\ & = pq+9q+3p+3.9& \text{Uitwerken } \\ & =pq+9q+3p+27 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{16}{15}-q)(p-\frac{-18}{7})& =(\color{red}{-q}+\color{orange}{\frac{16}{15}}).(\color{green}{p}+\color{blue}{\frac{18}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{18}{7})} + \color{orange}{(\frac{16}{15})} . \color{green}{(p)} + \color{orange}{(\frac{16}{15})} . \color{blue}{(\frac{18}{7})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{18}{7}q+\frac{16}{15}p+\frac{16}{15}.\frac{18}{7}& \text{Uitwerken } \\ & =-pq-\frac{18}{7}q+\frac{16}{15}p+\frac{288}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{18}{7}q+\frac{16}{15}p+\frac{96}{35} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{15}{5}+q)(q+\frac{-11}{7})& =(\color{red}{q}+\color{orange}{3}).(\color{green}{q}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(3)} . \color{green}{(q)} + \color{orange}{(3)} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{11}{7}q+3q-3.\frac{11}{7}& \text{Uitwerken } \\ & =q^2+((\frac{-11}{7})+3)q-(\frac{-33}{7}) & \text{Neem samen} \\ &=q^2+\frac{10}{7}q-(\frac{-33}{7}) & \text{Maak de som} \\\end{align}\)
4. \(\begin{align}(p+\frac{-16}{19})(\frac{11}{5}-p)& =(\color{red}{p}+\color{orange}{\frac{-16}{19}}).(\color{green}{-p}+\color{blue}{\frac{11}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(\frac{11}{5})} + \color{orange}{(\frac{-16}{19})} . \color{green}{(-p)} + \color{orange}{(\frac{-16}{19})} . \color{blue}{(\frac{11}{5})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{11}{5}p+\frac{16}{19}p-\frac{16}{19}.\frac{11}{5}& \text{Uitwerken } \\ & =-p^2+(\frac{11}{5}+\frac{16}{19})p-\frac{176}{95} & \text{Neem samen} \\ &=-p^2+\frac{289}{95}p-\frac{176}{95} & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(\frac{-6}{16}+q)(x-\frac{-2}{20})& =(\color{red}{q}+\color{orange}{\frac{-3}{8}}).(\color{green}{x}+\color{blue}{\frac{1}{10}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{1}{10})} + \color{orange}{(\frac{-3}{8})} . \color{green}{(x)} + \color{orange}{(\frac{-3}{8})} . \color{blue}{(\frac{1}{10})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{1}{10}q-\frac{3}{8}x-\frac{3}{8}.\frac{1}{10}& \text{Uitwerken } \\ & =qx+\frac{1}{10}q-\frac{3}{8}x-\frac{3}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-5}{6}+p)(\frac{-2}{11}+a)& =(\color{red}{p}+\color{orange}{\frac{-5}{6}}).(\color{green}{a}+\color{blue}{\frac{-2}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(\frac{-2}{11})} + \color{orange}{(\frac{-5}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{6})} . \color{blue}{(\frac{-2}{11})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{2}{11}p-\frac{5}{6}a+\frac{5}{6}.\frac{2}{11}& \text{Uitwerken } \\ & =ap-\frac{2}{11}p-\frac{5}{6}a+\frac{10}{66} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-\frac{2}{11}p-\frac{5}{6}a+\frac{5}{33} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(p+\frac{-17}{9})(\frac{-19}{9}+x)& =(\color{red}{p}+\color{orange}{\frac{-17}{9}}).(\color{green}{x}+\color{blue}{\frac{-19}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(\frac{-19}{9})} + \color{orange}{(\frac{-17}{9})} . \color{green}{(x)} + \color{orange}{(\frac{-17}{9})} . \color{blue}{(\frac{-19}{9})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{19}{9}p-\frac{17}{9}x+\frac{17}{9}.\frac{19}{9}& \text{Uitwerken } \\ & =px-\frac{19}{9}p-\frac{17}{9}x+\frac{323}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p-\frac{-8}{19})(\frac{-3}{3}-x)& =(\color{red}{p}+\color{orange}{\frac{8}{19}}).(\color{green}{-x}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(-1)} + \color{orange}{(\frac{8}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{8}{19})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -px-1p-\frac{8}{19}x-\frac{8}{19}.1& \text{Uitwerken } \\ & =-px-1p-\frac{8}{19}x-\frac{8}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{14}{18}-p)(\frac{-18}{10}-p)& =(\color{red}{-p}+\color{orange}{\frac{7}{9}}).(\color{green}{-p}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-p)} + \color{red}{(-p)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{7}{9})} . \color{green}{(-p)} + \color{orange}{(\frac{7}{9})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = pp+\frac{9}{5}p-\frac{7}{9}p-\frac{7}{9}.\frac{9}{5}& \text{Uitwerken } \\ & =p^2+(\frac{9}{5}+(\frac{-7}{9}))p-(\frac{-63}{45}) & \text{Neem samen} \\ &=p^2+\frac{46}{45}p-(\frac{-63}{45}) & \text{Maak de som} \\ &=p^2+\frac{46}{45}p+\frac{7}{5} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
10. \(\begin{align}(b+\frac{-2}{4})(b+\frac{-1}{16})& =(\color{red}{b}+\color{orange}{\frac{-1}{2}}).(\color{green}{b}+\color{blue}{\frac{-1}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{16})} + \color{orange}{(\frac{-1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(\frac{-1}{16})}& \text{Boogjes en uitschrijven} \\ & = bb-\frac{1}{16}b-\frac{1}{2}b+\frac{1}{2}.\frac{1}{16}& \text{Uitwerken } \\ & =b^2+((\frac{-1}{16})+(\frac{-1}{2}))b+\frac{1}{32} & \text{Neem samen} \\ &=b^2-\frac{9}{16}b+\frac{1}{32} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}((-16)-a)(q+\frac{-20}{2})& =(\color{red}{-a}+\color{orange}{(-16)}).(\color{green}{q}+\color{blue}{(-10)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(q)} + \color{red}{(-a)} . \color{blue}{(-10)} + \color{orange}{(-16)} . \color{green}{(q)} + \color{orange}{(-16)} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -aq+10a-16q+16.10& \text{Uitwerken } \\ & =-aq+10a-16q+160 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(a+\frac{17}{9})(a+\frac{-7}{2})& =(\color{red}{a}+\color{orange}{\frac{17}{9}}).(\color{green}{a}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(\frac{17}{9})} . \color{green}{(a)} + \color{orange}{(\frac{17}{9})} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{7}{2}a+\frac{17}{9}a-\frac{17}{9}.\frac{7}{2}& \text{Uitwerken } \\ & =a^2+((\frac{-7}{2})+\frac{17}{9})a-(\frac{-119}{18}) & \text{Neem samen} \\ &=a^2-\frac{29}{18}a-(\frac{-119}{18}) & \text{Maak de som} \\\end{align}\)