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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}((-3)-p)(a-\frac{11}{20})& =(\color{red}{-p}+\color{orange}{(-3)}).(\color{green}{a}+\color{blue}{\frac{-11}{20}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(a)} + \color{red}{(-p)} . \color{blue}{(\frac{-11}{20})} + \color{orange}{(-3)} . \color{green}{(a)} + \color{orange}{(-3)} . \color{blue}{(\frac{-11}{20})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{11}{20}p-3a+3.\frac{11}{20}& \text{Uitwerken } \\ & =-ap+\frac{11}{20}p-3a+\frac{33}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{11}{13}+q)(\frac{11}{13}+a)& =(\color{red}{q}+\color{orange}{\frac{11}{13}}).(\color{green}{a}+\color{blue}{\frac{11}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{11}{13})} + \color{orange}{(\frac{11}{13})} . \color{green}{(a)} + \color{orange}{(\frac{11}{13})} . \color{blue}{(\frac{11}{13})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{11}{13}q+\frac{11}{13}a+\frac{11}{13}.\frac{11}{13}& \text{Uitwerken } \\ & =aq+\frac{11}{13}q+\frac{11}{13}a+\frac{121}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-20}{2}+p)(\frac{5}{2}-b)& =(\color{red}{p}+\color{orange}{(-10)}).(\color{green}{-b}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(-10)} . \color{green}{(-b)} + \color{orange}{(-10)} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{5}{2}p+10b-10.\frac{5}{2}& \text{Uitwerken } \\ & =-bp+\frac{5}{2}p+10b-\frac{50}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{5}{2}p+10b-25 & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(a-\frac{-10}{16})(\frac{-3}{3}-p)& =(\color{red}{a}+\color{orange}{\frac{5}{8}}).(\color{green}{-p}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{5}{8})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{8})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -ap-1a-\frac{5}{8}p-\frac{5}{8}.1& \text{Uitwerken } \\ & =-ap-1a-\frac{5}{8}p-\frac{5}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-16}{11}-q)(q-\frac{-1}{17})& =(\color{red}{-q}+\color{orange}{\frac{-16}{11}}).(\color{green}{q}+\color{blue}{\frac{1}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(q)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{17})} + \color{orange}{(\frac{-16}{11})} . \color{green}{(q)} + \color{orange}{(\frac{-16}{11})} . \color{blue}{(\frac{1}{17})}& \text{Boogjes en uitschrijven} \\ & = -qq-\frac{1}{17}q-\frac{16}{11}q-\frac{16}{11}.\frac{1}{17}& \text{Uitwerken } \\ & =-q^2+((\frac{-1}{17})+(\frac{-16}{11}))q-\frac{16}{187} & \text{Neem samen} \\ &=-q^2-\frac{283}{187}q-\frac{16}{187} & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(x+\frac{-5}{17})(a+\frac{12}{17})& =(\color{red}{x}+\color{orange}{\frac{-5}{17}}).(\color{green}{a}+\color{blue}{\frac{12}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(\frac{12}{17})} + \color{orange}{(\frac{-5}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-5}{17})} . \color{blue}{(\frac{12}{17})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{12}{17}x-\frac{5}{17}a-\frac{5}{17}.\frac{12}{17}& \text{Uitwerken } \\ & =ax+\frac{12}{17}x-\frac{5}{17}a-\frac{60}{289} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(x+\frac{-11}{9})(q+\frac{5}{8})& =(\color{red}{x}+\color{orange}{\frac{-11}{9}}).(\color{green}{q}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{-11}{9})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{5}{8}x-\frac{11}{9}q-\frac{11}{9}.\frac{5}{8}& \text{Uitwerken } \\ & =qx+\frac{5}{8}x-\frac{11}{9}q-\frac{55}{72} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{15}{16}-q)(a-\frac{20}{10})& =(\color{red}{-q}+\color{orange}{\frac{15}{16}}).(\color{green}{a}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(-2)} + \color{orange}{(\frac{15}{16})} . \color{green}{(a)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = -aq+2q+\frac{15}{16}a-\frac{15}{16}.2& \text{Uitwerken } \\ & =-aq+2q+\frac{15}{16}a-\frac{30}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -aq+2q+\frac{15}{16}a-\frac{15}{8} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-15}{8}-p)(\frac{18}{6}+b)& =(\color{red}{-p}+\color{orange}{\frac{-15}{8}}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(3)} + \color{orange}{(\frac{-15}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{8})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -bp-3p-\frac{15}{8}b-\frac{15}{8}.3& \text{Uitwerken } \\ & =-bp-3p-\frac{15}{8}b-\frac{45}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-4}{12}+a)(p+\frac{12}{3})& =(\color{red}{a}+\color{orange}{\frac{-1}{3}}).(\color{green}{p}+\color{blue}{4})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(4)} + \color{orange}{(\frac{-1}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(4)}& \text{Boogjes en uitschrijven} \\ & = ap+4a-\frac{1}{3}p-\frac{1}{3}.4& \text{Uitwerken } \\ & =ap+4a-\frac{1}{3}p-\frac{4}{3} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(p-\frac{11}{12})(q+\frac{-16}{10})& =(\color{red}{p}+\color{orange}{\frac{-11}{12}}).(\color{green}{q}+\color{blue}{\frac{-8}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-8}{5})} + \color{orange}{(\frac{-11}{12})} . \color{green}{(q)} + \color{orange}{(\frac{-11}{12})} . \color{blue}{(\frac{-8}{5})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{8}{5}p-\frac{11}{12}q+\frac{11}{12}.\frac{8}{5}& \text{Uitwerken } \\ & =pq-\frac{8}{5}p-\frac{11}{12}q+\frac{88}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = pq-\frac{8}{5}p-\frac{11}{12}q+\frac{22}{15} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-7}{5}+q)(p-\frac{2}{6})& =(\color{red}{q}+\color{orange}{\frac{-7}{5}}).(\color{green}{p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-7}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{5})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{1}{3}q-\frac{7}{5}p+\frac{7}{5}.\frac{1}{3}& \text{Uitwerken } \\ & =pq-\frac{1}{3}q-\frac{7}{5}p+\frac{7}{15} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)