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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a-\frac{-15}{16})(\frac{2}{9}-a)& =(\color{red}{a}+\color{orange}{\frac{15}{16}}).(\color{green}{-a}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{15}{16})} . \color{green}{(-a)} + \color{orange}{(\frac{15}{16})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{2}{9}a-\frac{15}{16}a+\frac{15}{16}.\frac{2}{9}& \text{Uitwerken } \\ & =-a^2+(\frac{2}{9}+(\frac{-15}{16}))a+(\frac{-30}{144}) & \text{Neem samen} \\ &=-a^2-\frac{103}{144}a+(\frac{-30}{144}) & \text{Maak de som} \\ &=-a^2-\frac{103}{144}a+(\frac{-5}{24}) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
2. \(\begin{align}(a+\frac{-4}{12})(\frac{-20}{18}+b)& =(\color{red}{a}+\color{orange}{\frac{-1}{3}}).(\color{green}{b}+\color{blue}{\frac{-10}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-10}{9})} + \color{orange}{(\frac{-1}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{3})} . \color{blue}{(\frac{-10}{9})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{10}{9}a-\frac{1}{3}b+\frac{1}{3}.\frac{10}{9}& \text{Uitwerken } \\ & =ab-\frac{10}{9}a-\frac{1}{3}b+\frac{10}{27} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-20}{18}+b)(\frac{5}{16}-q)& =(\color{red}{b}+\color{orange}{\frac{-10}{9}}).(\color{green}{-q}+\color{blue}{\frac{5}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-q)} + \color{red}{(b)} . \color{blue}{(\frac{5}{16})} + \color{orange}{(\frac{-10}{9})} . \color{green}{(-q)} + \color{orange}{(\frac{-10}{9})} . \color{blue}{(\frac{5}{16})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{16}b+\frac{10}{9}q-\frac{10}{9}.\frac{5}{16}& \text{Uitwerken } \\ & =-bq+\frac{5}{16}b+\frac{10}{9}q-\frac{50}{144} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{5}{16}b+\frac{10}{9}q-\frac{25}{72} & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(b-\frac{-1}{5})(a+\frac{-16}{2})& =(\color{red}{b}+\color{orange}{\frac{1}{5}}).(\color{green}{a}+\color{blue}{(-8)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-8)} + \color{orange}{(\frac{1}{5})} . \color{green}{(a)} + \color{orange}{(\frac{1}{5})} . \color{blue}{(-8)}& \text{Boogjes en uitschrijven} \\ & = ab-8b+\frac{1}{5}a-\frac{1}{5}.8& \text{Uitwerken } \\ & =ab-8b+\frac{1}{5}a-\frac{8}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{6}{18}-b)(\frac{20}{4}-b)& =(\color{red}{-b}+\color{orange}{\frac{1}{3}}).(\color{green}{-b}+\color{blue}{5})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-b)} + \color{red}{(-b)} . \color{blue}{(5)} + \color{orange}{(\frac{1}{3})} . \color{green}{(-b)} + \color{orange}{(\frac{1}{3})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = bb-5b-\frac{1}{3}b+\frac{1}{3}.5& \text{Uitwerken } \\ & =b^2+((-5)+(\frac{-1}{3}))b+\frac{5}{3} & \text{Neem samen} \\ &=b^2-\frac{16}{3}b+\frac{5}{3} & \text{Maak de som} \\\end{align}\)
6. \(\begin{align}(b-\frac{8}{14})(\frac{13}{17}+b)& =(\color{red}{b}+\color{orange}{\frac{-4}{7}}).(\color{green}{b}+\color{blue}{\frac{13}{17}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{13}{17})} + \color{orange}{(\frac{-4}{7})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{7})} . \color{blue}{(\frac{13}{17})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{13}{17}b-\frac{4}{7}b-\frac{4}{7}.\frac{13}{17}& \text{Uitwerken } \\ & =b^2+(\frac{13}{17}+(\frac{-4}{7}))b-(\frac{-52}{119}) & \text{Neem samen} \\ &=b^2+\frac{23}{119}b-(\frac{-52}{119}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{12}{19}+p)(x+\frac{15}{15})& =(\color{red}{p}+\color{orange}{\frac{12}{19}}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(x)} + \color{red}{(p)} . \color{blue}{(1)} + \color{orange}{(\frac{12}{19})} . \color{green}{(x)} + \color{orange}{(\frac{12}{19})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = px+1p+\frac{12}{19}x+\frac{12}{19}.1& \text{Uitwerken } \\ & =px+1p+\frac{12}{19}x+\frac{12}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a+\frac{-2}{8})(\frac{-5}{15}-p)& =(\color{red}{a}+\color{orange}{\frac{-1}{4}}).(\color{green}{-p}+\color{blue}{\frac{-1}{3}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{3})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-p)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-1}{3})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{3}a+\frac{1}{4}p+\frac{1}{4}.\frac{1}{3}& \text{Uitwerken } \\ & =-ap-\frac{1}{3}a+\frac{1}{4}p+\frac{1}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x+\frac{1}{9})(p-\frac{-12}{16})& =(\color{red}{x}+\color{orange}{\frac{1}{9}}).(\color{green}{p}+\color{blue}{\frac{3}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{4})} + \color{orange}{(\frac{1}{9})} . \color{green}{(p)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{3}{4})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{4}x+\frac{1}{9}p+\frac{1}{9}.\frac{3}{4}& \text{Uitwerken } \\ & =px+\frac{3}{4}x+\frac{1}{9}p+\frac{3}{36} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{3}{4}x+\frac{1}{9}p+\frac{1}{12} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-15}{20}+x)(q-\frac{-9}{3})& =(\color{red}{x}+\color{orange}{\frac{-3}{4}}).(\color{green}{q}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(3)} + \color{orange}{(\frac{-3}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-3}{4})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = qx+3x-\frac{3}{4}q-\frac{3}{4}.3& \text{Uitwerken } \\ & =qx+3x-\frac{3}{4}q-\frac{9}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-\frac{15}{14})(a-\frac{13}{9})& =(\color{red}{a}+\color{orange}{\frac{-15}{14}}).(\color{green}{a}+\color{blue}{\frac{-13}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{9})} + \color{orange}{(\frac{-15}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{14})} . \color{blue}{(\frac{-13}{9})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{13}{9}a-\frac{15}{14}a+\frac{15}{14}.\frac{13}{9}& \text{Uitwerken } \\ & =a^2+((\frac{-13}{9})+(\frac{-15}{14}))a+\frac{195}{126} & \text{Neem samen} \\ &=a^2-\frac{317}{126}a+\frac{195}{126} & \text{Maak de som} \\ &=a^2-\frac{317}{126}a+\frac{65}{42} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
12. \(\begin{align}(\frac{-11}{9}+b)(p+\frac{-12}{3})& =(\color{red}{b}+\color{orange}{\frac{-11}{9}}).(\color{green}{p}+\color{blue}{(-4)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(-4)} + \color{orange}{(\frac{-11}{9})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{9})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = bp-4b-\frac{11}{9}p+\frac{11}{9}.4& \text{Uitwerken } \\ & =bp-4b-\frac{11}{9}p+\frac{44}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)