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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p+\frac{3}{2})(\frac{-12}{4}+b)& =(\color{red}{p}+\color{orange}{\frac{3}{2}}).(\color{green}{b}+\color{blue}{(-3)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-3)} + \color{orange}{(\frac{3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bp-3p+\frac{3}{2}b-\frac{3}{2}.3& \text{Uitwerken } \\ & =bp-3p+\frac{3}{2}b-\frac{9}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q-\frac{-1}{9})(\frac{2}{9}+x)& =(\color{red}{q}+\color{orange}{\frac{1}{9}}).(\color{green}{x}+\color{blue}{\frac{2}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{2}{9})} + \color{orange}{(\frac{1}{9})} . \color{green}{(x)} + \color{orange}{(\frac{1}{9})} . \color{blue}{(\frac{2}{9})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{2}{9}q+\frac{1}{9}x+\frac{1}{9}.\frac{2}{9}& \text{Uitwerken } \\ & =qx+\frac{2}{9}q+\frac{1}{9}x+\frac{2}{81} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(p+\frac{6}{19})(\frac{12}{10}-b)& =(\color{red}{p}+\color{orange}{\frac{6}{19}}).(\color{green}{-b}+\color{blue}{\frac{6}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{6}{5})} + \color{orange}{(\frac{6}{19})} . \color{green}{(-b)} + \color{orange}{(\frac{6}{19})} . \color{blue}{(\frac{6}{5})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{6}{5}p-\frac{6}{19}b+\frac{6}{19}.\frac{6}{5}& \text{Uitwerken } \\ & =-bp+\frac{6}{5}p-\frac{6}{19}b+\frac{36}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{4}{13}-q)(p-\frac{3}{17})& =(\color{red}{-q}+\color{orange}{\frac{4}{13}}).(\color{green}{p}+\color{blue}{\frac{-3}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{-3}{17})} + \color{orange}{(\frac{4}{13})} . \color{green}{(p)} + \color{orange}{(\frac{4}{13})} . \color{blue}{(\frac{-3}{17})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{3}{17}q+\frac{4}{13}p-\frac{4}{13}.\frac{3}{17}& \text{Uitwerken } \\ & =-pq+\frac{3}{17}q+\frac{4}{13}p-\frac{12}{221} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(a-\frac{-12}{14})(\frac{-2}{15}+b)& =(\color{red}{a}+\color{orange}{\frac{6}{7}}).(\color{green}{b}+\color{blue}{\frac{-2}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-2}{15})} + \color{orange}{(\frac{6}{7})} . \color{green}{(b)} + \color{orange}{(\frac{6}{7})} . \color{blue}{(\frac{-2}{15})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{2}{15}a+\frac{6}{7}b-\frac{6}{7}.\frac{2}{15}& \text{Uitwerken } \\ & =ab-\frac{2}{15}a+\frac{6}{7}b-\frac{12}{105} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{2}{15}a+\frac{6}{7}b-\frac{4}{35} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(q+\frac{12}{8})(\frac{6}{16}+q)& =(\color{red}{q}+\color{orange}{\frac{3}{2}}).(\color{green}{q}+\color{blue}{\frac{3}{8}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{3}{8})} + \color{orange}{(\frac{3}{2})} . \color{green}{(q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(\frac{3}{8})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{3}{8}q+\frac{3}{2}q+\frac{3}{2}.\frac{3}{8}& \text{Uitwerken } \\ & =q^2+(\frac{3}{8}+\frac{3}{2})q+\frac{9}{16} & \text{Neem samen} \\ &=q^2+\frac{15}{8}q+\frac{9}{16} & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(q-\frac{3}{12})(q-\frac{11}{4})& =(\color{red}{q}+\color{orange}{\frac{-1}{4}}).(\color{green}{q}+\color{blue}{\frac{-11}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{-11}{4})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-11}{4})}& \text{Boogjes en uitschrijven} \\ & = qq-\frac{11}{4}q-\frac{1}{4}q+\frac{1}{4}.\frac{11}{4}& \text{Uitwerken } \\ & =q^2+((\frac{-11}{4})+(\frac{-1}{4}))q+\frac{11}{16} & \text{Neem samen} \\ &=q^2-\frac{12}{4}q+\frac{11}{16} & \text{Maak de som} \\ &=q^2-3q+\frac{11}{16} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
8. \(\begin{align}(\frac{2}{4}-q)(\frac{11}{5}-x)& =(\color{red}{-q}+\color{orange}{\frac{1}{2}}).(\color{green}{-x}+\color{blue}{\frac{11}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-x)} + \color{red}{(-q)} . \color{blue}{(\frac{11}{5})} + \color{orange}{(\frac{1}{2})} . \color{green}{(-x)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{11}{5})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{11}{5}q-\frac{1}{2}x+\frac{1}{2}.\frac{11}{5}& \text{Uitwerken } \\ & =qx-\frac{11}{5}q-\frac{1}{2}x+\frac{11}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-7}{17}-x)(p-(-3))& =(\color{red}{-x}+\color{orange}{\frac{-7}{17}}).(\color{green}{p}+\color{blue}{3})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(p)} + \color{red}{(-x)} . \color{blue}{(3)} + \color{orange}{(\frac{-7}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-7}{17})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -px-3x-\frac{7}{17}p-\frac{7}{17}.3& \text{Uitwerken } \\ & =-px-3x-\frac{7}{17}p-\frac{21}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(q-\frac{1}{18})(b+\frac{-12}{4})& =(\color{red}{q}+\color{orange}{\frac{-1}{18}}).(\color{green}{b}+\color{blue}{(-3)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(-3)} + \color{orange}{(\frac{-1}{18})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{18})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = bq-3q-\frac{1}{18}b+\frac{1}{18}.3& \text{Uitwerken } \\ & =bq-3q-\frac{1}{18}b+\frac{3}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq-3q-\frac{1}{18}b+\frac{1}{6} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(q-\frac{12}{6})(\frac{-16}{20}+b)& =(\color{red}{q}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{-4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{5})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{-4}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{4}{5}q-2b+2.\frac{4}{5}& \text{Uitwerken } \\ & =bq-\frac{4}{5}q-2b+\frac{8}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(a-\frac{-1}{20})(\frac{12}{15}+a)& =(\color{red}{a}+\color{orange}{\frac{1}{20}}).(\color{green}{a}+\color{blue}{\frac{4}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{4}{5})} + \color{orange}{(\frac{1}{20})} . \color{green}{(a)} + \color{orange}{(\frac{1}{20})} . \color{blue}{(\frac{4}{5})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{4}{5}a+\frac{1}{20}a+\frac{1}{20}.\frac{4}{5}& \text{Uitwerken } \\ & =a^2+(\frac{4}{5}+\frac{1}{20})a+\frac{4}{100} & \text{Neem samen} \\ &=a^2+\frac{17}{20}a+\frac{4}{100} & \text{Maak de som} \\ &=a^2+\frac{17}{20}a+\frac{1}{25} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)