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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(x-\frac{14}{12})(\frac{8}{9}+b)& =(\color{red}{x}+\color{orange}{\frac{-7}{6}}).(\color{green}{b}+\color{blue}{\frac{8}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{8}{9})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{8}{9})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{8}{9}x-\frac{7}{6}b-\frac{7}{6}.\frac{8}{9}& \text{Uitwerken } \\ & =bx+\frac{8}{9}x-\frac{7}{6}b-\frac{56}{54} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx+\frac{8}{9}x-\frac{7}{6}b-\frac{28}{27} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{5}{6}+b)(\frac{-2}{4}-p)& =(\color{red}{b}+\color{orange}{\frac{5}{6}}).(\color{green}{-p}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-p)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{5}{6})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{6})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{2}b-\frac{5}{6}p-\frac{5}{6}.\frac{1}{2}& \text{Uitwerken } \\ & =-bp-\frac{1}{2}b-\frac{5}{6}p-\frac{5}{12} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-9}{6}-p)(\frac{-8}{3}+b)& =(\color{red}{-p}+\color{orange}{\frac{-3}{2}}).(\color{green}{b}+\color{blue}{\frac{-8}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(b)} + \color{red}{(-p)} . \color{blue}{(\frac{-8}{3})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{-8}{3})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{8}{3}p-\frac{3}{2}b+\frac{3}{2}.\frac{8}{3}& \text{Uitwerken } \\ & =-bp+\frac{8}{3}p-\frac{3}{2}b+\frac{24}{6} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp+\frac{8}{3}p-\frac{3}{2}b+4 & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(\frac{14}{15}+b)(\frac{15}{19}+a)& =(\color{red}{b}+\color{orange}{\frac{14}{15}}).(\color{green}{a}+\color{blue}{\frac{15}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{15}{19})} + \color{orange}{(\frac{14}{15})} . \color{green}{(a)} + \color{orange}{(\frac{14}{15})} . \color{blue}{(\frac{15}{19})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{15}{19}b+\frac{14}{15}a+\frac{14}{15}.\frac{15}{19}& \text{Uitwerken } \\ & =ab+\frac{15}{19}b+\frac{14}{15}a+\frac{210}{285} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{15}{19}b+\frac{14}{15}a+\frac{14}{19} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(b-\frac{6}{5})(a-\frac{13}{6})& =(\color{red}{b}+\color{orange}{\frac{-6}{5}}).(\color{green}{a}+\color{blue}{\frac{-13}{6}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-13}{6})} + \color{orange}{(\frac{-6}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-6}{5})} . \color{blue}{(\frac{-13}{6})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{6}b-\frac{6}{5}a+\frac{6}{5}.\frac{13}{6}& \text{Uitwerken } \\ & =ab-\frac{13}{6}b-\frac{6}{5}a+\frac{78}{30} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{13}{6}b-\frac{6}{5}a+\frac{13}{5} & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(\frac{-15}{3}+q)(x+\frac{-6}{3})& =(\color{red}{q}+\color{orange}{(-5)}).(\color{green}{x}+\color{blue}{(-2)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(-2)} + \color{orange}{(-5)} . \color{green}{(x)} + \color{orange}{(-5)} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = qx-2q-5x+5.2& \text{Uitwerken } \\ & =qx-2q-5x+10 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{9}{18}+b)(q+\frac{-12}{20})& =(\color{red}{b}+\color{orange}{\frac{1}{2}}).(\color{green}{q}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{1}{2})} . \color{green}{(q)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{3}{5}b+\frac{1}{2}q-\frac{1}{2}.\frac{3}{5}& \text{Uitwerken } \\ & =bq-\frac{3}{5}b+\frac{1}{2}q-\frac{3}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(p+\frac{13}{8})(\frac{7}{14}+q)& =(\color{red}{p}+\color{orange}{\frac{13}{8}}).(\color{green}{q}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{13}{8})} . \color{green}{(q)} + \color{orange}{(\frac{13}{8})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = pq+\frac{1}{2}p+\frac{13}{8}q+\frac{13}{8}.\frac{1}{2}& \text{Uitwerken } \\ & =pq+\frac{1}{2}p+\frac{13}{8}q+\frac{13}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}((-6)+q)(19+p)& =(\color{red}{q}+\color{orange}{(-6)}).(\color{green}{p}+\color{blue}{19})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(19)} + \color{orange}{(-6)} . \color{green}{(p)} + \color{orange}{(-6)} . \color{blue}{(19)}& \text{Boogjes en uitschrijven} \\ & = pq+19q-6p-6.19& \text{Uitwerken } \\ & =pq+19q-6p-114 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(p+\frac{-13}{17})(\frac{-11}{7}+p)& =(\color{red}{p}+\color{orange}{\frac{-13}{17}}).(\color{green}{p}+\color{blue}{\frac{-11}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(p)} + \color{red}{(p)} . \color{blue}{(\frac{-11}{7})} + \color{orange}{(\frac{-13}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{17})} . \color{blue}{(\frac{-11}{7})}& \text{Boogjes en uitschrijven} \\ & = pp-\frac{11}{7}p-\frac{13}{17}p+\frac{13}{17}.\frac{11}{7}& \text{Uitwerken } \\ & =p^2+((\frac{-11}{7})+(\frac{-13}{17}))p+\frac{143}{119} & \text{Neem samen} \\ &=p^2-\frac{278}{119}p+\frac{143}{119} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(b+\frac{19}{16})(q+\frac{20}{10})& =(\color{red}{b}+\color{orange}{\frac{19}{16}}).(\color{green}{q}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(\frac{19}{16})} . \color{green}{(q)} + \color{orange}{(\frac{19}{16})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bq+2b+\frac{19}{16}q+\frac{19}{16}.2& \text{Uitwerken } \\ & =bq+2b+\frac{19}{16}q+\frac{38}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bq+2b+\frac{19}{16}q+\frac{19}{8} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(2+p)((-10)-x)& =(\color{red}{p}+\color{orange}{2}).(\color{green}{-x}+\color{blue}{(-10)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(-10)} + \color{orange}{(2)} . \color{green}{(-x)} + \color{orange}{(2)} . \color{blue}{(-10)}& \text{Boogjes en uitschrijven} \\ & = -px-10p-2x-2.10& \text{Uitwerken } \\ & =-px-10p-2x-20 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)