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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{16}{15}+p)(\frac{7}{4}-q)& =(\color{red}{p}+\color{orange}{\frac{16}{15}}).(\color{green}{-q}+\color{blue}{\frac{7}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(\frac{7}{4})} + \color{orange}{(\frac{16}{15})} . \color{green}{(-q)} + \color{orange}{(\frac{16}{15})} . \color{blue}{(\frac{7}{4})}& \text{Boogjes en uitschrijven} \\ & = -pq+\frac{7}{4}p-\frac{16}{15}q+\frac{16}{15}.\frac{7}{4}& \text{Uitwerken } \\ & =-pq+\frac{7}{4}p-\frac{16}{15}q+\frac{112}{60} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+\frac{7}{4}p-\frac{16}{15}q+\frac{28}{15} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-16}{16}+a)(\frac{-13}{10}+b)& =(\color{red}{a}+\color{orange}{(-1)}).(\color{green}{b}+\color{blue}{\frac{-13}{10}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{10})} + \color{orange}{(-1)} . \color{green}{(b)} + \color{orange}{(-1)} . \color{blue}{(\frac{-13}{10})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{13}{10}a-1b+1.\frac{13}{10}& \text{Uitwerken } \\ & =ab-\frac{13}{10}a-1b+\frac{13}{10} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(q+16)(x-\frac{1}{13})& =(\color{red}{q}+\color{orange}{16}).(\color{green}{x}+\color{blue}{\frac{-1}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(\frac{-1}{13})} + \color{orange}{(16)} . \color{green}{(x)} + \color{orange}{(16)} . \color{blue}{(\frac{-1}{13})}& \text{Boogjes en uitschrijven} \\ & = qx-\frac{1}{13}q+16x-16.\frac{1}{13}& \text{Uitwerken } \\ & =qx-\frac{1}{13}q+16x-\frac{16}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-20}{3}-b)(p+\frac{3}{17})& =(\color{red}{-b}+\color{orange}{\frac{-20}{3}}).(\color{green}{p}+\color{blue}{\frac{3}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{3}{17})} + \color{orange}{(\frac{-20}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-20}{3})} . \color{blue}{(\frac{3}{17})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{3}{17}b-\frac{20}{3}p-\frac{20}{3}.\frac{3}{17}& \text{Uitwerken } \\ & =-bp-\frac{3}{17}b-\frac{20}{3}p-\frac{60}{51} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bp-\frac{3}{17}b-\frac{20}{3}p-\frac{20}{17} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-11}{8}-a)(p+\frac{-13}{19})& =(\color{red}{-a}+\color{orange}{\frac{-11}{8}}).(\color{green}{p}+\color{blue}{\frac{-13}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{19})} + \color{orange}{(\frac{-11}{8})} . \color{green}{(p)} + \color{orange}{(\frac{-11}{8})} . \color{blue}{(\frac{-13}{19})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{13}{19}a-\frac{11}{8}p+\frac{11}{8}.\frac{13}{19}& \text{Uitwerken } \\ & =-ap+\frac{13}{19}a-\frac{11}{8}p+\frac{143}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(x+\frac{-13}{9})(a-\frac{19}{19})& =(\color{red}{x}+\color{orange}{\frac{-13}{9}}).(\color{green}{a}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(-1)} + \color{orange}{(\frac{-13}{9})} . \color{green}{(a)} + \color{orange}{(\frac{-13}{9})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax-1x-\frac{13}{9}a+\frac{13}{9}.1& \text{Uitwerken } \\ & =ax-1x-\frac{13}{9}a+\frac{13}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(\frac{-18}{13}+q)(a-\frac{18}{13})& =(\color{red}{q}+\color{orange}{\frac{-18}{13}}).(\color{green}{a}+\color{blue}{\frac{-18}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{-18}{13})} + \color{orange}{(\frac{-18}{13})} . \color{green}{(a)} + \color{orange}{(\frac{-18}{13})} . \color{blue}{(\frac{-18}{13})}& \text{Boogjes en uitschrijven} \\ & = aq-\frac{18}{13}q-\frac{18}{13}a+\frac{18}{13}.\frac{18}{13}& \text{Uitwerken } \\ & =aq-\frac{18}{13}q-\frac{18}{13}a+\frac{324}{169} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a+\frac{5}{18})(b+\frac{-7}{5})& =(\color{red}{a}+\color{orange}{\frac{5}{18}}).(\color{green}{b}+\color{blue}{\frac{-7}{5}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-7}{5})} + \color{orange}{(\frac{5}{18})} . \color{green}{(b)} + \color{orange}{(\frac{5}{18})} . \color{blue}{(\frac{-7}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{5}a+\frac{5}{18}b-\frac{5}{18}.\frac{7}{5}& \text{Uitwerken } \\ & =ab-\frac{7}{5}a+\frac{5}{18}b-\frac{35}{90} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{7}{5}a+\frac{5}{18}b-\frac{7}{18} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(\frac{-9}{19}+a)(q-\frac{-6}{10})& =(\color{red}{a}+\color{orange}{\frac{-9}{19}}).(\color{green}{q}+\color{blue}{\frac{3}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{3}{5})} + \color{orange}{(\frac{-9}{19})} . \color{green}{(q)} + \color{orange}{(\frac{-9}{19})} . \color{blue}{(\frac{3}{5})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{3}{5}a-\frac{9}{19}q-\frac{9}{19}.\frac{3}{5}& \text{Uitwerken } \\ & =aq+\frac{3}{5}a-\frac{9}{19}q-\frac{27}{95} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-11}{14}-p)(x+\frac{-3}{8})& =(\color{red}{-p}+\color{orange}{\frac{-11}{14}}).(\color{green}{x}+\color{blue}{\frac{-3}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(x)} + \color{red}{(-p)} . \color{blue}{(\frac{-3}{8})} + \color{orange}{(\frac{-11}{14})} . \color{green}{(x)} + \color{orange}{(\frac{-11}{14})} . \color{blue}{(\frac{-3}{8})}& \text{Boogjes en uitschrijven} \\ & = -px+\frac{3}{8}p-\frac{11}{14}x+\frac{11}{14}.\frac{3}{8}& \text{Uitwerken } \\ & =-px+\frac{3}{8}p-\frac{11}{14}x+\frac{33}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(1-p)(p-\frac{-14}{10})& =(\color{red}{-p}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{7}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{7}{5})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{7}{5})}& \text{Boogjes en uitschrijven} \\ & = -pp-\frac{7}{5}p+1p+1.\frac{7}{5}& \text{Uitwerken } \\ & =-p^2+((\frac{-7}{5})+1)p+(\frac{-7}{5}) & \text{Neem samen} \\ &=-p^2-\frac{2}{5}p+(\frac{-7}{5}) & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(\frac{-7}{20}+x)(b-\frac{-2}{4})& =(\color{red}{x}+\color{orange}{\frac{-7}{20}}).(\color{green}{b}+\color{blue}{\frac{1}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{1}{2})} + \color{orange}{(\frac{-7}{20})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{20})} . \color{blue}{(\frac{1}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{1}{2}x-\frac{7}{20}b-\frac{7}{20}.\frac{1}{2}& \text{Uitwerken } \\ & =bx+\frac{1}{2}x-\frac{7}{20}b-\frac{7}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)