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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(b+\frac{-4}{3})(\frac{-19}{7}-a)& =(\color{red}{b}+\color{orange}{\frac{-4}{3}}).(\color{green}{-a}+\color{blue}{\frac{-19}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-19}{7})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(-a)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-19}{7})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{19}{7}b+\frac{4}{3}a+\frac{4}{3}.\frac{19}{7}& \text{Uitwerken } \\ & =-ab-\frac{19}{7}b+\frac{4}{3}a+\frac{76}{21} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(q+\frac{-15}{2})(b+\frac{9}{19})& =(\color{red}{q}+\color{orange}{\frac{-15}{2}}).(\color{green}{b}+\color{blue}{\frac{9}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{9}{19})} + \color{orange}{(\frac{-15}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{2})} . \color{blue}{(\frac{9}{19})}& \text{Boogjes en uitschrijven} \\ & = bq+\frac{9}{19}q-\frac{15}{2}b-\frac{15}{2}.\frac{9}{19}& \text{Uitwerken } \\ & =bq+\frac{9}{19}q-\frac{15}{2}b-\frac{135}{38} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{11}{14}+q)(\frac{13}{8}-b)& =(\color{red}{q}+\color{orange}{\frac{11}{14}}).(\color{green}{-b}+\color{blue}{\frac{13}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-b)} + \color{red}{(q)} . \color{blue}{(\frac{13}{8})} + \color{orange}{(\frac{11}{14})} . \color{green}{(-b)} + \color{orange}{(\frac{11}{14})} . \color{blue}{(\frac{13}{8})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{13}{8}q-\frac{11}{14}b+\frac{11}{14}.\frac{13}{8}& \text{Uitwerken } \\ & =-bq+\frac{13}{8}q-\frac{11}{14}b+\frac{143}{112} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{-4}{3}+b)(\frac{-7}{11}+a)& =(\color{red}{b}+\color{orange}{\frac{-4}{3}}).(\color{green}{a}+\color{blue}{\frac{-7}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{-7}{11})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(a)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{-7}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{7}{11}b-\frac{4}{3}a+\frac{4}{3}.\frac{7}{11}& \text{Uitwerken } \\ & =ab-\frac{7}{11}b-\frac{4}{3}a+\frac{28}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(b-\frac{13}{5})(p-(-11))& =(\color{red}{b}+\color{orange}{\frac{-13}{5}}).(\color{green}{p}+\color{blue}{11})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(11)} + \color{orange}{(\frac{-13}{5})} . \color{green}{(p)} + \color{orange}{(\frac{-13}{5})} . \color{blue}{(11)}& \text{Boogjes en uitschrijven} \\ & = bp+11b-\frac{13}{5}p-\frac{13}{5}.11& \text{Uitwerken } \\ & =bp+11b-\frac{13}{5}p-\frac{143}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-16}{4}-x)(x+\frac{-12}{9})& =(\color{red}{-x}+\color{orange}{(-4)}).(\color{green}{x}+\color{blue}{\frac{-4}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{-4}{3})} + \color{orange}{(-4)} . \color{green}{(x)} + \color{orange}{(-4)} . \color{blue}{(\frac{-4}{3})}& \text{Boogjes en uitschrijven} \\ & = -xx+\frac{4}{3}x-4x+4.\frac{4}{3}& \text{Uitwerken } \\ & =-x^2+(\frac{4}{3}+(-4))x+(\frac{-16}{3}) & \text{Neem samen} \\ &=-x^2-\frac{8}{3}x+(\frac{-16}{3}) & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(10-a)(p-\frac{-7}{2})& =(\color{red}{-a}+\color{orange}{10}).(\color{green}{p}+\color{blue}{\frac{7}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{7}{2})} + \color{orange}{(10)} . \color{green}{(p)} + \color{orange}{(10)} . \color{blue}{(\frac{7}{2})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{7}{2}a+10p+10.\frac{7}{2}& \text{Uitwerken } \\ & =-ap-\frac{7}{2}a+10p+\frac{70}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{7}{2}a+10p+35 & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{-10}{13}+a)(\frac{19}{20}+p)& =(\color{red}{a}+\color{orange}{\frac{-10}{13}}).(\color{green}{p}+\color{blue}{\frac{19}{20}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{19}{20})} + \color{orange}{(\frac{-10}{13})} . \color{green}{(p)} + \color{orange}{(\frac{-10}{13})} . \color{blue}{(\frac{19}{20})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{19}{20}a-\frac{10}{13}p-\frac{10}{13}.\frac{19}{20}& \text{Uitwerken } \\ & =ap+\frac{19}{20}a-\frac{10}{13}p-\frac{190}{260} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{19}{20}a-\frac{10}{13}p-\frac{19}{26} & \text{Vereenvoudig} \\\end{align}\)
9. \(\begin{align}(b+\frac{12}{15})(p+\frac{5}{2})& =(\color{red}{b}+\color{orange}{\frac{4}{5}}).(\color{green}{p}+\color{blue}{\frac{5}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{5}{2})} + \color{orange}{(\frac{4}{5})} . \color{green}{(p)} + \color{orange}{(\frac{4}{5})} . \color{blue}{(\frac{5}{2})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{5}{2}b+\frac{4}{5}p+\frac{4}{5}.\frac{5}{2}& \text{Uitwerken } \\ & =bp+\frac{5}{2}b+\frac{4}{5}p+\frac{20}{10} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{5}{2}b+\frac{4}{5}p+2 & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(p-\frac{-16}{17})(q+\frac{-14}{9})& =(\color{red}{p}+\color{orange}{\frac{16}{17}}).(\color{green}{q}+\color{blue}{\frac{-14}{9}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(\frac{-14}{9})} + \color{orange}{(\frac{16}{17})} . \color{green}{(q)} + \color{orange}{(\frac{16}{17})} . \color{blue}{(\frac{-14}{9})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{14}{9}p+\frac{16}{17}q-\frac{16}{17}.\frac{14}{9}& \text{Uitwerken } \\ & =pq-\frac{14}{9}p+\frac{16}{17}q-\frac{224}{153} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(a-(-16))(b-\frac{5}{8})& =(\color{red}{a}+\color{orange}{16}).(\color{green}{b}+\color{blue}{\frac{-5}{8}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-5}{8})} + \color{orange}{(16)} . \color{green}{(b)} + \color{orange}{(16)} . \color{blue}{(\frac{-5}{8})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{5}{8}a+16b-16.\frac{5}{8}& \text{Uitwerken } \\ & =ab-\frac{5}{8}a+16b-\frac{80}{8} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{5}{8}a+16b-10 & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{12}{17}-p)(q+\frac{10}{16})& =(\color{red}{-p}+\color{orange}{\frac{12}{17}}).(\color{green}{q}+\color{blue}{\frac{5}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(q)} + \color{red}{(-p)} . \color{blue}{(\frac{5}{8})} + \color{orange}{(\frac{12}{17})} . \color{green}{(q)} + \color{orange}{(\frac{12}{17})} . \color{blue}{(\frac{5}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{5}{8}p+\frac{12}{17}q+\frac{12}{17}.\frac{5}{8}& \text{Uitwerken } \\ & =-pq-\frac{5}{8}p+\frac{12}{17}q+\frac{60}{136} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq-\frac{5}{8}p+\frac{12}{17}q+\frac{15}{34} & \text{Vereenvoudig} \\\end{align}\)