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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-9}{14}+a)(b-\frac{-5}{17})& =(\color{red}{a}+\color{orange}{\frac{-9}{14}}).(\color{green}{b}+\color{blue}{\frac{5}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{5}{17})} + \color{orange}{(\frac{-9}{14})} . \color{green}{(b)} + \color{orange}{(\frac{-9}{14})} . \color{blue}{(\frac{5}{17})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{5}{17}a-\frac{9}{14}b-\frac{9}{14}.\frac{5}{17}& \text{Uitwerken } \\ & =ab+\frac{5}{17}a-\frac{9}{14}b-\frac{45}{238} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(a-\frac{-16}{19})(\frac{-19}{10}+b)& =(\color{red}{a}+\color{orange}{\frac{16}{19}}).(\color{green}{b}+\color{blue}{\frac{-19}{10}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-19}{10})} + \color{orange}{(\frac{16}{19})} . \color{green}{(b)} + \color{orange}{(\frac{16}{19})} . \color{blue}{(\frac{-19}{10})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{19}{10}a+\frac{16}{19}b-\frac{16}{19}.\frac{19}{10}& \text{Uitwerken } \\ & =ab-\frac{19}{10}a+\frac{16}{19}b-\frac{304}{190} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab-\frac{19}{10}a+\frac{16}{19}b-\frac{8}{5} & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(\frac{-7}{4}+x)(b+\frac{-9}{5})& =(\color{red}{x}+\color{orange}{\frac{-7}{4}}).(\color{green}{b}+\color{blue}{\frac{-9}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{5})} + \color{orange}{(\frac{-7}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-7}{4})} . \color{blue}{(\frac{-9}{5})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{9}{5}x-\frac{7}{4}b+\frac{7}{4}.\frac{9}{5}& \text{Uitwerken } \\ & =bx-\frac{9}{5}x-\frac{7}{4}b+\frac{63}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(q+\frac{-15}{17})(\frac{-16}{14}+p)& =(\color{red}{q}+\color{orange}{\frac{-15}{17}}).(\color{green}{p}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(p)} + \color{red}{(q)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{-15}{17})} . \color{green}{(p)} + \color{orange}{(\frac{-15}{17})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = pq-\frac{8}{7}q-\frac{15}{17}p+\frac{15}{17}.\frac{8}{7}& \text{Uitwerken } \\ & =pq-\frac{8}{7}q-\frac{15}{17}p+\frac{120}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-18}{2}+a)(p-\frac{-14}{3})& =(\color{red}{a}+\color{orange}{(-9)}).(\color{green}{p}+\color{blue}{\frac{14}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(\frac{14}{3})} + \color{orange}{(-9)} . \color{green}{(p)} + \color{orange}{(-9)} . \color{blue}{(\frac{14}{3})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{14}{3}a-9p-9.\frac{14}{3}& \text{Uitwerken } \\ & =ap+\frac{14}{3}a-9p-\frac{126}{3} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{14}{3}a-9p-42 & \text{Vereenvoudig} \\\end{align}\)
6. \(\begin{align}(a-\frac{18}{8})(a+\frac{-13}{16})& =(\color{red}{a}+\color{orange}{\frac{-9}{4}}).(\color{green}{a}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(\frac{-9}{4})} . \color{green}{(a)} + \color{orange}{(\frac{-9}{4})} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = aa-\frac{13}{16}a-\frac{9}{4}a+\frac{9}{4}.\frac{13}{16}& \text{Uitwerken } \\ & =a^2+((\frac{-13}{16})+(\frac{-9}{4}))a+\frac{117}{64} & \text{Neem samen} \\ &=a^2-\frac{49}{16}a+\frac{117}{64} & \text{Maak de som} \\\end{align}\)
7. \(\begin{align}(\frac{7}{11}+a)(b-\frac{6}{5})& =(\color{red}{a}+\color{orange}{\frac{7}{11}}).(\color{green}{b}+\color{blue}{\frac{-6}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-6}{5})} + \color{orange}{(\frac{7}{11})} . \color{green}{(b)} + \color{orange}{(\frac{7}{11})} . \color{blue}{(\frac{-6}{5})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{6}{5}a+\frac{7}{11}b-\frac{7}{11}.\frac{6}{5}& \text{Uitwerken } \\ & =ab-\frac{6}{5}a+\frac{7}{11}b-\frac{42}{55} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{6}{2}-b)(x-\frac{-2}{2})& =(\color{red}{-b}+\color{orange}{3}).(\color{green}{x}+\color{blue}{1})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(x)} + \color{red}{(-b)} . \color{blue}{(1)} + \color{orange}{(3)} . \color{green}{(x)} + \color{orange}{(3)} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = -bx-1b+3x+3.1& \text{Uitwerken } \\ & =-bx-1b+3x+3 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(x-\frac{4}{10})(\frac{20}{2}+a)& =(\color{red}{x}+\color{orange}{\frac{-2}{5}}).(\color{green}{a}+\color{blue}{10})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(a)} + \color{red}{(x)} . \color{blue}{(10)} + \color{orange}{(\frac{-2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(10)}& \text{Boogjes en uitschrijven} \\ & = ax+10x-\frac{2}{5}a-\frac{2}{5}.10& \text{Uitwerken } \\ & =ax+10x-\frac{2}{5}a-\frac{20}{5} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ax+10x-\frac{2}{5}a-4 & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-12}{14}-q)(\frac{-19}{5}-q)& =(\color{red}{-q}+\color{orange}{\frac{-6}{7}}).(\color{green}{-q}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(-q)} + \color{red}{(-q)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(\frac{-6}{7})} . \color{green}{(-q)} + \color{orange}{(\frac{-6}{7})} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{19}{5}q+\frac{6}{7}q+\frac{6}{7}.\frac{19}{5}& \text{Uitwerken } \\ & =q^2+(\frac{19}{5}+\frac{6}{7})q+\frac{114}{35} & \text{Neem samen} \\ &=q^2+\frac{163}{35}q+\frac{114}{35} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(\frac{18}{17}-q)(b+\frac{-5}{14})& =(\color{red}{-q}+\color{orange}{\frac{18}{17}}).(\color{green}{b}+\color{blue}{\frac{-5}{14}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{-5}{14})} + \color{orange}{(\frac{18}{17})} . \color{green}{(b)} + \color{orange}{(\frac{18}{17})} . \color{blue}{(\frac{-5}{14})}& \text{Boogjes en uitschrijven} \\ & = -bq+\frac{5}{14}q+\frac{18}{17}b-\frac{18}{17}.\frac{5}{14}& \text{Uitwerken } \\ & =-bq+\frac{5}{14}q+\frac{18}{17}b-\frac{90}{238} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq+\frac{5}{14}q+\frac{18}{17}b-\frac{45}{119} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(\frac{-15}{4}-b)(\frac{14}{16}+q)& =(\color{red}{-b}+\color{orange}{\frac{-15}{4}}).(\color{green}{q}+\color{blue}{\frac{7}{8}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{7}{8})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(q)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{7}{8})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{7}{8}b-\frac{15}{4}q-\frac{15}{4}.\frac{7}{8}& \text{Uitwerken } \\ & =-bq-\frac{7}{8}b-\frac{15}{4}q-\frac{105}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)