# Distributiviteit $$(a+r)(b+s)$$

#### Werk uit en vereenvoudig

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

#### Werk uit en vereenvoudig

##### Verbetersleutel

1. \begin{align}(a-\frac{19}{7})(\frac{-1}{19}-p)& =(\color{red}{a}+\color{orange}{\frac{-19}{7}}).(\color{green}{-p}+\color{blue}{\frac{-1}{19}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-p)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{19})} + \color{orange}{(\frac{-19}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{-19}{7})} . \color{blue}{(\frac{-1}{19})}& \text{Boogjes en uitschrijven} \\ & = -ap-\frac{1}{19}a+\frac{19}{7}p+\frac{19}{7}.\frac{1}{19}& \text{Uitwerken } \\ & =-ap-\frac{1}{19}a+\frac{19}{7}p+\frac{19}{133} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ap-\frac{1}{19}a+\frac{19}{7}p+\frac{1}{7} & \text{Vereenvoudig} \\\end{align}
2. \begin{align}(b+\frac{-16}{8})(\frac{9}{3}-b)& =(\color{red}{b}+\color{orange}{(-2)}).(\color{green}{-b}+\color{blue}{3})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-b)} + \color{red}{(b)} . \color{blue}{(3)} + \color{orange}{(-2)} . \color{green}{(-b)} + \color{orange}{(-2)} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = -bb+3b+2b-2.3& \text{Uitwerken } \\ & =-b^2+(3+2)b-6 & \text{Neem samen} \\ &=-b^2+5b-6 & \text{Maak de som} \\\end{align}
3. \begin{align}(p-\frac{-3}{2})(\frac{6}{3}-q)& =(\color{red}{p}+\color{orange}{\frac{3}{2}}).(\color{green}{-q}+\color{blue}{2})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-q)} + \color{red}{(p)} . \color{blue}{(2)} + \color{orange}{(\frac{3}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{3}{2})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = -pq+2p-\frac{3}{2}q+\frac{3}{2}.2& \text{Uitwerken } \\ & =-pq+2p-\frac{3}{2}q+\frac{6}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -pq+2p-\frac{3}{2}q+3 & \text{Vereenvoudig} \\\end{align}
4. \begin{align}(b+\frac{6}{15})(a+\frac{19}{19})& =(\color{red}{b}+\color{orange}{\frac{2}{5}}).(\color{green}{a}+\color{blue}{1})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(1)} + \color{orange}{(\frac{2}{5})} . \color{green}{(a)} + \color{orange}{(\frac{2}{5})} . \color{blue}{(1)}& \text{Boogjes en uitschrijven} \\ & = ab+1b+\frac{2}{5}a+\frac{2}{5}.1& \text{Uitwerken } \\ & =ab+1b+\frac{2}{5}a+\frac{2}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}
5. \begin{align}(\frac{-15}{4}+b)(b-\frac{-5}{15})& =(\color{red}{b}+\color{orange}{\frac{-15}{4}}).(\color{green}{b}+\color{blue}{\frac{1}{3}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(\frac{1}{3})} + \color{orange}{(\frac{-15}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{4})} . \color{blue}{(\frac{1}{3})}& \text{Boogjes en uitschrijven} \\ & = bb+\frac{1}{3}b-\frac{15}{4}b-\frac{15}{4}.\frac{1}{3}& \text{Uitwerken } \\ & =b^2+(\frac{1}{3}+(\frac{-15}{4}))b-(\frac{-15}{12}) & \text{Neem samen} \\ &=b^2-\frac{41}{12}b-(\frac{-15}{12}) & \text{Maak de som} \\ &=b^2-\frac{41}{12}b+\frac{5}{4} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}
6. \begin{align}(q+\frac{-9}{8})(\frac{-17}{17}-q)& =(\color{red}{q}+\color{orange}{\frac{-9}{8}}).(\color{green}{-q}+\color{blue}{(-1)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(-q)} + \color{red}{(q)} . \color{blue}{(-1)} + \color{orange}{(\frac{-9}{8})} . \color{green}{(-q)} + \color{orange}{(\frac{-9}{8})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = -qq-1q+\frac{9}{8}q+\frac{9}{8}.1& \text{Uitwerken } \\ & =-q^2+((-1)+\frac{9}{8})q+(\frac{-9}{8}) & \text{Neem samen} \\ &=-q^2+\frac{1}{8}q+(\frac{-9}{8}) & \text{Maak de som} \\\end{align}
7. \begin{align}(\frac{-12}{6}-b)(p+\frac{-4}{13})& =(\color{red}{-b}+\color{orange}{(-2)}).(\color{green}{p}+\color{blue}{\frac{-4}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(p)} + \color{red}{(-b)} . \color{blue}{(\frac{-4}{13})} + \color{orange}{(-2)} . \color{green}{(p)} + \color{orange}{(-2)} . \color{blue}{(\frac{-4}{13})}& \text{Boogjes en uitschrijven} \\ & = -bp+\frac{4}{13}b-2p+2.\frac{4}{13}& \text{Uitwerken } \\ & =-bp+\frac{4}{13}b-2p+\frac{8}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}
8. \begin{align}(x-\frac{-8}{16})(b-\frac{8}{7})& =(\color{red}{x}+\color{orange}{\frac{1}{2}}).(\color{green}{b}+\color{blue}{\frac{-8}{7}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-8}{7})} + \color{orange}{(\frac{1}{2})} . \color{green}{(b)} + \color{orange}{(\frac{1}{2})} . \color{blue}{(\frac{-8}{7})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{8}{7}x+\frac{1}{2}b-\frac{1}{2}.\frac{8}{7}& \text{Uitwerken } \\ & =bx-\frac{8}{7}x+\frac{1}{2}b-\frac{8}{14} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bx-\frac{8}{7}x+\frac{1}{2}b-\frac{4}{7} & \text{Vereenvoudig} \\\end{align}
9. \begin{align}(p-\frac{14}{2})(b+\frac{-7}{2})& =(\color{red}{p}+\color{orange}{(-7)}).(\color{green}{b}+\color{blue}{\frac{-7}{2}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-7}{2})} + \color{orange}{(-7)} . \color{green}{(b)} + \color{orange}{(-7)} . \color{blue}{(\frac{-7}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{7}{2}p-7b+7.\frac{7}{2}& \text{Uitwerken } \\ & =bp-\frac{7}{2}p-7b+\frac{49}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}
10. \begin{align}(\frac{-7}{11}+b)(\frac{-10}{15}-a)& =(\color{red}{b}+\color{orange}{\frac{-7}{11}}).(\color{green}{-a}+\color{blue}{\frac{-2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(-a)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{3})} + \color{orange}{(\frac{-7}{11})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{11})} . \color{blue}{(\frac{-2}{3})}& \text{Boogjes en uitschrijven} \\ & = -ab-\frac{2}{3}b+\frac{7}{11}a+\frac{7}{11}.\frac{2}{3}& \text{Uitwerken } \\ & =-ab-\frac{2}{3}b+\frac{7}{11}a+\frac{14}{33} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}
11. \begin{align}(\frac{1}{19}+x)(x+\frac{-20}{17})& =(\color{red}{x}+\color{orange}{\frac{1}{19}}).(\color{green}{x}+\color{blue}{\frac{-20}{17}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{-20}{17})} + \color{orange}{(\frac{1}{19})} . \color{green}{(x)} + \color{orange}{(\frac{1}{19})} . \color{blue}{(\frac{-20}{17})}& \text{Boogjes en uitschrijven} \\ & = xx-\frac{20}{17}x+\frac{1}{19}x-\frac{1}{19}.\frac{20}{17}& \text{Uitwerken } \\ & =x^2+((\frac{-20}{17})+\frac{1}{19})x-(\frac{-20}{323}) & \text{Neem samen} \\ &=x^2-\frac{363}{323}x-(\frac{-20}{323}) & \text{Maak de som} \\\end{align}
12. \begin{align}(p+\frac{5}{7})(7-p)& =(\color{red}{p}+\color{orange}{\frac{5}{7}}).(\color{green}{-p}+\color{blue}{7})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-p)} + \color{red}{(p)} . \color{blue}{(7)} + \color{orange}{(\frac{5}{7})} . \color{green}{(-p)} + \color{orange}{(\frac{5}{7})} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = -pp+7p-\frac{5}{7}p+\frac{5}{7}.7& \text{Uitwerken } \\ & =-p^2+(7+(\frac{-5}{7}))p+(\frac{-35}{7}) & \text{Neem samen} \\ &=-p^2+\frac{44}{7}p+(\frac{-35}{7}) & \text{Maak de som} \\ &=-p^2+\frac{44}{7}p+(-5) & \text{Vereenvoudig indien mogelijk 0} \\\end{align}
Oefeningengenerator vanhoeckes.be/wiskunde 2022-06-27 07:29:10