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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-19}{20}+p)(\frac{-6}{8}-x)& =(\color{red}{p}+\color{orange}{\frac{-19}{20}}).(\color{green}{-x}+\color{blue}{\frac{-3}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-x)} + \color{red}{(p)} . \color{blue}{(\frac{-3}{4})} + \color{orange}{(\frac{-19}{20})} . \color{green}{(-x)} + \color{orange}{(\frac{-19}{20})} . \color{blue}{(\frac{-3}{4})}& \text{Boogjes en uitschrijven} \\ & = -px-\frac{3}{4}p+\frac{19}{20}x+\frac{19}{20}.\frac{3}{4}& \text{Uitwerken } \\ & =-px-\frac{3}{4}p+\frac{19}{20}x+\frac{57}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(x+5)(x+\frac{3}{11})& =(\color{red}{x}+\color{orange}{5}).(\color{green}{x}+\color{blue}{\frac{3}{11}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{3}{11})} + \color{orange}{(5)} . \color{green}{(x)} + \color{orange}{(5)} . \color{blue}{(\frac{3}{11})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{3}{11}x+5x+5.\frac{3}{11}& \text{Uitwerken } \\ & =x^2+(\frac{3}{11}+5)x+\frac{15}{11} & \text{Neem samen} \\ &=x^2+\frac{58}{11}x+\frac{15}{11} & \text{Maak de som} \\\end{align}\)
3. \(\begin{align}(x-\frac{15}{19})(b+\frac{-7}{19})& =(\color{red}{x}+\color{orange}{\frac{-15}{19}}).(\color{green}{b}+\color{blue}{\frac{-7}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-7}{19})} + \color{orange}{(\frac{-15}{19})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{19})} . \color{blue}{(\frac{-7}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{7}{19}x-\frac{15}{19}b+\frac{15}{19}.\frac{7}{19}& \text{Uitwerken } \\ & =bx-\frac{7}{19}x-\frac{15}{19}b+\frac{105}{361} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(b-\frac{15}{14})(a-\frac{-2}{19})& =(\color{red}{b}+\color{orange}{\frac{-15}{14}}).(\color{green}{a}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(\frac{-15}{14})} . \color{green}{(a)} + \color{orange}{(\frac{-15}{14})} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{19}b-\frac{15}{14}a-\frac{15}{14}.\frac{2}{19}& \text{Uitwerken } \\ & =ab+\frac{2}{19}b-\frac{15}{14}a-\frac{30}{266} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{2}{19}b-\frac{15}{14}a-\frac{15}{133} & \text{Vereenvoudig} \\\end{align}\)
5. \(\begin{align}(\frac{-2}{8}+p)(\frac{-2}{8}-b)& =(\color{red}{p}+\color{orange}{\frac{-1}{4}}).(\color{green}{-b}+\color{blue}{\frac{-1}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{4})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(-b)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-1}{4})}& \text{Boogjes en uitschrijven} \\ & = -bp-\frac{1}{4}p+\frac{1}{4}b+\frac{1}{4}.\frac{1}{4}& \text{Uitwerken } \\ & =-bp-\frac{1}{4}p+\frac{1}{4}b+\frac{1}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(b+\frac{-7}{6})(a+\frac{15}{16})& =(\color{red}{b}+\color{orange}{\frac{-7}{6}}).(\color{green}{a}+\color{blue}{\frac{15}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(\frac{15}{16})} + \color{orange}{(\frac{-7}{6})} . \color{green}{(a)} + \color{orange}{(\frac{-7}{6})} . \color{blue}{(\frac{15}{16})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{15}{16}b-\frac{7}{6}a-\frac{7}{6}.\frac{15}{16}& \text{Uitwerken } \\ & =ab+\frac{15}{16}b-\frac{7}{6}a-\frac{105}{96} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ab+\frac{15}{16}b-\frac{7}{6}a-\frac{35}{32} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}(q+\frac{7}{20})(a-\frac{-15}{17})& =(\color{red}{q}+\color{orange}{\frac{7}{20}}).(\color{green}{a}+\color{blue}{\frac{15}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{15}{17})} + \color{orange}{(\frac{7}{20})} . \color{green}{(a)} + \color{orange}{(\frac{7}{20})} . \color{blue}{(\frac{15}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{15}{17}q+\frac{7}{20}a+\frac{7}{20}.\frac{15}{17}& \text{Uitwerken } \\ & =aq+\frac{15}{17}q+\frac{7}{20}a+\frac{105}{340} & \text{Uitrekenen (Geen Smoothie!)} \\ & = aq+\frac{15}{17}q+\frac{7}{20}a+\frac{21}{68} & \text{Vereenvoudig} \\\end{align}\)
8. \(\begin{align}(\frac{12}{6}-x)(a-\frac{19}{5})& =(\color{red}{-x}+\color{orange}{2}).(\color{green}{a}+\color{blue}{\frac{-19}{5}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(\frac{-19}{5})} + \color{orange}{(2)} . \color{green}{(a)} + \color{orange}{(2)} . \color{blue}{(\frac{-19}{5})}& \text{Boogjes en uitschrijven} \\ & = -ax+\frac{19}{5}x+2a-2.\frac{19}{5}& \text{Uitwerken } \\ & =-ax+\frac{19}{5}x+2a-\frac{38}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{11}{18}-a)(b-\frac{9}{3})& =(\color{red}{-a}+\color{orange}{\frac{11}{18}}).(\color{green}{b}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(b)} + \color{red}{(-a)} . \color{blue}{(-3)} + \color{orange}{(\frac{11}{18})} . \color{green}{(b)} + \color{orange}{(\frac{11}{18})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = -ab+3a+\frac{11}{18}b-\frac{11}{18}.3& \text{Uitwerken } \\ & =-ab+3a+\frac{11}{18}b-\frac{33}{18} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -ab+3a+\frac{11}{18}b-\frac{11}{6} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{8}{13}+a)(\frac{2}{19}-a)& =(\color{red}{a}+\color{orange}{\frac{8}{13}}).(\color{green}{-a}+\color{blue}{\frac{2}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(-a)} + \color{red}{(a)} . \color{blue}{(\frac{2}{19})} + \color{orange}{(\frac{8}{13})} . \color{green}{(-a)} + \color{orange}{(\frac{8}{13})} . \color{blue}{(\frac{2}{19})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{2}{19}a-\frac{8}{13}a+\frac{8}{13}.\frac{2}{19}& \text{Uitwerken } \\ & =-a^2+(\frac{2}{19}+(\frac{-8}{13}))a+(\frac{-16}{247}) & \text{Neem samen} \\ &=-a^2-\frac{126}{247}a+(\frac{-16}{247}) & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(b-\frac{8}{2})(x-\frac{-18}{13})& =(\color{red}{b}+\color{orange}{(-4)}).(\color{green}{x}+\color{blue}{\frac{18}{13}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{18}{13})} + \color{orange}{(-4)} . \color{green}{(x)} + \color{orange}{(-4)} . \color{blue}{(\frac{18}{13})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{18}{13}b-4x-4.\frac{18}{13}& \text{Uitwerken } \\ & =bx+\frac{18}{13}b-4x-\frac{72}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(x-\frac{16}{17})(x-\frac{-18}{9})& =(\color{red}{x}+\color{orange}{\frac{-16}{17}}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(2)} + \color{orange}{(\frac{-16}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-16}{17})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = xx+2x-\frac{16}{17}x-\frac{16}{17}.2& \text{Uitwerken } \\ & =x^2+(2+(\frac{-16}{17}))x-(\frac{-32}{17}) & \text{Neem samen} \\ &=x^2+\frac{18}{17}x-(\frac{-32}{17}) & \text{Maak de som} \\\end{align}\)