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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(a+1)(b-\frac{19}{19})& =(\color{red}{a}+\color{orange}{1}).(\color{green}{b}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(1)} . \color{green}{(b)} + \color{orange}{(1)} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ab-1a+1b-1.1& \text{Uitwerken } \\ & =ab-1a+1b-1 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-2}{15}+q)(\frac{-4}{19}+b)& =(\color{red}{q}+\color{orange}{\frac{-2}{15}}).(\color{green}{b}+\color{blue}{\frac{-4}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(b)} + \color{red}{(q)} . \color{blue}{(\frac{-4}{19})} + \color{orange}{(\frac{-2}{15})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{15})} . \color{blue}{(\frac{-4}{19})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{4}{19}q-\frac{2}{15}b+\frac{2}{15}.\frac{4}{19}& \text{Uitwerken } \\ & =bq-\frac{4}{19}q-\frac{2}{15}b+\frac{8}{285} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{-1}{17}+a)(x+\frac{18}{14})& =(\color{red}{a}+\color{orange}{\frac{-1}{17}}).(\color{green}{x}+\color{blue}{\frac{9}{7}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(\frac{9}{7})} + \color{orange}{(\frac{-1}{17})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{17})} . \color{blue}{(\frac{9}{7})}& \text{Boogjes en uitschrijven} \\ & = ax+\frac{9}{7}a-\frac{1}{17}x-\frac{1}{17}.\frac{9}{7}& \text{Uitwerken } \\ & =ax+\frac{9}{7}a-\frac{1}{17}x-\frac{9}{119} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{11}{15}-a)(\frac{-13}{4}+p)& =(\color{red}{-a}+\color{orange}{\frac{11}{15}}).(\color{green}{p}+\color{blue}{\frac{-13}{4}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(p)} + \color{red}{(-a)} . \color{blue}{(\frac{-13}{4})} + \color{orange}{(\frac{11}{15})} . \color{green}{(p)} + \color{orange}{(\frac{11}{15})} . \color{blue}{(\frac{-13}{4})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{13}{4}a+\frac{11}{15}p-\frac{11}{15}.\frac{13}{4}& \text{Uitwerken } \\ & =-ap+\frac{13}{4}a+\frac{11}{15}p-\frac{143}{60} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{-1}{8}+p)(\frac{-13}{16}+b)& =(\color{red}{p}+\color{orange}{\frac{-1}{8}}).(\color{green}{b}+\color{blue}{\frac{-13}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-13}{16})} + \color{orange}{(\frac{-1}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-1}{8})} . \color{blue}{(\frac{-13}{16})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{13}{16}p-\frac{1}{8}b+\frac{1}{8}.\frac{13}{16}& \text{Uitwerken } \\ & =bp-\frac{13}{16}p-\frac{1}{8}b+\frac{13}{128} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-18}{12}-b)(\frac{11}{17}-q)& =(\color{red}{-b}+\color{orange}{\frac{-3}{2}}).(\color{green}{-q}+\color{blue}{\frac{11}{17}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-q)} + \color{red}{(-b)} . \color{blue}{(\frac{11}{17})} + \color{orange}{(\frac{-3}{2})} . \color{green}{(-q)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(\frac{11}{17})}& \text{Boogjes en uitschrijven} \\ & = bq-\frac{11}{17}b+\frac{3}{2}q-\frac{3}{2}.\frac{11}{17}& \text{Uitwerken } \\ & =bq-\frac{11}{17}b+\frac{3}{2}q-\frac{33}{34} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(b-\frac{-11}{4})(b+\frac{-10}{5})& =(\color{red}{b}+\color{orange}{\frac{11}{4}}).(\color{green}{b}+\color{blue}{(-2)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(b)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{11}{4})} . \color{green}{(b)} + \color{orange}{(\frac{11}{4})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bb-2b+\frac{11}{4}b-\frac{11}{4}.2& \text{Uitwerken } \\ & =b^2+((-2)+\frac{11}{4})b-(\frac{-22}{4}) & \text{Neem samen} \\ &=b^2+\frac{3}{4}b-(\frac{-22}{4}) & \text{Maak de som} \\ &=b^2+\frac{3}{4}b+\frac{11}{2} & \text{Vereenvoudig indien mogelijk 1} \\\end{align}\)
8. \(\begin{align}(q+\frac{4}{3})(q+\frac{3}{16})& =(\color{red}{q}+\color{orange}{\frac{4}{3}}).(\color{green}{q}+\color{blue}{\frac{3}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(q)} + \color{red}{(q)} . \color{blue}{(\frac{3}{16})} + \color{orange}{(\frac{4}{3})} . \color{green}{(q)} + \color{orange}{(\frac{4}{3})} . \color{blue}{(\frac{3}{16})}& \text{Boogjes en uitschrijven} \\ & = qq+\frac{3}{16}q+\frac{4}{3}q+\frac{4}{3}.\frac{3}{16}& \text{Uitwerken } \\ & =q^2+(\frac{3}{16}+\frac{4}{3})q+\frac{12}{48} & \text{Neem samen} \\ &=q^2+\frac{73}{48}q+\frac{12}{48} & \text{Maak de som} \\ &=q^2+\frac{73}{48}q+\frac{1}{4} & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
9. \(\begin{align}(\frac{2}{14}-x)(a+\frac{-20}{5})& =(\color{red}{-x}+\color{orange}{\frac{1}{7}}).(\color{green}{a}+\color{blue}{(-4)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(a)} + \color{red}{(-x)} . \color{blue}{(-4)} + \color{orange}{(\frac{1}{7})} . \color{green}{(a)} + \color{orange}{(\frac{1}{7})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = -ax+4x+\frac{1}{7}a-\frac{1}{7}.4& \text{Uitwerken } \\ & =-ax+4x+\frac{1}{7}a-\frac{4}{7} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{-10}{17}+b)(a+\frac{-9}{3})& =(\color{red}{b}+\color{orange}{\frac{-10}{17}}).(\color{green}{a}+\color{blue}{(-3)})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(-3)} + \color{orange}{(\frac{-10}{17})} . \color{green}{(a)} + \color{orange}{(\frac{-10}{17})} . \color{blue}{(-3)}& \text{Boogjes en uitschrijven} \\ & = ab-3b-\frac{10}{17}a+\frac{10}{17}.3& \text{Uitwerken } \\ & =ab-3b-\frac{10}{17}a+\frac{30}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
11. \(\begin{align}(x+\frac{-19}{3})(p+\frac{3}{16})& =(\color{red}{x}+\color{orange}{\frac{-19}{3}}).(\color{green}{p}+\color{blue}{\frac{3}{16}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(p)} + \color{red}{(x)} . \color{blue}{(\frac{3}{16})} + \color{orange}{(\frac{-19}{3})} . \color{green}{(p)} + \color{orange}{(\frac{-19}{3})} . \color{blue}{(\frac{3}{16})}& \text{Boogjes en uitschrijven} \\ & = px+\frac{3}{16}x-\frac{19}{3}p-\frac{19}{3}.\frac{3}{16}& \text{Uitwerken } \\ & =px+\frac{3}{16}x-\frac{19}{3}p-\frac{57}{48} & \text{Uitrekenen (Geen Smoothie!)} \\ & = px+\frac{3}{16}x-\frac{19}{3}p-\frac{19}{16} & \text{Vereenvoudig} \\\end{align}\)
12. \(\begin{align}(a+20)(7+x)& =(\color{red}{a}+\color{orange}{20}).(\color{green}{x}+\color{blue}{7})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(x)} + \color{red}{(a)} . \color{blue}{(7)} + \color{orange}{(20)} . \color{green}{(x)} + \color{orange}{(20)} . \color{blue}{(7)}& \text{Boogjes en uitschrijven} \\ & = ax+7a+20x+20.7& \text{Uitwerken } \\ & =ax+7a+20x+140 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)