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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{19}{20}-b)(\frac{-9}{6}-x)& =(\color{red}{-b}+\color{orange}{\frac{19}{20}}).(\color{green}{-x}+\color{blue}{\frac{-3}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(-x)} + \color{red}{(-b)} . \color{blue}{(\frac{-3}{2})} + \color{orange}{(\frac{19}{20})} . \color{green}{(-x)} + \color{orange}{(\frac{19}{20})} . \color{blue}{(\frac{-3}{2})}& \text{Boogjes en uitschrijven} \\ & = bx+\frac{3}{2}b-\frac{19}{20}x-\frac{19}{20}.\frac{3}{2}& \text{Uitwerken } \\ & =bx+\frac{3}{2}b-\frac{19}{20}x-\frac{57}{40} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(b+\frac{-3}{12})(\frac{-3}{5}+p)& =(\color{red}{b}+\color{orange}{\frac{-1}{4}}).(\color{green}{p}+\color{blue}{\frac{-3}{5}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-3}{5})} + \color{orange}{(\frac{-1}{4})} . \color{green}{(p)} + \color{orange}{(\frac{-1}{4})} . \color{blue}{(\frac{-3}{5})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{3}{5}b-\frac{1}{4}p+\frac{1}{4}.\frac{3}{5}& \text{Uitwerken } \\ & =bp-\frac{3}{5}b-\frac{1}{4}p+\frac{3}{20} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(b+(-15))(\frac{-2}{15}+p)& =(\color{red}{b}+\color{orange}{(-15)}).(\color{green}{p}+\color{blue}{\frac{-2}{15}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{-2}{15})} + \color{orange}{(-15)} . \color{green}{(p)} + \color{orange}{(-15)} . \color{blue}{(\frac{-2}{15})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{2}{15}b-15p+15.\frac{2}{15}& \text{Uitwerken } \\ & =bp-\frac{2}{15}b-15p+\frac{30}{15} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp-\frac{2}{15}b-15p+2 & \text{Vereenvoudig} \\\end{align}\)
4. \(\begin{align}(p-\frac{11}{4})(b+3)& =(\color{red}{p}+\color{orange}{\frac{-11}{4}}).(\color{green}{b}+\color{blue}{3})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(3)} + \color{orange}{(\frac{-11}{4})} . \color{green}{(b)} + \color{orange}{(\frac{-11}{4})} . \color{blue}{(3)}& \text{Boogjes en uitschrijven} \\ & = bp+3p-\frac{11}{4}b-\frac{11}{4}.3& \text{Uitwerken } \\ & =bp+3p-\frac{11}{4}b-\frac{33}{4} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{10}{10}-p)(\frac{14}{13}-a)& =(\color{red}{-p}+\color{orange}{1}).(\color{green}{-a}+\color{blue}{\frac{14}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{14}{13})} + \color{orange}{(1)} . \color{green}{(-a)} + \color{orange}{(1)} . \color{blue}{(\frac{14}{13})}& \text{Boogjes en uitschrijven} \\ & = ap-\frac{14}{13}p-1a+1.\frac{14}{13}& \text{Uitwerken } \\ & =ap-\frac{14}{13}p-1a+\frac{14}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-15}{8}+a)(b-\frac{1}{11})& =(\color{red}{a}+\color{orange}{\frac{-15}{8}}).(\color{green}{b}+\color{blue}{\frac{-1}{11}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{-1}{11})} + \color{orange}{(\frac{-15}{8})} . \color{green}{(b)} + \color{orange}{(\frac{-15}{8})} . \color{blue}{(\frac{-1}{11})}& \text{Boogjes en uitschrijven} \\ & = ab-\frac{1}{11}a-\frac{15}{8}b+\frac{15}{8}.\frac{1}{11}& \text{Uitwerken } \\ & =ab-\frac{1}{11}a-\frac{15}{8}b+\frac{15}{88} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(a+16)(q-\frac{-6}{17})& =(\color{red}{a}+\color{orange}{16}).(\color{green}{q}+\color{blue}{\frac{6}{17}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(q)} + \color{red}{(a)} . \color{blue}{(\frac{6}{17})} + \color{orange}{(16)} . \color{green}{(q)} + \color{orange}{(16)} . \color{blue}{(\frac{6}{17})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{6}{17}a+16q+16.\frac{6}{17}& \text{Uitwerken } \\ & =aq+\frac{6}{17}a+16q+\frac{96}{17} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-14}{6}+b)(x+\frac{-3}{18})& =(\color{red}{b}+\color{orange}{\frac{-7}{3}}).(\color{green}{x}+\color{blue}{\frac{-1}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(\frac{-1}{6})} + \color{orange}{(\frac{-7}{3})} . \color{green}{(x)} + \color{orange}{(\frac{-7}{3})} . \color{blue}{(\frac{-1}{6})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{1}{6}b-\frac{7}{3}x+\frac{7}{3}.\frac{1}{6}& \text{Uitwerken } \\ & =bx-\frac{1}{6}b-\frac{7}{3}x+\frac{7}{18} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{-20}{8}-q)(b+\frac{12}{13})& =(\color{red}{-q}+\color{orange}{\frac{-5}{2}}).(\color{green}{b}+\color{blue}{\frac{12}{13}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(b)} + \color{red}{(-q)} . \color{blue}{(\frac{12}{13})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{12}{13})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{12}{13}q-\frac{5}{2}b-\frac{5}{2}.\frac{12}{13}& \text{Uitwerken } \\ & =-bq-\frac{12}{13}q-\frac{5}{2}b-\frac{60}{26} & \text{Uitrekenen (Geen Smoothie!)} \\ & = -bq-\frac{12}{13}q-\frac{5}{2}b-\frac{30}{13} & \text{Vereenvoudig} \\\end{align}\)
10. \(\begin{align}(\frac{-12}{6}-x)(x+\frac{12}{8})& =(\color{red}{-x}+\color{orange}{(-2)}).(\color{green}{x}+\color{blue}{\frac{3}{2}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-x)} . \color{green}{(x)} + \color{red}{(-x)} . \color{blue}{(\frac{3}{2})} + \color{orange}{(-2)} . \color{green}{(x)} + \color{orange}{(-2)} . \color{blue}{(\frac{3}{2})}& \text{Boogjes en uitschrijven} \\ & = -xx-\frac{3}{2}x-2x-2.\frac{3}{2}& \text{Uitwerken } \\ & =-x^2+((\frac{-3}{2})+(-2))x-\frac{6}{2} & \text{Neem samen} \\ &=-x^2-\frac{7}{2}x-\frac{6}{2} & \text{Maak de som} \\ &=-x^2-\frac{7}{2}x-3 & \text{Vereenvoudig indien mogelijk 0} \\\end{align}\)
11. \(\begin{align}(\frac{8}{8}-a)(a+\frac{-1}{15})& =(\color{red}{-a}+\color{orange}{1}).(\color{green}{a}+\color{blue}{\frac{-1}{15}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(a)} + \color{red}{(-a)} . \color{blue}{(\frac{-1}{15})} + \color{orange}{(1)} . \color{green}{(a)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{15})}& \text{Boogjes en uitschrijven} \\ & = -aa+\frac{1}{15}a+1a-1.\frac{1}{15}& \text{Uitwerken } \\ & =-a^2+(\frac{1}{15}+1)a-\frac{1}{15} & \text{Neem samen} \\ &=-a^2+\frac{16}{15}a-\frac{1}{15} & \text{Maak de som} \\\end{align}\)
12. \(\begin{align}(b+\frac{14}{13})(\frac{-8}{4}+q)& =(\color{red}{b}+\color{orange}{\frac{14}{13}}).(\color{green}{q}+\color{blue}{(-2)})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(q)} + \color{red}{(b)} . \color{blue}{(-2)} + \color{orange}{(\frac{14}{13})} . \color{green}{(q)} + \color{orange}{(\frac{14}{13})} . \color{blue}{(-2)}& \text{Boogjes en uitschrijven} \\ & = bq-2b+\frac{14}{13}q-\frac{14}{13}.2& \text{Uitwerken } \\ & =bq-2b+\frac{14}{13}q-\frac{28}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)