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

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Werk uit en vereenvoudig

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(\frac{-5}{2}-b)(q+\frac{19}{16})& =(\color{red}{-b}+\color{orange}{\frac{-5}{2}}).(\color{green}{q}+\color{blue}{\frac{19}{16}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-b)} . \color{green}{(q)} + \color{red}{(-b)} . \color{blue}{(\frac{19}{16})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(q)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{19}{16})}& \text{Boogjes en uitschrijven} \\ & = -bq-\frac{19}{16}b-\frac{5}{2}q-\frac{5}{2}.\frac{19}{16}& \text{Uitwerken } \\ & =-bq-\frac{19}{16}b-\frac{5}{2}q-\frac{95}{32} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
2. \(\begin{align}(\frac{-1}{16}-p)(\frac{19}{11}-x)& =(\color{red}{-p}+\color{orange}{\frac{-1}{16}}).(\color{green}{-x}+\color{blue}{\frac{19}{11}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-x)} + \color{red}{(-p)} . \color{blue}{(\frac{19}{11})} + \color{orange}{(\frac{-1}{16})} . \color{green}{(-x)} + \color{orange}{(\frac{-1}{16})} . \color{blue}{(\frac{19}{11})}& \text{Boogjes en uitschrijven} \\ & = px-\frac{19}{11}p+\frac{1}{16}x-\frac{1}{16}.\frac{19}{11}& \text{Uitwerken } \\ & =px-\frac{19}{11}p+\frac{1}{16}x-\frac{19}{176} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
3. \(\begin{align}(\frac{13}{19}-a)((-1)-x)& =(\color{red}{-a}+\color{orange}{\frac{13}{19}}).(\color{green}{-x}+\color{blue}{(-1)})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-a)} . \color{green}{(-x)} + \color{red}{(-a)} . \color{blue}{(-1)} + \color{orange}{(\frac{13}{19})} . \color{green}{(-x)} + \color{orange}{(\frac{13}{19})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ax+1a-\frac{13}{19}x-\frac{13}{19}.1& \text{Uitwerken } \\ & =ax+1a-\frac{13}{19}x-\frac{13}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(x-\frac{8}{19})(\frac{13}{9}+x)& =(\color{red}{x}+\color{orange}{\frac{-8}{19}}).(\color{green}{x}+\color{blue}{\frac{13}{9}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(x)} + \color{red}{(x)} . \color{blue}{(\frac{13}{9})} + \color{orange}{(\frac{-8}{19})} . \color{green}{(x)} + \color{orange}{(\frac{-8}{19})} . \color{blue}{(\frac{13}{9})}& \text{Boogjes en uitschrijven} \\ & = xx+\frac{13}{9}x-\frac{8}{19}x-\frac{8}{19}.\frac{13}{9}& \text{Uitwerken } \\ & =x^2+(\frac{13}{9}+(\frac{-8}{19}))x-(\frac{-104}{171}) & \text{Neem samen} \\ &=x^2+\frac{175}{171}x-(\frac{-104}{171}) & \text{Maak de som} \\\end{align}\)
5. \(\begin{align}(b+\frac{-9}{9})(x-\frac{-4}{2})& =(\color{red}{b}+\color{orange}{(-1)}).(\color{green}{x}+\color{blue}{2})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(x)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(-1)} . \color{green}{(x)} + \color{orange}{(-1)} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = bx+2b-1x-1.2& \text{Uitwerken } \\ & =bx+2b-1x-2 & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{1}{8}-q)(\frac{7}{19}+p)& =(\color{red}{-q}+\color{orange}{\frac{1}{8}}).(\color{green}{p}+\color{blue}{\frac{7}{19}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{7}{19})} + \color{orange}{(\frac{1}{8})} . \color{green}{(p)} + \color{orange}{(\frac{1}{8})} . \color{blue}{(\frac{7}{19})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{7}{19}q+\frac{1}{8}p+\frac{1}{8}.\frac{7}{19}& \text{Uitwerken } \\ & =-pq-\frac{7}{19}q+\frac{1}{8}p+\frac{7}{152} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
7. \(\begin{align}(p+\frac{7}{8})(q+\frac{15}{3})& =(\color{red}{p}+\color{orange}{\frac{7}{8}}).(\color{green}{q}+\color{blue}{5})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(q)} + \color{red}{(p)} . \color{blue}{(5)} + \color{orange}{(\frac{7}{8})} . \color{green}{(q)} + \color{orange}{(\frac{7}{8})} . \color{blue}{(5)}& \text{Boogjes en uitschrijven} \\ & = pq+5p+\frac{7}{8}q+\frac{7}{8}.5& \text{Uitwerken } \\ & =pq+5p+\frac{7}{8}q+\frac{35}{8} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(a+\frac{-16}{12})(b+\frac{6}{9})& =(\color{red}{a}+\color{orange}{\frac{-4}{3}}).(\color{green}{b}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(b)} + \color{red}{(a)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{-4}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-4}{3})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = ab+\frac{2}{3}a-\frac{4}{3}b-\frac{4}{3}.\frac{2}{3}& \text{Uitwerken } \\ & =ab+\frac{2}{3}a-\frac{4}{3}b-\frac{8}{9} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(\frac{13}{13}-p)(\frac{-1}{7}+p)& =(\color{red}{-p}+\color{orange}{1}).(\color{green}{p}+\color{blue}{\frac{-1}{7}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(p)} + \color{red}{(-p)} . \color{blue}{(\frac{-1}{7})} + \color{orange}{(1)} . \color{green}{(p)} + \color{orange}{(1)} . \color{blue}{(\frac{-1}{7})}& \text{Boogjes en uitschrijven} \\ & = -pp+\frac{1}{7}p+1p-1.\frac{1}{7}& \text{Uitwerken } \\ & =-p^2+(\frac{1}{7}+1)p-\frac{1}{7} & \text{Neem samen} \\ &=-p^2+\frac{8}{7}p-\frac{1}{7} & \text{Maak de som} \\\end{align}\)
10. \(\begin{align}(b+\frac{5}{19})(p-\frac{-19}{4})& =(\color{red}{b}+\color{orange}{\frac{5}{19}}).(\color{green}{p}+\color{blue}{\frac{19}{4}})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(p)} + \color{red}{(b)} . \color{blue}{(\frac{19}{4})} + \color{orange}{(\frac{5}{19})} . \color{green}{(p)} + \color{orange}{(\frac{5}{19})} . \color{blue}{(\frac{19}{4})}& \text{Boogjes en uitschrijven} \\ & = bp+\frac{19}{4}b+\frac{5}{19}p+\frac{5}{19}.\frac{19}{4}& \text{Uitwerken } \\ & =bp+\frac{19}{4}b+\frac{5}{19}p+\frac{95}{76} & \text{Uitrekenen (Geen Smoothie!)} \\ & = bp+\frac{19}{4}b+\frac{5}{19}p+\frac{5}{4} & \text{Vereenvoudig} \\\end{align}\)
11. \(\begin{align}(\frac{-15}{9}+p)(\frac{-1}{2}+b)& =(\color{red}{p}+\color{orange}{\frac{-5}{3}}).(\color{green}{b}+\color{blue}{\frac{-1}{2}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(\frac{-1}{2})} + \color{orange}{(\frac{-5}{3})} . \color{green}{(b)} + \color{orange}{(\frac{-5}{3})} . \color{blue}{(\frac{-1}{2})}& \text{Boogjes en uitschrijven} \\ & = bp-\frac{1}{2}p-\frac{5}{3}b+\frac{5}{3}.\frac{1}{2}& \text{Uitwerken } \\ & =bp-\frac{1}{2}p-\frac{5}{3}b+\frac{5}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(p-\frac{17}{4})(\frac{3}{20}-a)& =(\color{red}{p}+\color{orange}{\frac{-17}{4}}).(\color{green}{-a}+\color{blue}{\frac{3}{20}})& \text{Vereenvoud2g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(-a)} + \color{red}{(p)} . \color{blue}{(\frac{3}{20})} + \color{orange}{(\frac{-17}{4})} . \color{green}{(-a)} + \color{orange}{(\frac{-17}{4})} . \color{blue}{(\frac{3}{20})}& \text{Boogjes en uitschrijven} \\ & = -ap+\frac{3}{20}p+\frac{17}{4}a-\frac{17}{4}.\frac{3}{20}& \text{Uitwerken } \\ & =-ap+\frac{3}{20}p+\frac{17}{4}a-\frac{51}{80} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)