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

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

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Werk uit en vereenvoudig

Verbetersleutel

1. \(\begin{align}(p-\frac{1}{16})(a-\frac{12}{2})& =(\color{red}{p}+\color{orange}{\frac{-1}{16}}).(\color{green}{a}+\color{blue}{(-6)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(a)} + \color{red}{(p)} . \color{blue}{(-6)} + \color{orange}{(\frac{-1}{16})} . \color{green}{(a)} + \color{orange}{(\frac{-1}{16})} . \color{blue}{(-6)}& \text{Boogjes en uitschrijven} \\ & = ap-6p-\frac{1}{16}a+\frac{1}{16}.6& \text{Uitwerken } \\ & =ap-6p-\frac{1}{16}a+\frac{6}{16} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap-6p-\frac{1}{16}a+\frac{3}{8} & \text{Vereenvoudig} \\\end{align}\)
2. \(\begin{align}(\frac{-9}{18}+q)(20+x)& =(\color{red}{q}+\color{orange}{\frac{-1}{2}}).(\color{green}{x}+\color{blue}{20})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(x)} + \color{red}{(q)} . \color{blue}{(20)} + \color{orange}{(\frac{-1}{2})} . \color{green}{(x)} + \color{orange}{(\frac{-1}{2})} . \color{blue}{(20)}& \text{Boogjes en uitschrijven} \\ & = qx+20q-\frac{1}{2}x-\frac{1}{2}.20& \text{Uitwerken } \\ & =qx+20q-\frac{1}{2}x-\frac{20}{2} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+20q-\frac{1}{2}x-10 & \text{Vereenvoudig} \\\end{align}\)
3. \(\begin{align}(p+\frac{-8}{20})(b-\frac{16}{4})& =(\color{red}{p}+\color{orange}{\frac{-2}{5}}).(\color{green}{b}+\color{blue}{(-4)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(p)} . \color{green}{(b)} + \color{red}{(p)} . \color{blue}{(-4)} + \color{orange}{(\frac{-2}{5})} . \color{green}{(b)} + \color{orange}{(\frac{-2}{5})} . \color{blue}{(-4)}& \text{Boogjes en uitschrijven} \\ & = bp-4p-\frac{2}{5}b+\frac{2}{5}.4& \text{Uitwerken } \\ & =bp-4p-\frac{2}{5}b+\frac{8}{5} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
4. \(\begin{align}(\frac{18}{3}-q)(\frac{-12}{13}+a)& =(\color{red}{-q}+\color{orange}{6}).(\color{green}{a}+\color{blue}{\frac{-12}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(a)} + \color{red}{(-q)} . \color{blue}{(\frac{-12}{13})} + \color{orange}{(6)} . \color{green}{(a)} + \color{orange}{(6)} . \color{blue}{(\frac{-12}{13})}& \text{Boogjes en uitschrijven} \\ & = -aq+\frac{12}{13}q+6a-6.\frac{12}{13}& \text{Uitwerken } \\ & =-aq+\frac{12}{13}q+6a-\frac{72}{13} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
5. \(\begin{align}(\frac{18}{19}+b)(\frac{12}{6}+a)& =(\color{red}{b}+\color{orange}{\frac{18}{19}}).(\color{green}{a}+\color{blue}{2})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(b)} . \color{green}{(a)} + \color{red}{(b)} . \color{blue}{(2)} + \color{orange}{(\frac{18}{19})} . \color{green}{(a)} + \color{orange}{(\frac{18}{19})} . \color{blue}{(2)}& \text{Boogjes en uitschrijven} \\ & = ab+2b+\frac{18}{19}a+\frac{18}{19}.2& \text{Uitwerken } \\ & =ab+2b+\frac{18}{19}a+\frac{36}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
6. \(\begin{align}(\frac{-7}{12}-p)(\frac{-9}{16}-a)& =(\color{red}{-p}+\color{orange}{\frac{-7}{12}}).(\color{green}{-a}+\color{blue}{\frac{-9}{16}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-p)} . \color{green}{(-a)} + \color{red}{(-p)} . \color{blue}{(\frac{-9}{16})} + \color{orange}{(\frac{-7}{12})} . \color{green}{(-a)} + \color{orange}{(\frac{-7}{12})} . \color{blue}{(\frac{-9}{16})}& \text{Boogjes en uitschrijven} \\ & = ap+\frac{9}{16}p+\frac{7}{12}a+\frac{7}{12}.\frac{9}{16}& \text{Uitwerken } \\ & =ap+\frac{9}{16}p+\frac{7}{12}a+\frac{63}{192} & \text{Uitrekenen (Geen Smoothie!)} \\ & = ap+\frac{9}{16}p+\frac{7}{12}a+\frac{21}{64} & \text{Vereenvoudig} \\\end{align}\)
7. \(\begin{align}((-11)+q)(a+\frac{7}{6})& =(\color{red}{q}+\color{orange}{(-11)}).(\color{green}{a}+\color{blue}{\frac{7}{6}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(q)} . \color{green}{(a)} + \color{red}{(q)} . \color{blue}{(\frac{7}{6})} + \color{orange}{(-11)} . \color{green}{(a)} + \color{orange}{(-11)} . \color{blue}{(\frac{7}{6})}& \text{Boogjes en uitschrijven} \\ & = aq+\frac{7}{6}q-11a-11.\frac{7}{6}& \text{Uitwerken } \\ & =aq+\frac{7}{6}q-11a-\frac{77}{6} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
8. \(\begin{align}(\frac{-10}{4}-q)(p-\frac{-1}{8})& =(\color{red}{-q}+\color{orange}{\frac{-5}{2}}).(\color{green}{p}+\color{blue}{\frac{1}{8}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(-q)} . \color{green}{(p)} + \color{red}{(-q)} . \color{blue}{(\frac{1}{8})} + \color{orange}{(\frac{-5}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-5}{2})} . \color{blue}{(\frac{1}{8})}& \text{Boogjes en uitschrijven} \\ & = -pq-\frac{1}{8}q-\frac{5}{2}p-\frac{5}{2}.\frac{1}{8}& \text{Uitwerken } \\ & =-pq-\frac{1}{8}q-\frac{5}{2}p-\frac{5}{16} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
9. \(\begin{align}(a-\frac{6}{4})(p-\frac{12}{12})& =(\color{red}{a}+\color{orange}{\frac{-3}{2}}).(\color{green}{p}+\color{blue}{(-1)})& \text{Vereenvoud1g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(p)} + \color{red}{(a)} . \color{blue}{(-1)} + \color{orange}{(\frac{-3}{2})} . \color{green}{(p)} + \color{orange}{(\frac{-3}{2})} . \color{blue}{(-1)}& \text{Boogjes en uitschrijven} \\ & = ap-1a-\frac{3}{2}p+\frac{3}{2}.1& \text{Uitwerken } \\ & =ap-1a-\frac{3}{2}p+\frac{3}{2} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
10. \(\begin{align}(\frac{19}{14}+a)(\frac{9}{13}+a)& =(\color{red}{a}+\color{orange}{\frac{19}{14}}).(\color{green}{a}+\color{blue}{\frac{9}{13}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(a)} . \color{green}{(a)} + \color{red}{(a)} . \color{blue}{(\frac{9}{13})} + \color{orange}{(\frac{19}{14})} . \color{green}{(a)} + \color{orange}{(\frac{19}{14})} . \color{blue}{(\frac{9}{13})}& \text{Boogjes en uitschrijven} \\ & = aa+\frac{9}{13}a+\frac{19}{14}a+\frac{19}{14}.\frac{9}{13}& \text{Uitwerken } \\ & =a^2+(\frac{9}{13}+\frac{19}{14})a+\frac{171}{182} & \text{Neem samen} \\ &=a^2+\frac{373}{182}a+\frac{171}{182} & \text{Maak de som} \\\end{align}\)
11. \(\begin{align}(\frac{-4}{2}+x)(b+\frac{-9}{19})& =(\color{red}{x}+\color{orange}{(-2)}).(\color{green}{b}+\color{blue}{\frac{-9}{19}})& \text{Vereenvoud3g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(b)} + \color{red}{(x)} . \color{blue}{(\frac{-9}{19})} + \color{orange}{(-2)} . \color{green}{(b)} + \color{orange}{(-2)} . \color{blue}{(\frac{-9}{19})}& \text{Boogjes en uitschrijven} \\ & = bx-\frac{9}{19}x-2b+2.\frac{9}{19}& \text{Uitwerken } \\ & =bx-\frac{9}{19}x-2b+\frac{18}{19} & \text{Uitrekenen (Geen Smoothie!)} \\\end{align}\)
12. \(\begin{align}(\frac{6}{13}+x)(\frac{12}{18}+q)& =(\color{red}{x}+\color{orange}{\frac{6}{13}}).(\color{green}{q}+\color{blue}{\frac{2}{3}})& \text{Vereenvoud4g (verplicht!) en herschik (niet verplicht)} \\& = \color{red}{(x)} . \color{green}{(q)} + \color{red}{(x)} . \color{blue}{(\frac{2}{3})} + \color{orange}{(\frac{6}{13})} . \color{green}{(q)} + \color{orange}{(\frac{6}{13})} . \color{blue}{(\frac{2}{3})}& \text{Boogjes en uitschrijven} \\ & = qx+\frac{2}{3}x+\frac{6}{13}q+\frac{6}{13}.\frac{2}{3}& \text{Uitwerken } \\ & =qx+\frac{2}{3}x+\frac{6}{13}q+\frac{12}{39} & \text{Uitrekenen (Geen Smoothie!)} \\ & = qx+\frac{2}{3}x+\frac{6}{13}q+\frac{4}{13} & \text{Vereenvoudig} \\\end{align}\)