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a: \(=\dfrac{1}{3}-\dfrac{37}{100}+\dfrac{1}{8}-\dfrac{32}{25}+\dfrac{-5}{2}+\dfrac{3}{2}\)
\(=\dfrac{1}{3}+\dfrac{1}{8}-1-\dfrac{37}{100}-\dfrac{128}{100}\)
\(=\dfrac{8+3-24}{24}-\dfrac{165}{100}\)
\(=\dfrac{-263}{120}\)
b: \(=\dfrac{5}{22}+\dfrac{3}{13}-\dfrac{13}{8}-\dfrac{2}{11}+\dfrac{3}{2}\)
\(=\dfrac{5}{22}-\dfrac{4}{22}-\dfrac{13}{8}+\dfrac{12}{8}+\dfrac{3}{13}\)
\(=\dfrac{1}{22}-\dfrac{1}{8}+\dfrac{3}{13}=\dfrac{173}{1144}\)
a: \(=\dfrac{1}{3}-\dfrac{37}{100}+\dfrac{1}{8}-\dfrac{32}{25}-\dfrac{5}{2}+\dfrac{3}{2}\)
\(=\dfrac{11}{24}+\left(-\dfrac{37}{100}+\dfrac{1}{8}-1\right)\)
\(=\dfrac{11}{24}-\dfrac{249}{200}=-\dfrac{59}{75}\)
b: \(=\dfrac{5}{22}+\dfrac{3}{13}-\dfrac{13}{8}-\dfrac{2}{11}+\dfrac{3}{2}\)
\(=\dfrac{5}{22}-\dfrac{4}{22}+\dfrac{3}{13}-\dfrac{13}{8}+\dfrac{12}{8}\)
\(=\dfrac{1}{22}+\dfrac{3}{13}-\dfrac{1}{8}=\dfrac{173}{1144}\)
\(8-12x+6x^2-x^3\)
\(=\left(2-x\right)^3\)
\(125x^3-75x^2+15x-1\)
\(=\left(5x-1\right)^3\)
\(x^2-xz-9y^2+3yz\)
\(=\left(x-3y\right)\left(x+3y\right)-z\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x+3y-z\right)\)
\(x^3-x^2-5x+125\)
\(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)\)
\(=\left(x+5\right)\left(x^2-5x+25-x\right)\)
\(=\left(x+5\right)\left(x^2-6x+25\right)\)
\(x^3+2x^2-6x-27\)
\(=x^3+5x^2+9x-3x^2-15x-27\)
\(=x\left(x^2+5x+9\right)-3\left(x^2+5x+9\right)\)
\(=\left(x-3\right)\left(x^2+5x+9\right)\)
\(12x^3+4x^2-27x-9\)
\(=4x^2\left(3x+1\right)-9\left(3x+1\right)\)
\(=\left(3x+1\right)\left(4x^2-9\right)\)
\(=\left(3x+1\right)\left(2x-3\right)\left(2x+3\right)\)
\(4x^4+4x^3-x^2-x\)
\(=4x^3\left(x+1\right)-x\left(x+1\right)\)
\(=x\left(x+1\right)\left(4x^2-1\right)\)
\(=x\left(x+1\right)\left(2x-1\right)\left(2x+1\right)\)
\(=\dfrac{5}{22}+\dfrac{3}{13}-\dfrac{13}{8}-\dfrac{2}{11}+\dfrac{3}{2}\)
\(=\dfrac{5}{22}-\dfrac{4}{22}+\dfrac{3}{13}-\dfrac{13}{8}+\dfrac{12}{8}\)
\(=\dfrac{1}{22}+\dfrac{3}{13}-\dfrac{1}{8}=\dfrac{173}{1144}\)