a: \(\left(3x-1\right)^2+\left(3x+1\right)^2-2\left(3x-1\right)\left(3x+1\right)\)
\(=\left(3x-1\right)^2-2\left(3x-1\right)\left(3x+1\right)+\left(3x+1\right)^2\)
\(=\left(3x-1-3x-1\right)^2=\left(-2\right)^2=4\)
b: \(\left(2x-y\right)\left(4x^2+2xy+y^2\right)-\left(2x+y\right)^3-\left(6x^3y^2+3x^2y^3-12xy\right):\left(-\dfrac{1}{2}xy\right)\)
\(=8x^3-y^3-\left(8x^3+12x^2y+6xy^2+y^3\right)+\dfrac{xy\left(6x^2y+3xy^2-12\right)}{\dfrac{1}{2}xy}\)
\(=8x^3-y^3-8x^3-12x^2y-6xy^2-y^3+\dfrac{6x^2y+3xy^2-12}{\dfrac{1}{2}}\)
\(=-12x^2y-6xy^2-2y^3+12x^2y+6xy^2-24\)
\(=-2y^3-24\)
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