\(a.\left(2x-1\right)\left(x^2-5x+3\right)\\ =2x^3-10x^2+6x-x^2+5x-3\\ =2x^3-11x^2+11x-3\\ b.-\left(x+2\right)\left(x^2+2x+2\right)\\ =-\left(x^3+2x^2+2x+2x^2+4x+4\right)\\ =-\left(x^3+4x^2+6x+4\right)\\ =-x^3-4x^2-6x-4\\ c.\left(\dfrac{1}{2}x-1\right)\left(2x-3\right)\\ =x^2-\dfrac{3}{2}x-2x+3\\ =x^2-\dfrac{7}{2}x+3\\ d.\left(\dfrac{1}{2}x+3\right)\left(2x^2-4x-6\right)\\ =x^3-2x^2-3x+6x^2-12x-18\\ =x^3+4x^2-15x-18\\ e.\left(-4x^2+8x+12\right):\left(x-3\right)\\ =\left[\left(-4x^2+12x\right)+\left(-4x+12\right)\right]:\left(x-3\right)\\ =\left[-4x\left(x-3\right)-4\left(x-3\right)\right]:\left(x-3\right)\\ =\left(x-3\right)\left(-4x-4\right):\left(x-3\right)\\ =-4x-4\)
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