\(a.\dfrac{1}{2}x^3y.\left(2x^4y^3-4xy-6\right)\)
\(=\left(\dfrac{1}{2}x^3y.2x^4y^3\right)-\left(\dfrac{1}{2}x^3y.4xy\right)-\left(\dfrac{1}{2}x^3y.6\right)\)
\(=x^7y^4-2x^4y^2-3x^3y\)
\(b.2x.\left(2x^2-7x+5\right)\)
\(=\left(2x.2x^2\right)-\left(2x.7x\right)+\left(2x.5\right)\)
\(=4x^3-14x^2+10x\)
c.\(-x^2.\left(x^2-4x+3\right)+x\left(x^3-x^2+x-3\right)\)
\(=-x^4+4x^3-3x^2+x^4-x^3+x^2-3x\)
\(=3x^3-2x^2-3x\)
d.\(\left(-x+5\right)\left(x+3\right)+\left(2x+1\right)\left(x+3\right)\)
\(=-x^2-3x+5x+15+2x^2+6x+x+3\)
\(=x^2+9x+15+3\)
\(=x^2+9x+18\)
e.\(-4x\left(x+3\right)\left(x-4\right)-3x\left(x^2-x+1\right)\)
\(=(-4x^2-12x)\left(x-4\right)-3x\left(x^2-x+1\right)\)
\(=-4x^3+16x^2-12x^2+48x-3x^3+3x^2-3x\)
\(=-7x^3+7x^2+45x\)
