a: \(\left(x^2y+x\right)\left(-7xy+x-1\right)\)
\(=-7x^3y^2+x^3y-x^2y-7x^2y+x^2-x\)
\(=-7x^3y^2+x^3y-8x^2y+x^2-x\)
b: \(\left(x^3y^5-xy+\dfrac{2}{3}x^3\right)\left(x^2y^4-3y^2\right)\)
\(=x^5y^9-3x^3y^7-x^3y^5+3xy^3+\dfrac{2}{3}x^5y^4-2x^3y^2\)
c: \(\left(7x^2y^3-2x^5y^3+6x^4y^4-10x^2y^2\right):\left(-2x^2y^2\right)\)
\(=-\dfrac{7x^2y^3}{2x^2y^2}+\dfrac{2x^5y^3}{2x^2y^2}-\dfrac{6x^4y^4}{2x^2y^2}+\dfrac{10x^2y^2}{2x^2y^2}\)
\(=-\dfrac{7}{2}y+x^3y-3x^2y^2+5\)
d: \(\left(-3x^6y^5+\dfrac{1}{3}x^3y^4+5x^2y-\dfrac{3}{5}x^5y\right):\left(\dfrac{1}{5}x^2y\right)\)
\(=-3x^6y^5:\dfrac{1}{5}x^2y+\dfrac{1}{3}x^3y^4:\dfrac{1}{5}x^2y+5x^2y:\dfrac{1}{5}x^2y-\dfrac{3}{5}x^5y:\dfrac{1}{5}x^2y\)
\(=-15x^4y^4+\dfrac{5}{3}xy^3+25-3x^3\)
