a: \(\left(2x^2y^2-\dfrac{-1}{4}x^3y^5+2\right)\left(x-y\right)\)
\(=\left(2x^2y^2+\dfrac{1}{4}x^3y^5+2\right)\left(x-y\right)\)
\(=2x^3y^2-2x^2y^3+\dfrac{1}{4}x^4y^5-\dfrac{1}{4}x^3y^6+2x-2y\)
b: \(\left(-x^3y^2+3xy^2+x\right)\left(xy+y\right)\)
\(=-x^4y^3-x^3y^3+3x^2y^3+3xy^3+x^2y+xy\)
c: \(\dfrac{9x^6y^7-5x^5y^5+3xy^3+4x^4y^3}{-3xy^3}\)
\(=\dfrac{-9x^6y^7}{3xy^3}+\dfrac{5x^5y^5}{3xy^3}-\dfrac{3xy^3}{3xy^3}-\dfrac{4x^4y^3}{3xy^3}\)
\(=-3x^5y^4+\dfrac{5}{3}x^4y^2-1-\dfrac{4}{3}x^3\)
d: \(\left(-\dfrac{5}{6}x^7y^5-2x^3y^2+8x^3y^8+\dfrac{4}{3}x^4y^4\right):\left(\dfrac{2}{3}x^3y^2\right)\)
\(=-\dfrac{\dfrac{5}{6}x^7y^5}{\dfrac{2}{3}x^3y^2}-\dfrac{2x^3y^2}{\dfrac{2}{3}x^3y^2}+\dfrac{8x^3y^8}{\dfrac{2}{3}x^3y^2}+\dfrac{\dfrac{4}{3}x^4y^4}{\dfrac{2}{3}x^3y^2}\)
\(=-\dfrac{5}{4}x^4y^3-3+12y^6+2xy^2\)
