The product is:
[tex](-x^3y^2)(4x^2y+3xy-x^2)[/tex]What we have to do is to distribute the -x^3 y^2 term over the other three terms:
[tex]-4x^5y^3-3x^4y^3+x^5y^2[/tex]In the first term I did:
[tex]-x^3y^2\times4x^2y=-4x^5y^3[/tex]The second term was:
[tex]-x^3y^2\times3xy=-3x^4y^3[/tex]And finally, the third term:
[tex]-x^3y^2\times-x^2=x^5y^2[/tex]Then the answer is:
[tex]-4x^5y^3-3x^4y^3+x^5y^2[/tex]