Answer:
[tex]\large\boxed{-40x^2y^4+70x^2y^2-90xy^3}[/tex]
Step-by-step explanation:
Use the distributive property a(b + c) = ab + ac:
[tex]-10xy(4xy^3-7xy+9y^2)\\\\=(-10xy)(4xy^3)+(-10xy)(-7xy)+(-10xy)(9y^2)\\\\\text{use}\ a^na^m=a^{n+m}\\\\=-40x^{1+1}y^{1+3}+70x^{1+1}y^{1+1}-90xy^{1+2}\\\\=-40x^2y^4+70x^2y^2-90xy^3[/tex]
