Write as a polynomial: y^2(y+5)(y–3)

You mean expand

so first do the parnethesees bits becasue the rest can be done later

(y+5)(y-3)
foil aka distribute
y^2+5y-3y-15
y^2+2y-15

now remember tha tis all multilied by y^2
y^2(y^2+2y-15)
y^4+2y^3-15y^2