To simplify this expression we need to multiply the two terms. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
#(color(red)(6v^2) + color(red)(2v) - color(red)(9))(color(blue)(4) - color(blue)(5v^2))# becomes:
#(color(red)(6v^2) xx color(blue)(4)) - (color(red)(6v^2) xx color(blue)(5v^2)) + (color(red)(2v) xx color(blue)(4)) - (color(red)(2v) xx color(blue)(5v^2)) - (color(red)(9) xx color(blue)(4)) + (color(red)(9) xx color(blue)(5v^2))#
#24v^2 - 30v^4 + 8v - 10v^3 - 36 + 45v^2#
We can now group and combine like terms:
#-30v^4 - 10v^3 + 24v^2 + 45v^2 + 8v - 36#
#-30v^4 - 10v^3 + (24 + 45)v^2 + 8v - 36#
#-30v^4 - 10v^3 + 69v^2 + 8v - 36#
