Question

因式分解 （4x^2-9y^2)(3y-2x)+9(2x+3y)^3

Answer 1

（4x^2-9y^2)(3y-2x)+9(2x+3y)^3

= (2x+3y)(2x-3y)(3y-2x)+9(2x+3y)^3

= (2x+3y)[ 9(2x+3y)^2 - (2x-3y)^2 ]

= (2x+3y)[ 3(2x+3y) + (2x-3y) ][ 3(2x+3y) - (2x-3y) ]

= (2x+3y)(8x+6y)(4x+12y)

= 8(2x+3y)(4x+3y)(x+3y)