因式分解：81(x+y)^2-9(2x-3y)^2 详细过程

题目

因式分解：81(x+y)^2-9(2x-3y)^2 详细过程

答案

81(x+y)^2-9(2x-3y)^2
=[9(x+y)+3(2x-3y)][9(x+y)-3(2x-3y)]
=[(9x+9y)+(6x-9y)][(9x+9y)-(6x-9y)]
=(9x+9y+6x-9y)(9x+9y-6x+9y)
=(15x)(3x+18y)
=45x(x+6y)