因式分解-4(x+2y)²+9(2x-y)²

因式分解-4(x+2y)²+9(2x-y)²
因式分解-4(x+2y)²+9(2x-y)²

因式分解-4(x+2y)²+9(2x-y)²
-4(x+2y)²+9(2x-y)²
=9(2x-y)²-4(x+2y)²
=[3(2x-y)+2(x+2y)][3(2x-y)-2(x+2y)]
=(8x+y)(4x-7y)

-4(x+2y)^2+9(2x-y)^2=(6x-3y)^2-(2x+4y)^2
=(6x-3y+2x+4y)(6x-3y-2x-4y)
=(8x+y)(4x-7y)