因式分解：2(x-2y)²-8(2x-y)²

题目

因式分解：2(x-2y)²-8(2x-y)²

答案

2(x-2y)²-8(2x-y)²
=2[(x-2y)²-4(2x-y)²]
=2[(x-2y)²-2²(2x-y)²]
=2[x-2y+2(2x-y)][x-2y-2(2x-y)]
=2(x-2y+4x-2y)(x-2y-4x+2y)
=2(5x-4y)(-3x)
=-6x(5x-4y)